TSTP Solution File: ITP290^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP290^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:32:42 EDT 2023
% Result : Timeout 299.52s 300.16s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 3.00/3.06 % Problem : ITP290^3 : TPTP v8.1.2. Released v8.1.0.
% 3.00/3.08 % Command : do_cvc5 %s %d
% 3.05/3.29 % Computer : n028.cluster.edu
% 3.05/3.29 % Model : x86_64 x86_64
% 3.05/3.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 3.05/3.29 % Memory : 8042.1875MB
% 3.05/3.29 % OS : Linux 3.10.0-693.el7.x86_64
% 3.05/3.29 % CPULimit : 300
% 3.05/3.29 % WCLimit : 300
% 3.05/3.29 % DateTime : Sun Aug 27 16:09:41 EDT 2023
% 3.05/3.29 % CPUTime :
% 5.80/5.99 %----Proving TH0
% 5.80/6.00 %------------------------------------------------------------------------------
% 5.80/6.00 % File : ITP290^3 : TPTP v8.1.2. Released v8.1.0.
% 5.80/6.00 % Domain : Interactive Theorem Proving
% 5.80/6.00 % Problem : Sledgehammer problem VEBT_DelImperative 00505_031086
% 5.80/6.00 % Version : [Des22] axioms.
% 5.80/6.00 % English :
% 5.80/6.00
% 5.80/6.00 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.80/6.00 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.80/6.00 % Source : [Des22]
% 5.80/6.00 % Names : 0095_VEBT_DelImperative_00505_031086 [Des22]
% 5.80/6.00
% 5.80/6.00 % Status : Theorem
% 5.80/6.00 % Rating : 1.00 v8.1.0
% 5.80/6.00 % Syntax : Number of formulae : 11448 (4932 unt;1198 typ; 0 def)
% 5.80/6.00 % Number of atoms : 31429 (12909 equ; 0 cnn)
% 5.80/6.00 % Maximal formula atoms : 71 ( 3 avg)
% 5.80/6.00 % Number of connectives : 142418 (3139 ~; 513 |;2066 &;122985 @)
% 5.80/6.00 % ( 0 <=>;13715 =>; 0 <=; 0 <~>)
% 5.80/6.00 % Maximal formula depth : 39 ( 7 avg)
% 5.80/6.00 % Number of types : 134 ( 133 usr)
% 5.80/6.00 % Number of type conns : 5586 (5586 >; 0 *; 0 +; 0 <<)
% 5.80/6.00 % Number of symbols : 1068 (1065 usr; 92 con; 0-4 aty)
% 5.80/6.00 % Number of variables : 30514 (2409 ^;27159 !; 946 ?;30514 :)
% 5.80/6.00 % SPC : TH0_THM_EQU_NAR
% 5.80/6.00
% 5.80/6.00 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.80/6.00 % from the van Emde Boas Trees session in the Archive of Formal
% 5.80/6.00 % proofs -
% 5.80/6.00 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.80/6.00 % 2022-02-18 22:49:48.022
% 5.80/6.00 %------------------------------------------------------------------------------
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% 5.80/6.00 thf(sy_c_If_001t__Heap____Time____Monad__OHeap_I_Eo_J,type,
% 5.80/6.00 if_Heap_Time_Heap_o: $o > heap_Time_Heap_o > heap_Time_Heap_o > heap_Time_Heap_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Heap____Time____Monad__OHeap_It__Nat__Onat_J,type,
% 5.80/6.00 if_Hea2662716070787841314ap_nat: $o > heap_Time_Heap_nat > heap_Time_Heap_nat > heap_Time_Heap_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Heap____Time____Monad__OHeap_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.80/6.00 if_Hea5867803462524415986on_nat: $o > heap_T2636463487746394924on_nat > heap_T2636463487746394924on_nat > heap_T2636463487746394924on_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Heap____Time____Monad__OHeap_It__VEBT____BuildupMemImp__OVEBTi_J,type,
% 5.80/6.00 if_Hea8453224502484754311_VEBTi: $o > heap_T8145700208782473153_VEBTi > heap_T8145700208782473153_VEBTi > heap_T8145700208782473153_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Int__Oint,type,
% 5.80/6.00 if_int: $o > int > int > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 5.80/6.00 if_list_int: $o > list_int > list_int > list_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Nat__Onat,type,
% 5.80/6.00 if_nat: $o > nat > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Num__Onum,type,
% 5.80/6.00 if_num: $o > num > num > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.80/6.00 if_option_nat: $o > option_nat > option_nat > option_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.80/6.00 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.80/6.00 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.80/6.00 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Rat__Orat,type,
% 5.80/6.00 if_rat: $o > rat > rat > rat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Real__Oreal,type,
% 5.80/6.00 if_real: $o > real > real > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 5.80/6.00 if_set_int: $o > set_int > set_int > set_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oint__ge__less__than,type,
% 5.80/6.00 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oint__ge__less__than2,type,
% 5.80/6.00 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Onat,type,
% 5.80/6.00 nat2: int > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.80/6.00 ring_1_Ints_real: set_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.80/6.00 ring_18347121197199848620nteger: int > code_integer ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.80/6.00 ring_17405671764205052669omplex: int > complex ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.80/6.00 ring_1_of_int_int: int > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.80/6.00 ring_1_of_int_rat: int > rat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.80/6.00 ring_1_of_int_real: int > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 5.80/6.00 lattic8263393255366662781ax_int: set_int > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.80/6.00 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Least__significant__bit_Olsb__class_Olsb_001t__Int__Oint,type,
% 5.80/6.00 least_4859182151741483524sb_int: int > $o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.80/6.00 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 5.80/6.00 at_infinity_real: filter_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Ofoldr_001_Eo_001t__Nat__Onat,type,
% 5.80/6.00 foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.80/6.00 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.80/6.00 foldr_real_nat: ( real > nat > nat ) > list_real > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.80/6.00 foldr_real_real: ( real > real > real ) > list_real > real > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Ofoldr_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 5.80/6.00 foldr_VEBT_VEBTi_nat: ( vEBT_VEBTi > nat > nat ) > list_VEBT_VEBTi > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Ofoldr_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.80/6.00 foldr_VEBT_VEBT_nat: ( vEBT_VEBT > nat > nat ) > list_VEBT_VEBT > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.80/6.00 cons_int: int > list_int > list_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001_Eo_001t__Nat__Onat,type,
% 5.80/6.00 map_o_nat: ( $o > nat ) > list_o > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001_Eo_001t__Real__Oreal,type,
% 5.80/6.00 map_o_real: ( $o > real ) > list_o > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 map_o_VEBT_VEBT: ( $o > vEBT_VEBT ) > list_o > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Int__Oint,type,
% 5.80/6.00 map_int_int: ( int > int ) > list_int > list_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Real__Oreal,type,
% 5.80/6.00 map_int_real: ( int > real ) > list_int > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.80/6.00 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.80/6.00 map_nat_real: ( nat > real ) > list_nat > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 map_nat_VEBT_VEBT: ( nat > vEBT_VEBT ) > list_nat > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001_Eo,type,
% 5.80/6.00 map_real_o: ( real > $o ) > list_real > list_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.80/6.00 map_real_nat: ( real > nat ) > list_real > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.80/6.00 map_real_real: ( real > real ) > list_real > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 map_real_VEBT_VEBTi: ( real > vEBT_VEBTi ) > list_real > list_VEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 map_real_VEBT_VEBT: ( real > vEBT_VEBT ) > list_real > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001_Eo,type,
% 5.80/6.00 map_VEBT_VEBTi_o: ( vEBT_VEBTi > $o ) > list_VEBT_VEBTi > list_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 5.80/6.00 map_VEBT_VEBTi_nat: ( vEBT_VEBTi > nat ) > list_VEBT_VEBTi > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
% 5.80/6.00 map_VEBT_VEBTi_real: ( vEBT_VEBTi > real ) > list_VEBT_VEBTi > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 map_VE483055756984248624_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi ) > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 map_VE7998069337340375161T_VEBT: ( vEBT_VEBTi > vEBT_VEBT ) > list_VEBT_VEBTi > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.80/6.00 map_VEBT_VEBT_o: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > list_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.80/6.00 map_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.80/6.00 map_VEBT_VEBT_real: ( vEBT_VEBT > real ) > list_VEBT_VEBT > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 map_VE7029150624388687525_VEBTi: ( vEBT_VEBT > vEBT_VEBTi ) > list_VEBT_VEBT > list_VEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.80/6.00 set_o2: list_o > set_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__Code____Numeral__Ointeger,type,
% 5.80/6.00 set_Code_integer2: list_Code_integer > set_Code_integer ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.80/6.00 set_complex2: list_complex > set_complex ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.80/6.00 set_int2: list_int > set_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.80/6.00 set_nat2: list_nat > set_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.80/6.00 set_real2: list_real > set_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 set_VEBT_VEBTi2: list_VEBT_VEBTi > set_VEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.80/6.00 list_update_o: list_o > nat > $o > list_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.80/6.00 list_update_int: list_int > nat > int > list_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.80/6.00 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.80/6.00 list_update_real: list_real > nat > real > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist__update_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 list_u6098035379799741383_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi > list_VEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001_Eo,type,
% 5.80/6.00 nth_o: list_o > nat > $o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.80/6.00 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.80/6.00 nth_int: list_int > nat > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.80/6.00 nth_nat: list_nat > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.80/6.00 nth_num: list_num > nat > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.80/6.00 nth_option_nat: list_option_nat > nat > option_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.80/6.00 nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.80/6.00 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.80/6.00 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.80/6.00 nth_Pr7489471911767062336l_real: list_P8689742595348180415l_real > nat > produc2422161461964618553l_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.80/6.00 nth_Pr5429231388385915574T_VEBT: list_P877281246627933069T_VEBT > nat > produc3757001726724277373T_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.80/6.00 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.80/6.00 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J,type,
% 5.80/6.00 nth_Pr6842391030413306568T_real: list_P2623026923184700063T_real > nat > produc5170161368751668367T_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 5.80/6.00 nth_Pr316670251186196177_VEBTi: list_P735349106241217576_VEBTi > nat > produc3625547720036274456_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.80/6.00 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.80/6.00 nth_real: list_real > nat > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 nth_VEBT_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.80/6.00 produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 5.80/6.00 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.80/6.00 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Real__Oreal_001_Eo,type,
% 5.80/6.00 product_real_o: list_real > list_o > list_P3595434254542482545real_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.80/6.00 product_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.80/6.00 product_real_real: list_real > list_real > list_P8689742595348180415l_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Real__Oreal_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 produc5599769701989005224_VEBTi: list_real > list_VEBT_VEBTi > list_P2340519324556330824_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 produc3722688996059531265T_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.80/6.00 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.80/6.00 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.80/6.00 produc4908677263432625371T_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 produc316462671093861988_VEBTi: list_VEBT_VEBT > list_VEBT_VEBTi > list_P735349106241217576_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oreplicate_001_Eo,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.80/6.00 replicate_int: nat > int > list_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.80/6.00 replicate_nat: nat > nat > list_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.80/6.00 replicate_real: nat > real > list_real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oreplicate_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 replicate_VEBT_VEBTi: nat > vEBT_VEBTi > list_VEBT_VEBTi ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.00 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oupto__aux,type,
% 5.80/6.00 upto_aux: int > int > list_int > list_int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_List_Oupto__rel,type,
% 5.80/6.00 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_OSuc,type,
% 5.80/6.00 suc: nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.80/6.00 semiri4939895301339042750nteger: nat > code_integer ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.80/6.00 semiri8010041392384452111omplex: nat > complex ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.80/6.00 semiri1314217659103216013at_int: nat > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.80/6.00 semiri681578069525770553at_rat: nat > rat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.80/6.00 semiri5074537144036343181t_real: nat > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.80/6.00 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.80/6.00 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.80/6.00 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.80/6.00 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.80/6.00 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.80/6.00 size_size_list_o: list_o > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.80/6.00 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.80/6.00 size_s3451745648224563538omplex: list_complex > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.80/6.00 size_size_list_int: list_int > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.80/6.00 size_size_list_nat: list_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.80/6.00 size_size_list_num: list_num > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.80/6.00 size_s6086282163384603972on_nat: list_option_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_M_Eo_J_J,type,
% 5.80/6.00 size_s987546567493390085real_o: list_P3595434254542482545real_o > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
% 5.80/6.00 size_s1877336372972134351al_nat: list_P6834414599653733731al_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.80/6.00 size_s3932428310213730859l_real: list_P8689742595348180415l_real > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____BuildupMemImp__OVEBTi_J_J,type,
% 5.80/6.00 size_s6963394564282275252_VEBTi: list_P2340519324556330824_VEBTi > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.80/6.00 size_s3289364478449617953T_VEBT: list_P877281246627933069T_VEBT > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.80/6.00 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.80/6.00 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J_J,type,
% 5.80/6.00 size_s5035110155006384947T_real: list_P2623026923184700063T_real > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____BuildupMemImp__OVEBTi_J_J,type,
% 5.80/6.00 size_s3387956428969716412_VEBTi: list_P735349106241217576_VEBTi > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.80/6.00 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.80/6.00 size_size_list_real: list_real > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____BuildupMemImp__OVEBTi_J,type,
% 5.80/6.00 size_s7982070591426661849_VEBTi: list_VEBT_VEBTi > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.80/6.00 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.80/6.00 size_size_num: num > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.80/6.00 size_size_option_nat: option_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.80/6.00 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__Uint32__Ouint32,type,
% 5.80/6.00 size_size_uint32: uint32 > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.00 size_size_VEBT_VEBTi: vEBT_VEBTi > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.80/6.00 nat_set_decode: nat > set_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.80/6.00 nat_set_encode: set_nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.80/6.00 nat_triangle: nat > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_NthRoot_Oroot,type,
% 5.80/6.00 root: nat > real > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_NthRoot_Osqrt,type,
% 5.80/6.00 sqrt: real > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_OBitM,type,
% 5.80/6.00 bitM: num > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Oinc,type,
% 5.80/6.00 inc: num > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.80/6.00 neg_nu8557863876264182079omplex: complex > complex ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.80/6.00 neg_nu5851722552734809277nc_int: int > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.80/6.00 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.80/6.00 neg_nu8295874005876285629c_real: real > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onum_OBit0,type,
% 5.80/6.00 bit0: num > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onum_OBit1,type,
% 5.80/6.00 bit1: num > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onum_OOne,type,
% 5.80/6.00 one: num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onum_Osize__num,type,
% 5.80/6.00 size_num: num > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.80/6.00 numera6620942414471956472nteger: num > code_integer ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.80/6.00 numera6690914467698888265omplex: num > complex ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.80/6.00 numera1916890842035813515d_enat: num > extended_enat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 5.80/6.00 numeral_numeral_int: num > int ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 5.80/6.00 numeral_numeral_nat: num > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.80/6.00 numeral_numeral_rat: num > rat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 5.80/6.00 numeral_numeral_real: num > real ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Opow,type,
% 5.80/6.00 pow: num > num > num ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Num_Opred__numeral,type,
% 5.80/6.00 pred_numeral: num > nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 5.80/6.00 none_nat: option_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 5.80/6.00 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_OSome_001t__Int__Oint,type,
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% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 5.80/6.00 some_nat: nat > option_nat ).
% 5.80/6.00
% 5.80/6.00 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 5.80/6.00 some_num: num > option_num ).
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% 5.80/6.00 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 5.80/6.01 thf(sy_c_Time__Reasoning_Otime_001t__VEBT____BuildupMemImp__OVEBTi,type,
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% 5.80/6.01 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
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% 5.80/6.01 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
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% 5.80/6.01 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
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% 5.80/6.01 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
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% 5.80/6.01 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
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% 5.80/6.01 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
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% 5.80/6.01
% 5.80/6.01 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.80/6.01 tanh_real: real > real ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Enum__Ofinite____1,type,
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% 5.80/6.01 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,
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% 5.80/6.01 vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 5.80/6.01 vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 5.80/6.01 vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 5.80/6.01 vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 5.80/6.01 vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 5.80/6.01 vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi,type,
% 5.80/6.01 vEBT_V441764108873111860ildupi: nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi_H,type,
% 5.80/6.01 vEBT_V9176841429113362141ildupi: nat > int ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi_H__rel,type,
% 5.80/6.01 vEBT_V3352910403632780892pi_rel: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi__rel,type,
% 5.80/6.01 vEBT_V2957053500504383685pi_rel: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb,type,
% 5.80/6.01 vEBT_VEBT_Tb: nat > int ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb_H,type,
% 5.80/6.01 vEBT_VEBT_Tb2: nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb_H__rel,type,
% 5.80/6.01 vEBT_VEBT_Tb_rel: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb__rel,type,
% 5.80/6.01 vEBT_VEBT_Tb_rel2: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ohighi,type,
% 5.80/6.01 vEBT_VEBT_highi: nat > nat > heap_Time_Heap_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Olowi,type,
% 5.80/6.01 vEBT_VEBT_lowi: nat > nat > heap_Time_Heap_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OminNulli,type,
% 5.80/6.01 vEBT_VEBT_minNulli: vEBT_VEBTi > heap_Time_Heap_o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OminNulli__rel,type,
% 5.80/6.01 vEBT_V5740978063120863272li_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Oreplicatei_001_Eo,type,
% 5.80/6.01 vEBT_V2326993469660664182atei_o: nat > heap_Time_Heap_o > heap_T844314716496656296list_o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Oreplicatei_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_V7726092123322077554ei_nat: nat > heap_Time_Heap_nat > heap_T290393402774840812st_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Oreplicatei_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.80/6.01 vEBT_V792416675989592002on_nat: nat > heap_T2636463487746394924on_nat > heap_T5317711798761887292on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Oreplicatei_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 vEBT_V1859673955506687831_VEBTi: nat > heap_T8145700208782473153_VEBTi > heap_T4980287057938770641_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__buildupi_H,type,
% 5.80/6.01 vEBT_V739175172307565963ildupi: nat > heap_T8145700208782473153_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__inserti_H,type,
% 5.80/6.01 vEBT_V3964819847710782039nserti: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__memberi_H,type,
% 5.80/6.01 vEBT_V854960066525838166emberi: vEBT_VEBT > vEBT_VEBTi > nat > heap_Time_Heap_o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_OLeafi,type,
% 5.80/6.01 vEBT_Leafi: $o > $o > vEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_ONodei,type,
% 5.80/6.01 vEBT_Nodei: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > vEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Ocase__VEBTi_001t__Heap____Time____Monad__OHeap_I_Eo_J,type,
% 5.80/6.01 vEBT_c6104975476656191286Heap_o: ( option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_Time_Heap_o ) > ( $o > $o > heap_Time_Heap_o ) > vEBT_VEBTi > heap_Time_Heap_o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Ocase__VEBTi_001t__Heap____Time____Monad__OHeap_It__Nat__Onat_J,type,
% 5.80/6.01 vEBT_c1335663792808957512ap_nat: ( option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_Time_Heap_nat ) > ( $o > $o > heap_Time_Heap_nat ) > vEBT_VEBTi > heap_Time_Heap_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Ocase__VEBTi_001t__Heap____Time____Monad__OHeap_It__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.80/6.01 vEBT_c6250501799366334488on_nat: ( option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T2636463487746394924on_nat ) > ( $o > $o > heap_T2636463487746394924on_nat ) > vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Ocase__VEBTi_001t__Heap____Time____Monad__OHeap_It__VEBT____BuildupMemImp__OVEBTi_J,type,
% 5.80/6.01 vEBT_c6028912655521741485_VEBTi: ( option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T8145700208782473153_VEBTi ) > ( $o > $o > heap_T8145700208782473153_VEBTi ) > vEBT_VEBTi > heap_T8145700208782473153_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Ocase__VEBTi_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_case_VEBTi_nat: ( option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > nat ) > ( $o > $o > nat ) > vEBT_VEBTi > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Osize__VEBTi,type,
% 5.80/6.01 vEBT_size_VEBTi: vEBT_VEBTi > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw,type,
% 5.80/6.01 vEBT_vebt_assn_raw: vEBT_VEBT > vEBT_VEBTi > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw__rel,type,
% 5.80/6.01 vEBT_v8524038756793281170aw_rel: produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__buildupi,type,
% 5.80/6.01 vEBT_vebt_buildupi: nat > heap_T8145700208782473153_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__inserti,type,
% 5.80/6.01 vEBT_vebt_inserti: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__maxti,type,
% 5.80/6.01 vEBT_vebt_maxti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__maxti__rel,type,
% 5.80/6.01 vEBT_vebt_maxti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__memberi,type,
% 5.80/6.01 vEBT_vebt_memberi: vEBT_VEBTi > nat > heap_Time_Heap_o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__minti,type,
% 5.80/6.01 vEBT_vebt_minti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__BuildupMemImp_Ovebt__minti__rel,type,
% 5.80/6.01 vEBT_vebt_minti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.80/6.01 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.80/6.01 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.80/6.01 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.80/6.01 vEBT_VEBT_high: nat > nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.80/6.01 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.80/6.01 vEBT_VEBT_low: nat > nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.80/6.01 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.80/6.01 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.80/6.01 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.80/6.01 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.80/6.01 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.80/6.01 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.80/6.01 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.80/6.01 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.80/6.01 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__DelImperative_OVEBT__internal_Ovebt__deletei_H,type,
% 5.80/6.01 vEBT_V1365221501068881998eletei: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_V1232361888498592333_e_t_e: vEBT_VEBT > nat > nat ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_V6368547301243506412_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 5.80/6.01 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 5.80/6.01 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 5.80/6.01 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 5.80/6.01 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.80/6.01 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.80/6.01 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001_Eo_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 vEBT_L6286945158656146733_VEBTi: set_nat > ( $o > vEBT_VEBTi > assn ) > list_o > list_VEBT_VEBTi > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L1319876754960170684T_VEBT: set_nat > ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001_Eo,type,
% 5.80/6.01 vEBT_L7980206306069228746real_o: set_nat > ( real > $o > assn ) > list_real > list_o > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_L234762979517870878al_nat: set_nat > ( real > nat > assn ) > list_real > list_nat > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L5184575500739366650l_real: set_nat > ( real > real > assn ) > list_real > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 vEBT_L7851252805511451907_VEBTi: set_nat > ( real > vEBT_VEBTi > assn ) > list_real > list_VEBT_VEBTi > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L3095048238742455910T_VEBT: set_nat > ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.80/6.01 vEBT_L7058566406413635588VEBT_o: set_nat > ( vEBT_VEBT > $o > assn ) > list_VEBT_VEBT > list_o > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_L8650695023172932196BT_nat: set_nat > ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L4281036506115550016T_real: set_nat > ( vEBT_VEBT > real > assn ) > list_VEBT_VEBT > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 vEBT_L1528199826722428489_VEBTi: set_nat > ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L3204528365124325536T_VEBT: set_nat > ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L4725278957065240257o_real: ( $o > real > assn ) > list_o > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L1750719106661372127T_VEBT: ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Int__Oint,type,
% 5.80/6.01 vEBT_L74593716426352029nt_int: ( int > int > assn ) > list_int > list_int > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_L77084186935402305nt_nat: ( int > nat > assn ) > list_int > list_nat > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L8288995350762215837t_real: ( int > real > assn ) > list_int > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L1664421287176695555T_VEBT: ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L6102073776069194049t_real: ( nat > real > assn ) > list_nat > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L8158188754432654943T_VEBT: ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001_Eo,type,
% 5.80/6.01 vEBT_L6234343332106409831real_o: ( real > $o > assn ) > list_real > list_o > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Int__Oint,type,
% 5.80/6.01 vEBT_L1443519841834266653al_int: ( real > int > assn ) > list_real > list_int > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_L1446010312343316929al_nat: ( real > nat > assn ) > list_real > list_nat > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L1930518968523514909l_real: ( real > real > assn ) > list_real > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 vEBT_L9060850011106065574_VEBTi: ( real > vEBT_VEBTi > assn ) > list_real > list_VEBT_VEBTi > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L4595930785310033027T_VEBT: ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L8937798142398754470i_real: ( vEBT_VEBTi > real > assn ) > list_VEBT_VEBTi > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L7265847600308530106T_VEBT: ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.80/6.01 vEBT_L7489408758114837031VEBT_o: ( vEBT_VEBT > $o > assn ) > list_VEBT_VEBT > list_o > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.80/6.01 vEBT_L8294436054247626077BT_int: ( vEBT_VEBT > int > assn ) > list_VEBT_VEBT > list_int > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_L8296926524756676353BT_nat: ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.80/6.01 vEBT_L8010285020845282001on_nat: ( vEBT_VEBT > option_nat > assn ) > list_VEBT_VEBT > list_option_nat > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.80/6.01 vEBT_L5781919052683127133T_real: ( vEBT_VEBT > real > assn ) > list_VEBT_VEBT > list_real > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 vEBT_L6296928887356842470_VEBTi: ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 vEBT_L1279224858307276611T_VEBT: ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.80/6.01 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.80/6.01 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.80/6.01 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.80/6.01 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.80/6.01 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.80/6.01 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.80/6.01 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.80/6.01 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.80/6.01 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.80/6.01 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.80/6.01 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.80/6.01 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.80/6.01 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.80/6.01 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.80/6.01 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.80/6.01 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.80/6.01 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.80/6.01 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.80/6.01 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.80/6.01 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.80/6.01 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.80/6.01 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.80/6.01 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_V8646137997579335489_i_l_d: nat > nat ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_V8346862874174094_d_u_p: nat > nat ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_V1247956027447740395_p_rel: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 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,
% 5.80/6.01 vEBT_V5144397997797733112_d_rel: nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt,type,
% 5.80/6.01 vEBT_VEBT_cnt: vEBT_VEBT > real ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt_H,type,
% 5.80/6.01 vEBT_VEBT_cnt2: vEBT_VEBT > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt_H__rel,type,
% 5.80/6.01 vEBT_VEBT_cnt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt__rel,type,
% 5.80/6.01 vEBT_VEBT_cnt_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace,type,
% 5.80/6.01 vEBT_VEBT_space: vEBT_VEBT > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H,type,
% 5.80/6.01 vEBT_VEBT_space2: vEBT_VEBT > nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H__rel,type,
% 5.80/6.01 vEBT_VEBT_space_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace__rel,type,
% 5.80/6.01 vEBT_VEBT_space_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__SuccPredImperative_OVEBT__internal_Ovebt__predi_H,type,
% 5.80/6.01 vEBT_VEBT_vebt_predi: vEBT_VEBT > vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__SuccPredImperative_OVEBT__internal_Ovebt__succi_H,type,
% 5.80/6.01 vEBT_VEBT_vebt_succi: vEBT_VEBT > vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__SuccPredImperative_Ovebt__predi,type,
% 5.80/6.01 vEBT_vebt_predi: vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__SuccPredImperative_Ovebt__succi,type,
% 5.80/6.01 vEBT_vebt_succi: vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.80/6.01 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.80/6.01 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.80/6.01 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.80/6.01 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.80/6.01 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.80/6.01 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.80/6.01 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 5.80/6.01 accp_P7675410724331315407_VEBTi: ( produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ) > produc3625547720036274456_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 accp_VEBT_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > $o ) > vEBT_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.80/6.01 fChoice_real: ( real > $o ) > real ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001_Eo,type,
% 5.80/6.01 member_o: $o > set_o > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 5.80/6.01 member_Code_integer: code_integer > set_Code_integer > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.80/6.01 member_complex: complex > set_complex > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Int__Oint,type,
% 5.80/6.01 member_int: int > set_int > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.80/6.01 member_list_o: list_o > set_list_o > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.80/6.01 member_list_nat: list_nat > set_list_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__List__Olist_It__Real__Oreal_J,type,
% 5.80/6.01 member_list_real: list_real > set_list_real > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__List__Olist_It__VEBT____BuildupMemImp__OVEBTi_J,type,
% 5.80/6.01 member8117914210271334748_VEBTi: list_VEBT_VEBTi > set_list_VEBT_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.80/6.01 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Nat__Onat,type,
% 5.80/6.01 member_nat: nat > set_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Num__Onum,type,
% 5.80/6.01 member_num: num > set_num > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.80/6.01 member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 5.80/6.01 member6260224972018164377et_nat: produc3658429121746597890et_nat > set_Pr3948176798113811640et_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.80/6.01 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.80/6.01 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.80/6.01 member7279096912039735102um_num: product_prod_num_num > set_Pr8218934625190621173um_num > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Rat__Orat,type,
% 5.80/6.01 member_rat: rat > set_rat > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Real__Oreal,type,
% 5.80/6.01 member_real: real > set_real > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.80/6.01 member_set_int: set_int > set_set_int > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 5.80/6.01 member_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.80/6.01 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_aktnode____,type,
% 5.80/6.01 aktnode: vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_ma____,type,
% 5.80/6.01 ma: nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_mi____,type,
% 5.80/6.01 mi: nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_minew____,type,
% 5.80/6.01 minew: nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_na____,type,
% 5.80/6.01 na: nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_newnode____,type,
% 5.80/6.01 newnode: vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_summary____,type,
% 5.80/6.01 summary: vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_tia____,type,
% 5.80/6.01 tia: vEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_treeList____,type,
% 5.80/6.01 treeList: list_VEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_tree__is______,type,
% 5.80/6.01 tree_is: list_VEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_va____,type,
% 5.80/6.01 va: nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_x13______,type,
% 5.80/6.01 x13: array_VEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_x14______,type,
% 5.80/6.01 x14: vEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_xa____,type,
% 5.80/6.01 xa: nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_xaa______,type,
% 5.80/6.01 xaa: vEBT_VEBT ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_xb______,type,
% 5.80/6.01 xb: vEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_xba______,type,
% 5.80/6.01 xba: option_nat ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_xc,type,
% 5.80/6.01 xc: vEBT_VEBTi ).
% 5.80/6.01
% 5.80/6.01 thf(sy_v_xnew____,type,
% 5.80/6.01 xnew: nat ).
% 5.80/6.01
% 5.80/6.01 % Relevant facts (10198)
% 5.80/6.01 thf(fact_0_groupy,axiom,
% 5.80/6.01 ! [A: assn,B: assn,C: assn,D: assn,X: assn] :
% 5.80/6.01 ( ( entails @ ( times_times_assn @ ( times_times_assn @ A @ B ) @ ( times_times_assn @ C @ D ) ) @ X )
% 5.80/6.01 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ A @ B ) @ C ) @ D ) @ X ) ) ).
% 5.80/6.01
% 5.80/6.01 % groupy
% 5.80/6.01 thf(fact_1_midextr,axiom,
% 5.80/6.01 ! [P: assn,Q: assn,Q2: assn,R: assn,X: assn] :
% 5.80/6.01 ( ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ P @ Q ) @ Q2 ) @ R ) @ X )
% 5.80/6.01 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ P @ R ) @ Q ) @ Q2 ) @ X ) ) ).
% 5.80/6.01
% 5.80/6.01 % midextr
% 5.80/6.01 thf(fact_2_swappa,axiom,
% 5.80/6.01 ! [B: assn,A: assn,C: assn,X: assn] :
% 5.80/6.01 ( ( entails @ ( times_times_assn @ ( times_times_assn @ B @ A ) @ C ) @ X )
% 5.80/6.01 => ( entails @ ( times_times_assn @ ( times_times_assn @ A @ B ) @ C ) @ X ) ) ).
% 5.80/6.01
% 5.80/6.01 % swappa
% 5.80/6.01 thf(fact_3_minNullmin,axiom,
% 5.80/6.01 ! [T: vEBT_VEBT] :
% 5.80/6.01 ( ( vEBT_VEBT_minNull @ T )
% 5.80/6.01 => ( ( vEBT_vebt_mint @ T )
% 5.80/6.01 = none_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % minNullmin
% 5.80/6.01 thf(fact_4_minminNull,axiom,
% 5.80/6.01 ! [T: vEBT_VEBT] :
% 5.80/6.01 ( ( ( vEBT_vebt_mint @ T )
% 5.80/6.01 = none_nat )
% 5.80/6.01 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.80/6.01
% 5.80/6.01 % minminNull
% 5.80/6.01 thf(fact_5_bit__split__inv,axiom,
% 5.80/6.01 ! [X2: nat,D2: nat] :
% 5.80/6.01 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X2 @ D2 ) @ ( vEBT_VEBT_low @ X2 @ D2 ) @ D2 )
% 5.80/6.01 = X2 ) ).
% 5.80/6.01
% 5.80/6.01 % bit_split_inv
% 5.80/6.01 thf(fact_6_assnle,axiom,
% 5.80/6.01 ! [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 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % assnle
% 5.80/6.01 thf(fact_7_div2__Suc__Suc,axiom,
% 5.80/6.01 ! [M: nat] :
% 5.80/6.01 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.80/6.01 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % div2_Suc_Suc
% 5.80/6.01 thf(fact_8_nth__list__update__eq,axiom,
% 5.80/6.01 ! [I: nat,Xs: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.80/6.01 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.80/6.01 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) @ I )
% 5.80/6.01 = X2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_eq
% 5.80/6.01 thf(fact_9_nth__list__update__eq,axiom,
% 5.80/6.01 ! [I: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.80/6.01 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.80/6.01 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ I )
% 5.80/6.01 = X2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_eq
% 5.80/6.01 thf(fact_10_nth__list__update__eq,axiom,
% 5.80/6.01 ! [I: nat,Xs: list_real,X2: real] :
% 5.80/6.01 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.80/6.01 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X2 ) @ I )
% 5.80/6.01 = X2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_eq
% 5.80/6.01 thf(fact_11_nth__list__update__eq,axiom,
% 5.80/6.01 ! [I: nat,Xs: list_o,X2: $o] :
% 5.80/6.01 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.80/6.01 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X2 ) @ I )
% 5.80/6.01 = X2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_eq
% 5.80/6.01 thf(fact_12_nth__list__update__eq,axiom,
% 5.80/6.01 ! [I: nat,Xs: list_nat,X2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.80/6.01 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ I )
% 5.80/6.01 = X2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_eq
% 5.80/6.01 thf(fact_13_nth__update__invalid,axiom,
% 5.80/6.01 ! [I: nat,L: list_VEBT_VEBTi,J: nat,X2: vEBT_VEBTi] :
% 5.80/6.01 ( ~ ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 5.80/6.01 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ J @ X2 ) @ I )
% 5.80/6.01 = ( nth_VEBT_VEBTi @ L @ I ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_update_invalid
% 5.80/6.01 thf(fact_14_nth__update__invalid,axiom,
% 5.80/6.01 ! [I: nat,L: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 5.80/6.01 ( ~ ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.80/6.01 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ J @ X2 ) @ I )
% 5.80/6.01 = ( nth_VEBT_VEBT @ L @ I ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_update_invalid
% 5.80/6.01 thf(fact_15_nth__update__invalid,axiom,
% 5.80/6.01 ! [I: nat,L: list_real,J: nat,X2: real] :
% 5.80/6.01 ( ~ ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 5.80/6.01 => ( ( nth_real @ ( list_update_real @ L @ J @ X2 ) @ I )
% 5.80/6.01 = ( nth_real @ L @ I ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_update_invalid
% 5.80/6.01 thf(fact_16_nth__update__invalid,axiom,
% 5.80/6.01 ! [I: nat,L: list_o,J: nat,X2: $o] :
% 5.80/6.01 ( ~ ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 5.80/6.01 => ( ( nth_o @ ( list_update_o @ L @ J @ X2 ) @ I )
% 5.80/6.01 = ( nth_o @ L @ I ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_update_invalid
% 5.80/6.01 thf(fact_17_nth__update__invalid,axiom,
% 5.80/6.01 ! [I: nat,L: list_nat,J: nat,X2: nat] :
% 5.80/6.01 ( ~ ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 5.80/6.01 => ( ( nth_nat @ ( list_update_nat @ L @ J @ X2 ) @ I )
% 5.80/6.01 = ( nth_nat @ L @ I ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_update_invalid
% 5.80/6.01 thf(fact_18_divide__less__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [B2: real,W: num,A2: real] :
% 5.80/6.01 ( ( ord_less_real @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) @ A2 )
% 5.80/6.01 = ( ord_less_real @ B2 @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % divide_less_eq_numeral1(1)
% 5.80/6.01 thf(fact_19_divide__less__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [B2: rat,W: num,A2: rat] :
% 5.80/6.01 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) @ A2 )
% 5.80/6.01 = ( ord_less_rat @ B2 @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % divide_less_eq_numeral1(1)
% 5.80/6.01 thf(fact_20_less__divide__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [A2: real,B2: real,W: num] :
% 5.80/6.01 ( ( ord_less_real @ A2 @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) )
% 5.80/6.01 = ( ord_less_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) ) @ B2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_divide_eq_numeral1(1)
% 5.80/6.01 thf(fact_21_less__divide__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [A2: rat,B2: rat,W: num] :
% 5.80/6.01 ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) )
% 5.80/6.01 = ( ord_less_rat @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W ) ) @ B2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_divide_eq_numeral1(1)
% 5.80/6.01 thf(fact_22_delt__out__of__range,axiom,
% 5.80/6.01 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.80/6.01 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.80/6.01 | ( ord_less_nat @ Ma @ X2 ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.80/6.01 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.80/6.01 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % delt_out_of_range
% 5.80/6.01 thf(fact_23_list__update__id,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBTi,I: nat] :
% 5.80/6.01 ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ ( nth_VEBT_VEBTi @ Xs @ I ) )
% 5.80/6.01 = Xs ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_id
% 5.80/6.01 thf(fact_24_list__update__id,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBT,I: nat] :
% 5.80/6.01 ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 5.80/6.01 = Xs ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_id
% 5.80/6.01 thf(fact_25_list__update__id,axiom,
% 5.80/6.01 ! [Xs: list_nat,I: nat] :
% 5.80/6.01 ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 5.80/6.01 = Xs ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_id
% 5.80/6.01 thf(fact_26_list__update__id,axiom,
% 5.80/6.01 ! [Xs: list_o,I: nat] :
% 5.80/6.01 ( ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ I ) )
% 5.80/6.01 = Xs ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_id
% 5.80/6.01 thf(fact_27_list__update__id,axiom,
% 5.80/6.01 ! [Xs: list_real,I: nat] :
% 5.80/6.01 ( ( list_update_real @ Xs @ I @ ( nth_real @ Xs @ I ) )
% 5.80/6.01 = Xs ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_id
% 5.80/6.01 thf(fact_28_nth__list__update__neq,axiom,
% 5.80/6.01 ! [I: nat,J: nat,Xs: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.80/6.01 ( ( I != J )
% 5.80/6.01 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) @ J )
% 5.80/6.01 = ( nth_VEBT_VEBTi @ Xs @ J ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_neq
% 5.80/6.01 thf(fact_29_nth__list__update__neq,axiom,
% 5.80/6.01 ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.80/6.01 ( ( I != J )
% 5.80/6.01 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ J )
% 5.80/6.01 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_neq
% 5.80/6.01 thf(fact_30_nth__list__update__neq,axiom,
% 5.80/6.01 ! [I: nat,J: nat,Xs: list_nat,X2: nat] :
% 5.80/6.01 ( ( I != J )
% 5.80/6.01 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ J )
% 5.80/6.01 = ( nth_nat @ Xs @ J ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_neq
% 5.80/6.01 thf(fact_31_nth__list__update__neq,axiom,
% 5.80/6.01 ! [I: nat,J: nat,Xs: list_o,X2: $o] :
% 5.80/6.01 ( ( I != J )
% 5.80/6.01 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X2 ) @ J )
% 5.80/6.01 = ( nth_o @ Xs @ J ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_neq
% 5.80/6.01 thf(fact_32_nth__list__update__neq,axiom,
% 5.80/6.01 ! [I: nat,J: nat,Xs: list_real,X2: real] :
% 5.80/6.01 ( ( I != J )
% 5.80/6.01 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X2 ) @ J )
% 5.80/6.01 = ( nth_real @ Xs @ J ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nth_list_update_neq
% 5.80/6.01 thf(fact_33_length__list__update,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.80/6.01 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) )
% 5.80/6.01 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_list_update
% 5.80/6.01 thf(fact_34_length__list__update,axiom,
% 5.80/6.01 ! [Xs: list_real,I: nat,X2: real] :
% 5.80/6.01 ( ( size_size_list_real @ ( list_update_real @ Xs @ I @ X2 ) )
% 5.80/6.01 = ( size_size_list_real @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_list_update
% 5.80/6.01 thf(fact_35_length__list__update,axiom,
% 5.80/6.01 ! [Xs: list_o,I: nat,X2: $o] :
% 5.80/6.01 ( ( size_size_list_o @ ( list_update_o @ Xs @ I @ X2 ) )
% 5.80/6.01 = ( size_size_list_o @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_list_update
% 5.80/6.01 thf(fact_36_length__list__update,axiom,
% 5.80/6.01 ! [Xs: list_nat,I: nat,X2: nat] :
% 5.80/6.01 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X2 ) )
% 5.80/6.01 = ( size_size_list_nat @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_list_update
% 5.80/6.01 thf(fact_37_length__list__update,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBTi,I: nat,X2: vEBT_VEBTi] :
% 5.80/6.01 ( ( size_s7982070591426661849_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) )
% 5.80/6.01 = ( size_s7982070591426661849_VEBTi @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_list_update
% 5.80/6.01 thf(fact_38_not__None__eq,axiom,
% 5.80/6.01 ! [X2: option4927543243414619207at_nat] :
% 5.80/6.01 ( ( X2 != none_P5556105721700978146at_nat )
% 5.80/6.01 = ( ? [Y: product_prod_nat_nat] :
% 5.80/6.01 ( X2
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_None_eq
% 5.80/6.01 thf(fact_39_not__None__eq,axiom,
% 5.80/6.01 ! [X2: option_nat] :
% 5.80/6.01 ( ( X2 != none_nat )
% 5.80/6.01 = ( ? [Y: nat] :
% 5.80/6.01 ( X2
% 5.80/6.01 = ( some_nat @ Y ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_None_eq
% 5.80/6.01 thf(fact_40_not__Some__eq,axiom,
% 5.80/6.01 ! [X2: option4927543243414619207at_nat] :
% 5.80/6.01 ( ( ! [Y: product_prod_nat_nat] :
% 5.80/6.01 ( X2
% 5.80/6.01 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.80/6.01 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq
% 5.80/6.01 thf(fact_41_not__Some__eq,axiom,
% 5.80/6.01 ! [X2: option_nat] :
% 5.80/6.01 ( ( ! [Y: nat] :
% 5.80/6.01 ( X2
% 5.80/6.01 != ( some_nat @ Y ) ) )
% 5.80/6.01 = ( X2 = none_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq
% 5.80/6.01 thf(fact_42_lessI,axiom,
% 5.80/6.01 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % lessI
% 5.80/6.01 thf(fact_43_max__in__set__def,axiom,
% 5.80/6.01 ( vEBT_VEBT_max_in_set
% 5.80/6.01 = ( ^ [Xs2: set_nat,X3: nat] :
% 5.80/6.01 ( ( member_nat @ X3 @ Xs2 )
% 5.80/6.01 & ! [Y: nat] :
% 5.80/6.01 ( ( member_nat @ Y @ Xs2 )
% 5.80/6.01 => ( ord_less_eq_nat @ Y @ X3 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % max_in_set_def
% 5.80/6.01 thf(fact_44_min__in__set__def,axiom,
% 5.80/6.01 ( vEBT_VEBT_min_in_set
% 5.80/6.01 = ( ^ [Xs2: set_nat,X3: nat] :
% 5.80/6.01 ( ( member_nat @ X3 @ Xs2 )
% 5.80/6.01 & ! [Y: nat] :
% 5.80/6.01 ( ( member_nat @ Y @ Xs2 )
% 5.80/6.01 => ( ord_less_eq_nat @ X3 @ Y ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % min_in_set_def
% 5.80/6.01 thf(fact_45_numeral__eq__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ( numera6690914467698888265omplex @ M )
% 5.80/6.01 = ( numera6690914467698888265omplex @ N ) )
% 5.80/6.01 = ( M = N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_eq_iff
% 5.80/6.01 thf(fact_46_numeral__eq__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ( numeral_numeral_real @ M )
% 5.80/6.01 = ( numeral_numeral_real @ N ) )
% 5.80/6.01 = ( M = N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_eq_iff
% 5.80/6.01 thf(fact_47_numeral__eq__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ( numeral_numeral_rat @ M )
% 5.80/6.01 = ( numeral_numeral_rat @ N ) )
% 5.80/6.01 = ( M = N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_eq_iff
% 5.80/6.01 thf(fact_48_numeral__eq__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ( numeral_numeral_nat @ M )
% 5.80/6.01 = ( numeral_numeral_nat @ N ) )
% 5.80/6.01 = ( M = N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_eq_iff
% 5.80/6.01 thf(fact_49_numeral__eq__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ( numeral_numeral_int @ M )
% 5.80/6.01 = ( numeral_numeral_int @ N ) )
% 5.80/6.01 = ( M = N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_eq_iff
% 5.80/6.01 thf(fact_50_old_Onat_Oinject,axiom,
% 5.80/6.01 ! [Nat: nat,Nat2: nat] :
% 5.80/6.01 ( ( ( suc @ Nat )
% 5.80/6.01 = ( suc @ Nat2 ) )
% 5.80/6.01 = ( Nat = Nat2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % old.nat.inject
% 5.80/6.01 thf(fact_51_nat_Oinject,axiom,
% 5.80/6.01 ! [X22: nat,Y2: nat] :
% 5.80/6.01 ( ( ( suc @ X22 )
% 5.80/6.01 = ( suc @ Y2 ) )
% 5.80/6.01 = ( X22 = Y2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat.inject
% 5.80/6.01 thf(fact_52_option_Oinject,axiom,
% 5.80/6.01 ! [X22: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.80/6.01 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 5.80/6.01 = ( X22 = Y2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.inject
% 5.80/6.01 thf(fact_53_option_Oinject,axiom,
% 5.80/6.01 ! [X22: nat,Y2: nat] :
% 5.80/6.01 ( ( ( some_nat @ X22 )
% 5.80/6.01 = ( some_nat @ Y2 ) )
% 5.80/6.01 = ( X22 = Y2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.inject
% 5.80/6.01 thf(fact_54_list__update__overwrite,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBTi,I: nat,X2: vEBT_VEBTi,Y3: vEBT_VEBTi] :
% 5.80/6.01 ( ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) @ I @ Y3 )
% 5.80/6.01 = ( list_u6098035379799741383_VEBTi @ Xs @ I @ Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_overwrite
% 5.80/6.01 thf(fact_55_list__update__overwrite,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.80/6.01 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ I @ Y3 )
% 5.80/6.01 = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_overwrite
% 5.80/6.01 thf(fact_56_list__update__overwrite,axiom,
% 5.80/6.01 ! [Xs: list_nat,I: nat,X2: nat,Y3: nat] :
% 5.80/6.01 ( ( list_update_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ I @ Y3 )
% 5.80/6.01 = ( list_update_nat @ Xs @ I @ Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_overwrite
% 5.80/6.01 thf(fact_57_list__update__overwrite,axiom,
% 5.80/6.01 ! [Xs: list_o,I: nat,X2: $o,Y3: $o] :
% 5.80/6.01 ( ( list_update_o @ ( list_update_o @ Xs @ I @ X2 ) @ I @ Y3 )
% 5.80/6.01 = ( list_update_o @ Xs @ I @ Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_overwrite
% 5.80/6.01 thf(fact_58_list__update__overwrite,axiom,
% 5.80/6.01 ! [Xs: list_real,I: nat,X2: real,Y3: real] :
% 5.80/6.01 ( ( list_update_real @ ( list_update_real @ Xs @ I @ X2 ) @ I @ Y3 )
% 5.80/6.01 = ( list_update_real @ Xs @ I @ Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_overwrite
% 5.80/6.01 thf(fact_59_numeral__le__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.80/6.01 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_le_iff
% 5.80/6.01 thf(fact_60_numeral__le__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.80/6.01 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_le_iff
% 5.80/6.01 thf(fact_61_numeral__le__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.80/6.01 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_le_iff
% 5.80/6.01 thf(fact_62_numeral__le__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.80/6.01 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_le_iff
% 5.80/6.01 thf(fact_63_numeral__less__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.80/6.01 = ( ord_less_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_less_iff
% 5.80/6.01 thf(fact_64_numeral__less__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.80/6.01 = ( ord_less_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_less_iff
% 5.80/6.01 thf(fact_65_numeral__less__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.80/6.01 = ( ord_less_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_less_iff
% 5.80/6.01 thf(fact_66_numeral__less__iff,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.80/6.01 = ( ord_less_num @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_less_iff
% 5.80/6.01 thf(fact_67_num__double,axiom,
% 5.80/6.01 ! [N: num] :
% 5.80/6.01 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.80/6.01 = ( bit0 @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % num_double
% 5.80/6.01 thf(fact_68_mult__numeral__left__semiring__numeral,axiom,
% 5.80/6.01 ! [V: num,W: num,Z: complex] :
% 5.80/6.01 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.80/6.01 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_left_semiring_numeral
% 5.80/6.01 thf(fact_69_mult__numeral__left__semiring__numeral,axiom,
% 5.80/6.01 ! [V: num,W: num,Z: real] :
% 5.80/6.01 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.80/6.01 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_left_semiring_numeral
% 5.80/6.01 thf(fact_70_mult__numeral__left__semiring__numeral,axiom,
% 5.80/6.01 ! [V: num,W: num,Z: rat] :
% 5.80/6.01 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.80/6.01 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_left_semiring_numeral
% 5.80/6.01 thf(fact_71_mult__numeral__left__semiring__numeral,axiom,
% 5.80/6.01 ! [V: num,W: num,Z: nat] :
% 5.80/6.01 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.80/6.01 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_left_semiring_numeral
% 5.80/6.01 thf(fact_72_mult__numeral__left__semiring__numeral,axiom,
% 5.80/6.01 ! [V: num,W: num,Z: int] :
% 5.80/6.01 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.80/6.01 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_left_semiring_numeral
% 5.80/6.01 thf(fact_73_numeral__times__numeral,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.80/6.01 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_times_numeral
% 5.80/6.01 thf(fact_74_numeral__times__numeral,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.80/6.01 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_times_numeral
% 5.80/6.01 thf(fact_75_numeral__times__numeral,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.80/6.01 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_times_numeral
% 5.80/6.01 thf(fact_76_numeral__times__numeral,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.80/6.01 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_times_numeral
% 5.80/6.01 thf(fact_77_numeral__times__numeral,axiom,
% 5.80/6.01 ! [M: num,N: num] :
% 5.80/6.01 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.80/6.01 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % numeral_times_numeral
% 5.80/6.01 thf(fact_78_del__single__cont,axiom,
% 5.80/6.01 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.80/6.01 ( ( ( X2 = Mi )
% 5.80/6.01 & ( X2 = Ma ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.80/6.01 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.80/6.01 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % del_single_cont
% 5.80/6.01 thf(fact_79_Suc__less__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.80/6.01 = ( ord_less_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_less_eq
% 5.80/6.01 thf(fact_80_Suc__mono,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ N )
% 5.80/6.01 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_mono
% 5.80/6.01 thf(fact_81_Suc__le__mono,axiom,
% 5.80/6.01 ! [N: nat,M: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.80/6.01 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_le_mono
% 5.80/6.01 thf(fact_82_not__Some__eq2,axiom,
% 5.80/6.01 ! [V: option2651255830984564193nteger] :
% 5.80/6.01 ( ( ! [X3: code_integer,Y: code_integer] :
% 5.80/6.01 ( V
% 5.80/6.01 != ( some_P6772290148444788224nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) ) ) )
% 5.80/6.01 = ( V = none_P4506660739021792380nteger ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq2
% 5.80/6.01 thf(fact_83_not__Some__eq2,axiom,
% 5.80/6.01 ! [V: option936205604648967762et_nat] :
% 5.80/6.01 ( ( ! [X3: heap_e7401611519738050253t_unit,Y: set_nat] :
% 5.80/6.01 ( V
% 5.80/6.01 != ( some_P624177172695371229et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y ) ) ) )
% 5.80/6.01 = ( V = none_P533106815845188193et_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq2
% 5.80/6.01 thf(fact_84_not__Some__eq2,axiom,
% 5.80/6.01 ! [V: option2661157926820139483um_num] :
% 5.80/6.01 ( ( ! [X3: num,Y: num] :
% 5.80/6.01 ( V
% 5.80/6.01 != ( some_P6201964756284913402um_num @ ( product_Pair_num_num @ X3 @ Y ) ) ) )
% 5.80/6.01 = ( V = none_P4394680061957285238um_num ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq2
% 5.80/6.01 thf(fact_85_not__Some__eq2,axiom,
% 5.80/6.01 ! [V: option4624381673175914239nt_int] :
% 5.80/6.01 ( ( ! [X3: int,Y: int] :
% 5.80/6.01 ( V
% 5.80/6.01 != ( some_P4184893108420464158nt_int @ ( product_Pair_int_int @ X3 @ Y ) ) ) )
% 5.80/6.01 = ( V = none_P2377608414092835994nt_int ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq2
% 5.80/6.01 thf(fact_86_not__Some__eq2,axiom,
% 5.80/6.01 ! [V: option4927543243414619207at_nat] :
% 5.80/6.01 ( ( ! [X3: nat,Y: nat] :
% 5.80/6.01 ( V
% 5.80/6.01 != ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) ) ) )
% 5.80/6.01 = ( V = none_P5556105721700978146at_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_Some_eq2
% 5.80/6.01 thf(fact_87_lesseq__shift,axiom,
% 5.80/6.01 ( ord_less_eq_nat
% 5.80/6.01 = ( ^ [X3: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X3 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lesseq_shift
% 5.80/6.01 thf(fact_88_list__update__beyond,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 5.80/6.01 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 )
% 5.80/6.01 = Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_beyond
% 5.80/6.01 thf(fact_89_list__update__beyond,axiom,
% 5.80/6.01 ! [Xs: list_real,I: nat,X2: real] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ I )
% 5.80/6.01 => ( ( list_update_real @ Xs @ I @ X2 )
% 5.80/6.01 = Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_beyond
% 5.80/6.01 thf(fact_90_list__update__beyond,axiom,
% 5.80/6.01 ! [Xs: list_o,I: nat,X2: $o] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 5.80/6.01 => ( ( list_update_o @ Xs @ I @ X2 )
% 5.80/6.01 = Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_beyond
% 5.80/6.01 thf(fact_91_list__update__beyond,axiom,
% 5.80/6.01 ! [Xs: list_nat,I: nat,X2: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 5.80/6.01 => ( ( list_update_nat @ Xs @ I @ X2 )
% 5.80/6.01 = Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_beyond
% 5.80/6.01 thf(fact_92_list__update__beyond,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBTi,I: nat,X2: vEBT_VEBTi] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) @ I )
% 5.80/6.01 => ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 )
% 5.80/6.01 = Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_beyond
% 5.80/6.01 thf(fact_93_le__divide__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [A2: real,B2: real,W: num] :
% 5.80/6.01 ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) )
% 5.80/6.01 = ( ord_less_eq_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) ) @ B2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_divide_eq_numeral1(1)
% 5.80/6.01 thf(fact_94_le__divide__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [A2: rat,B2: rat,W: num] :
% 5.80/6.01 ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) )
% 5.80/6.01 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W ) ) @ B2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_divide_eq_numeral1(1)
% 5.80/6.01 thf(fact_95_divide__le__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [B2: real,W: num,A2: real] :
% 5.80/6.01 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) @ A2 )
% 5.80/6.01 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % divide_le_eq_numeral1(1)
% 5.80/6.01 thf(fact_96_divide__le__eq__numeral1_I1_J,axiom,
% 5.80/6.01 ! [B2: rat,W: num,A2: rat] :
% 5.80/6.01 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) @ A2 )
% 5.80/6.01 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % divide_le_eq_numeral1(1)
% 5.80/6.01 thf(fact_97_lift__Suc__mono__le,axiom,
% 5.80/6.01 ! [F: nat > set_int,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_le
% 5.80/6.01 thf(fact_98_lift__Suc__mono__le,axiom,
% 5.80/6.01 ! [F: nat > rat,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_le
% 5.80/6.01 thf(fact_99_lift__Suc__mono__le,axiom,
% 5.80/6.01 ! [F: nat > num,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_le
% 5.80/6.01 thf(fact_100_lift__Suc__mono__le,axiom,
% 5.80/6.01 ! [F: nat > nat,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_le
% 5.80/6.01 thf(fact_101_lift__Suc__mono__le,axiom,
% 5.80/6.01 ! [F: nat > int,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_le
% 5.80/6.01 thf(fact_102_lift__Suc__antimono__le,axiom,
% 5.80/6.01 ! [F: nat > set_int,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_antimono_le
% 5.80/6.01 thf(fact_103_lift__Suc__antimono__le,axiom,
% 5.80/6.01 ! [F: nat > rat,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_antimono_le
% 5.80/6.01 thf(fact_104_lift__Suc__antimono__le,axiom,
% 5.80/6.01 ! [F: nat > num,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_antimono_le
% 5.80/6.01 thf(fact_105_lift__Suc__antimono__le,axiom,
% 5.80/6.01 ! [F: nat > nat,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_antimono_le
% 5.80/6.01 thf(fact_106_lift__Suc__antimono__le,axiom,
% 5.80/6.01 ! [F: nat > int,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_antimono_le
% 5.80/6.01 thf(fact_107_le__cube,axiom,
% 5.80/6.01 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_cube
% 5.80/6.01 thf(fact_108_mem__Collect__eq,axiom,
% 5.80/6.01 ! [A2: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.80/6.01 ( ( member_VEBT_VEBT @ A2 @ ( collect_VEBT_VEBT @ P ) )
% 5.80/6.01 = ( P @ A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % mem_Collect_eq
% 5.80/6.01 thf(fact_109_mem__Collect__eq,axiom,
% 5.80/6.01 ! [A2: real,P: real > $o] :
% 5.80/6.01 ( ( member_real @ A2 @ ( collect_real @ P ) )
% 5.80/6.01 = ( P @ A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % mem_Collect_eq
% 5.80/6.01 thf(fact_110_mem__Collect__eq,axiom,
% 5.80/6.01 ! [A2: nat,P: nat > $o] :
% 5.80/6.01 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 5.80/6.01 = ( P @ A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % mem_Collect_eq
% 5.80/6.01 thf(fact_111_mem__Collect__eq,axiom,
% 5.80/6.01 ! [A2: int,P: int > $o] :
% 5.80/6.01 ( ( member_int @ A2 @ ( collect_int @ P ) )
% 5.80/6.01 = ( P @ A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % mem_Collect_eq
% 5.80/6.01 thf(fact_112_mem__Collect__eq,axiom,
% 5.80/6.01 ! [A2: complex,P: complex > $o] :
% 5.80/6.01 ( ( member_complex @ A2 @ ( collect_complex @ P ) )
% 5.80/6.01 = ( P @ A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % mem_Collect_eq
% 5.80/6.01 thf(fact_113_mem__Collect__eq,axiom,
% 5.80/6.01 ! [A2: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.80/6.01 ( ( member5262025264175285858nt_int @ A2 @ ( collec213857154873943460nt_int @ P ) )
% 5.80/6.01 = ( P @ A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % mem_Collect_eq
% 5.80/6.01 thf(fact_114_Collect__mem__eq,axiom,
% 5.80/6.01 ! [A: set_VEBT_VEBT] :
% 5.80/6.01 ( ( collect_VEBT_VEBT
% 5.80/6.01 @ ^ [X3: vEBT_VEBT] : ( member_VEBT_VEBT @ X3 @ A ) )
% 5.80/6.01 = A ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_mem_eq
% 5.80/6.01 thf(fact_115_Collect__mem__eq,axiom,
% 5.80/6.01 ! [A: set_real] :
% 5.80/6.01 ( ( collect_real
% 5.80/6.01 @ ^ [X3: real] : ( member_real @ X3 @ A ) )
% 5.80/6.01 = A ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_mem_eq
% 5.80/6.01 thf(fact_116_Collect__mem__eq,axiom,
% 5.80/6.01 ! [A: set_nat] :
% 5.80/6.01 ( ( collect_nat
% 5.80/6.01 @ ^ [X3: nat] : ( member_nat @ X3 @ A ) )
% 5.80/6.01 = A ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_mem_eq
% 5.80/6.01 thf(fact_117_Collect__mem__eq,axiom,
% 5.80/6.01 ! [A: set_int] :
% 5.80/6.01 ( ( collect_int
% 5.80/6.01 @ ^ [X3: int] : ( member_int @ X3 @ A ) )
% 5.80/6.01 = A ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_mem_eq
% 5.80/6.01 thf(fact_118_Collect__mem__eq,axiom,
% 5.80/6.01 ! [A: set_complex] :
% 5.80/6.01 ( ( collect_complex
% 5.80/6.01 @ ^ [X3: complex] : ( member_complex @ X3 @ A ) )
% 5.80/6.01 = A ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_mem_eq
% 5.80/6.01 thf(fact_119_Collect__mem__eq,axiom,
% 5.80/6.01 ! [A: set_Pr958786334691620121nt_int] :
% 5.80/6.01 ( ( collec213857154873943460nt_int
% 5.80/6.01 @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A ) )
% 5.80/6.01 = A ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_mem_eq
% 5.80/6.01 thf(fact_120_Collect__cong,axiom,
% 5.80/6.01 ! [P: nat > $o,Q: nat > $o] :
% 5.80/6.01 ( ! [X4: nat] :
% 5.80/6.01 ( ( P @ X4 )
% 5.80/6.01 = ( Q @ X4 ) )
% 5.80/6.01 => ( ( collect_nat @ P )
% 5.80/6.01 = ( collect_nat @ Q ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_cong
% 5.80/6.01 thf(fact_121_Collect__cong,axiom,
% 5.80/6.01 ! [P: int > $o,Q: int > $o] :
% 5.80/6.01 ( ! [X4: int] :
% 5.80/6.01 ( ( P @ X4 )
% 5.80/6.01 = ( Q @ X4 ) )
% 5.80/6.01 => ( ( collect_int @ P )
% 5.80/6.01 = ( collect_int @ Q ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_cong
% 5.80/6.01 thf(fact_122_Collect__cong,axiom,
% 5.80/6.01 ! [P: complex > $o,Q: complex > $o] :
% 5.80/6.01 ( ! [X4: complex] :
% 5.80/6.01 ( ( P @ X4 )
% 5.80/6.01 = ( Q @ X4 ) )
% 5.80/6.01 => ( ( collect_complex @ P )
% 5.80/6.01 = ( collect_complex @ Q ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_cong
% 5.80/6.01 thf(fact_123_Collect__cong,axiom,
% 5.80/6.01 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.80/6.01 ( ! [X4: product_prod_int_int] :
% 5.80/6.01 ( ( P @ X4 )
% 5.80/6.01 = ( Q @ X4 ) )
% 5.80/6.01 => ( ( collec213857154873943460nt_int @ P )
% 5.80/6.01 = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Collect_cong
% 5.80/6.01 thf(fact_124_le__refl,axiom,
% 5.80/6.01 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.80/6.01
% 5.80/6.01 % le_refl
% 5.80/6.01 thf(fact_125_le__trans,axiom,
% 5.80/6.01 ! [I: nat,J: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ( ord_less_eq_nat @ J @ K )
% 5.80/6.01 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_trans
% 5.80/6.01 thf(fact_126_eq__imp__le,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( M = N )
% 5.80/6.01 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % eq_imp_le
% 5.80/6.01 thf(fact_127_le__square,axiom,
% 5.80/6.01 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_square
% 5.80/6.01 thf(fact_128_le__antisym,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ( ord_less_eq_nat @ N @ M )
% 5.80/6.01 => ( M = N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_antisym
% 5.80/6.01 thf(fact_129_mult__le__mono,axiom,
% 5.80/6.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ( ord_less_eq_nat @ K @ L )
% 5.80/6.01 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_le_mono
% 5.80/6.01 thf(fact_130_le__some__optE,axiom,
% 5.80/6.01 ! [M: set_int,X2: option_set_int] :
% 5.80/6.01 ( ( ord_le353528952715127954et_int @ ( some_set_int @ M ) @ X2 )
% 5.80/6.01 => ~ ! [M2: set_int] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_set_int @ M2 ) )
% 5.80/6.01 => ~ ( ord_less_eq_set_int @ M @ M2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_some_optE
% 5.80/6.01 thf(fact_131_le__some__optE,axiom,
% 5.80/6.01 ! [M: rat,X2: option_rat] :
% 5.80/6.01 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M ) @ X2 )
% 5.80/6.01 => ~ ! [M2: rat] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_rat @ M2 ) )
% 5.80/6.01 => ~ ( ord_less_eq_rat @ M @ M2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_some_optE
% 5.80/6.01 thf(fact_132_le__some__optE,axiom,
% 5.80/6.01 ! [M: num,X2: option_num] :
% 5.80/6.01 ( ( ord_le6622620407824499402on_num @ ( some_num @ M ) @ X2 )
% 5.80/6.01 => ~ ! [M2: num] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_num @ M2 ) )
% 5.80/6.01 => ~ ( ord_less_eq_num @ M @ M2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_some_optE
% 5.80/6.01 thf(fact_133_le__some__optE,axiom,
% 5.80/6.01 ! [M: nat,X2: option_nat] :
% 5.80/6.01 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M ) @ X2 )
% 5.80/6.01 => ~ ! [M2: nat] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_nat @ M2 ) )
% 5.80/6.01 => ~ ( ord_less_eq_nat @ M @ M2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_some_optE
% 5.80/6.01 thf(fact_134_le__some__optE,axiom,
% 5.80/6.01 ! [M: int,X2: option_int] :
% 5.80/6.01 ( ( ord_le1736525451366464988on_int @ ( some_int @ M ) @ X2 )
% 5.80/6.01 => ~ ! [M2: int] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_int @ M2 ) )
% 5.80/6.01 => ~ ( ord_less_eq_int @ M @ M2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_some_optE
% 5.80/6.01 thf(fact_135_mult__le__mono1,axiom,
% 5.80/6.01 ! [I: nat,J: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_le_mono1
% 5.80/6.01 thf(fact_136_mult__le__mono2,axiom,
% 5.80/6.01 ! [I: nat,J: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % mult_le_mono2
% 5.80/6.01 thf(fact_137_nat__le__linear,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_le_linear
% 5.80/6.01 thf(fact_138_ord__eq__le__eq__trans,axiom,
% 5.80/6.01 ! [A2: set_int,B2: set_int,C2: set_int,D2: set_int] :
% 5.80/6.01 ( ( A2 = B2 )
% 5.80/6.01 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.80/6.01 => ( ( C2 = D2 )
% 5.80/6.01 => ( ord_less_eq_set_int @ A2 @ D2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % ord_eq_le_eq_trans
% 5.80/6.01 thf(fact_139_ord__eq__le__eq__trans,axiom,
% 5.80/6.01 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.80/6.01 ( ( A2 = B2 )
% 5.80/6.01 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.80/6.01 => ( ( C2 = D2 )
% 5.80/6.01 => ( ord_less_eq_rat @ A2 @ D2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % ord_eq_le_eq_trans
% 5.80/6.01 thf(fact_140_ord__eq__le__eq__trans,axiom,
% 5.80/6.01 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.80/6.01 ( ( A2 = B2 )
% 5.80/6.01 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.80/6.01 => ( ( C2 = D2 )
% 5.80/6.01 => ( ord_less_eq_num @ A2 @ D2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % ord_eq_le_eq_trans
% 5.80/6.01 thf(fact_141_ord__eq__le__eq__trans,axiom,
% 5.80/6.01 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.80/6.01 ( ( A2 = B2 )
% 5.80/6.01 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.80/6.01 => ( ( C2 = D2 )
% 5.80/6.01 => ( ord_less_eq_nat @ A2 @ D2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % ord_eq_le_eq_trans
% 5.80/6.01 thf(fact_142_ord__eq__le__eq__trans,axiom,
% 5.80/6.01 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.80/6.01 ( ( A2 = B2 )
% 5.80/6.01 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.80/6.01 => ( ( C2 = D2 )
% 5.80/6.01 => ( ord_less_eq_int @ A2 @ D2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % ord_eq_le_eq_trans
% 5.80/6.01 thf(fact_143_Suc__mult__le__cancel1,axiom,
% 5.80/6.01 ! [K: nat,M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.80/6.01 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_mult_le_cancel1
% 5.80/6.01 thf(fact_144_Nat_Oex__has__greatest__nat,axiom,
% 5.80/6.01 ! [P: nat > $o,K: nat,B2: nat] :
% 5.80/6.01 ( ( P @ K )
% 5.80/6.01 => ( ! [Y4: nat] :
% 5.80/6.01 ( ( P @ Y4 )
% 5.80/6.01 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.80/6.01 => ? [X4: nat] :
% 5.80/6.01 ( ( P @ X4 )
% 5.80/6.01 & ! [Y5: nat] :
% 5.80/6.01 ( ( P @ Y5 )
% 5.80/6.01 => ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Nat.ex_has_greatest_nat
% 5.80/6.01 thf(fact_145_div__times__less__eq__dividend,axiom,
% 5.80/6.01 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.80/6.01
% 5.80/6.01 % div_times_less_eq_dividend
% 5.80/6.01 thf(fact_146_times__div__less__eq__dividend,axiom,
% 5.80/6.01 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.80/6.01
% 5.80/6.01 % times_div_less_eq_dividend
% 5.80/6.01 thf(fact_147_Suc__mult__cancel1,axiom,
% 5.80/6.01 ! [K: nat,M: nat,N: nat] :
% 5.80/6.01 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.80/6.01 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.80/6.01 = ( M = N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_mult_cancel1
% 5.80/6.01 thf(fact_148_transitive__stepwise__le,axiom,
% 5.80/6.01 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 5.80/6.01 => ( ! [X4: nat,Y4: nat,Z2: nat] :
% 5.80/6.01 ( ( R @ X4 @ Y4 )
% 5.80/6.01 => ( ( R @ Y4 @ Z2 )
% 5.80/6.01 => ( R @ X4 @ Z2 ) ) )
% 5.80/6.01 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.80/6.01 => ( R @ M @ N ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % transitive_stepwise_le
% 5.80/6.01 thf(fact_149_nat__induct__at__least,axiom,
% 5.80/6.01 ! [M: nat,N: nat,P: nat > $o] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ( P @ M )
% 5.80/6.01 => ( ! [N3: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N3 )
% 5.80/6.01 => ( ( P @ N3 )
% 5.80/6.01 => ( P @ ( suc @ N3 ) ) ) )
% 5.80/6.01 => ( P @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_induct_at_least
% 5.80/6.01 thf(fact_150_full__nat__induct,axiom,
% 5.80/6.01 ! [P: nat > $o,N: nat] :
% 5.80/6.01 ( ! [N3: nat] :
% 5.80/6.01 ( ! [M3: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 5.80/6.01 => ( P @ M3 ) )
% 5.80/6.01 => ( P @ N3 ) )
% 5.80/6.01 => ( P @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % full_nat_induct
% 5.80/6.01 thf(fact_151_not__less__eq__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.80/6.01 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_less_eq_eq
% 5.80/6.01 thf(fact_152_Suc__n__not__le__n,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_n_not_le_n
% 5.80/6.01 thf(fact_153_le__Suc__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.80/6.01 = ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 | ( M
% 5.80/6.01 = ( suc @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_Suc_eq
% 5.80/6.01 thf(fact_154_Suc__le__D,axiom,
% 5.80/6.01 ! [N: nat,M4: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 5.80/6.01 => ? [M5: nat] :
% 5.80/6.01 ( M4
% 5.80/6.01 = ( suc @ M5 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_le_D
% 5.80/6.01 thf(fact_155_le__SucI,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_SucI
% 5.80/6.01 thf(fact_156_le__SucE,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.80/6.01 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( M
% 5.80/6.01 = ( suc @ N ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_SucE
% 5.80/6.01 thf(fact_157_Suc__leD,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.80/6.01 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_leD
% 5.80/6.01 thf(fact_158_less__mono__imp__le__mono,axiom,
% 5.80/6.01 ! [F: nat > nat,I: nat,J: nat] :
% 5.80/6.01 ( ! [I2: nat,J2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ J2 )
% 5.80/6.01 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 5.80/6.01 => ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_mono_imp_le_mono
% 5.80/6.01 thf(fact_159_le__neq__implies__less,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ( M != N )
% 5.80/6.01 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_neq_implies_less
% 5.80/6.01 thf(fact_160_less__or__eq__imp__le,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ( ord_less_nat @ M @ N )
% 5.80/6.01 | ( M = N ) )
% 5.80/6.01 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_or_eq_imp_le
% 5.80/6.01 thf(fact_161_le__eq__less__or__eq,axiom,
% 5.80/6.01 ( ord_less_eq_nat
% 5.80/6.01 = ( ^ [M6: nat,N4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M6 @ N4 )
% 5.80/6.01 | ( M6 = N4 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_eq_less_or_eq
% 5.80/6.01 thf(fact_162_less__imp__le__nat,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ N )
% 5.80/6.01 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_imp_le_nat
% 5.80/6.01 thf(fact_163_nat__less__le,axiom,
% 5.80/6.01 ( ord_less_nat
% 5.80/6.01 = ( ^ [M6: nat,N4: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M6 @ N4 )
% 5.80/6.01 & ( M6 != N4 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_less_le
% 5.80/6.01 thf(fact_164_exists__leI,axiom,
% 5.80/6.01 ! [N: nat,P: nat > $o] :
% 5.80/6.01 ( ( ! [N5: nat] :
% 5.80/6.01 ( ( ord_less_nat @ N5 @ N )
% 5.80/6.01 => ~ ( P @ N5 ) )
% 5.80/6.01 => ( P @ N ) )
% 5.80/6.01 => ? [N6: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ N6 @ N )
% 5.80/6.01 & ( P @ N6 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % exists_leI
% 5.80/6.01 thf(fact_165_div__mult2__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat,Q3: nat] :
% 5.80/6.01 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q3 ) )
% 5.80/6.01 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % div_mult2_eq
% 5.80/6.01 thf(fact_166_div__le__dividend,axiom,
% 5.80/6.01 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.80/6.01
% 5.80/6.01 % div_le_dividend
% 5.80/6.01 thf(fact_167_div__le__mono,axiom,
% 5.80/6.01 ! [M: nat,N: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % div_le_mono
% 5.80/6.01 thf(fact_168_div__nat__eqI,axiom,
% 5.80/6.01 ! [N: nat,Q3: nat,M: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 5.80/6.01 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 5.80/6.01 => ( ( divide_divide_nat @ M @ N )
% 5.80/6.01 = Q3 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % div_nat_eqI
% 5.80/6.01 thf(fact_169_div__mult2__numeral__eq,axiom,
% 5.80/6.01 ! [A2: nat,K: num,L: num] :
% 5.80/6.01 ( ( divide_divide_nat @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.80/6.01 = ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % div_mult2_numeral_eq
% 5.80/6.01 thf(fact_170_div__mult2__numeral__eq,axiom,
% 5.80/6.01 ! [A2: int,K: num,L: num] :
% 5.80/6.01 ( ( divide_divide_int @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.80/6.01 = ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % div_mult2_numeral_eq
% 5.80/6.01 thf(fact_171_Suc__mult__less__cancel1,axiom,
% 5.80/6.01 ! [K: nat,M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.80/6.01 = ( ord_less_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_mult_less_cancel1
% 5.80/6.01 thf(fact_172_le__imp__less__Suc,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_imp_less_Suc
% 5.80/6.01 thf(fact_173_less__eq__Suc__le,axiom,
% 5.80/6.01 ( ord_less_nat
% 5.80/6.01 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_eq_Suc_le
% 5.80/6.01 thf(fact_174_less__Suc__eq__le,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.80/6.01 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_Suc_eq_le
% 5.80/6.01 thf(fact_175_le__less__Suc__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.80/6.01 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.80/6.01 = ( N = M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % le_less_Suc_eq
% 5.80/6.01 thf(fact_176_Suc__le__lessD,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.80/6.01 => ( ord_less_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_le_lessD
% 5.80/6.01 thf(fact_177_inc__induct,axiom,
% 5.80/6.01 ! [I: nat,J: nat,P: nat > $o] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ( P @ J )
% 5.80/6.01 => ( ! [N3: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ N3 )
% 5.80/6.01 => ( ( ord_less_nat @ N3 @ J )
% 5.80/6.01 => ( ( P @ ( suc @ N3 ) )
% 5.80/6.01 => ( P @ N3 ) ) ) )
% 5.80/6.01 => ( P @ I ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % inc_induct
% 5.80/6.01 thf(fact_178_dec__induct,axiom,
% 5.80/6.01 ! [I: nat,J: nat,P: nat > $o] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.80/6.01 => ( ( P @ I )
% 5.80/6.01 => ( ! [N3: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ I @ N3 )
% 5.80/6.01 => ( ( ord_less_nat @ N3 @ J )
% 5.80/6.01 => ( ( P @ N3 )
% 5.80/6.01 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.80/6.01 => ( P @ J ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % dec_induct
% 5.80/6.01 thf(fact_179_Suc__le__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.80/6.01 = ( ord_less_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_le_eq
% 5.80/6.01 thf(fact_180_Suc__leI,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ N )
% 5.80/6.01 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_leI
% 5.80/6.01 thf(fact_181_nat__in__between__eq_I1_J,axiom,
% 5.80/6.01 ! [A2: nat,B2: nat] :
% 5.80/6.01 ( ( ( ord_less_nat @ A2 @ B2 )
% 5.80/6.01 & ( ord_less_eq_nat @ B2 @ ( suc @ A2 ) ) )
% 5.80/6.01 = ( B2
% 5.80/6.01 = ( suc @ A2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_in_between_eq(1)
% 5.80/6.01 thf(fact_182_nat__in__between__eq_I2_J,axiom,
% 5.80/6.01 ! [A2: nat,B2: nat] :
% 5.80/6.01 ( ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.80/6.01 & ( ord_less_nat @ B2 @ ( suc @ A2 ) ) )
% 5.80/6.01 = ( B2 = A2 ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_in_between_eq(2)
% 5.80/6.01 thf(fact_183_less__mult__imp__div__less,axiom,
% 5.80/6.01 ! [M: nat,I: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.80/6.01 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_mult_imp_div_less
% 5.80/6.01 thf(fact_184_Suc__div__le__mono,axiom,
% 5.80/6.01 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_div_le_mono
% 5.80/6.01 thf(fact_185_bex2I,axiom,
% 5.80/6.01 ! [A2: code_integer,B2: code_integer,S: set_Pr4811707699266497531nteger,P: code_integer > code_integer > $o] :
% 5.80/6.01 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( P @ A2 @ B2 ) )
% 5.80/6.01 => ? [A3: code_integer,B3: code_integer] :
% 5.80/6.01 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A3 @ B3 ) @ S )
% 5.80/6.01 & ( P @ A3 @ B3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % bex2I
% 5.80/6.01 thf(fact_186_bex2I,axiom,
% 5.80/6.01 ! [A2: heap_e7401611519738050253t_unit,B2: set_nat,S: set_Pr3948176798113811640et_nat,P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 5.80/6.01 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( P @ A2 @ B2 ) )
% 5.80/6.01 => ? [A3: heap_e7401611519738050253t_unit,B3: set_nat] :
% 5.80/6.01 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A3 @ B3 ) @ S )
% 5.80/6.01 & ( P @ A3 @ B3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % bex2I
% 5.80/6.01 thf(fact_187_bex2I,axiom,
% 5.80/6.01 ! [A2: num,B2: num,S: set_Pr8218934625190621173um_num,P: num > num > $o] :
% 5.80/6.01 ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( P @ A2 @ B2 ) )
% 5.80/6.01 => ? [A3: num,B3: num] :
% 5.80/6.01 ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ A3 @ B3 ) @ S )
% 5.80/6.01 & ( P @ A3 @ B3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % bex2I
% 5.80/6.01 thf(fact_188_bex2I,axiom,
% 5.80/6.01 ! [A2: nat,B2: nat,S: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 5.80/6.01 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( P @ A2 @ B2 ) )
% 5.80/6.01 => ? [A3: nat,B3: nat] :
% 5.80/6.01 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ S )
% 5.80/6.01 & ( P @ A3 @ B3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % bex2I
% 5.80/6.01 thf(fact_189_bex2I,axiom,
% 5.80/6.01 ! [A2: int,B2: int,S: set_Pr958786334691620121nt_int,P: int > int > $o] :
% 5.80/6.01 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ S )
% 5.80/6.01 => ( P @ A2 @ B2 ) )
% 5.80/6.01 => ? [A3: int,B3: int] :
% 5.80/6.01 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ S )
% 5.80/6.01 & ( P @ A3 @ B3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % bex2I
% 5.80/6.01 thf(fact_190_n__not__Suc__n,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ( N
% 5.80/6.01 != ( suc @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % n_not_Suc_n
% 5.80/6.01 thf(fact_191_Suc__inject,axiom,
% 5.80/6.01 ! [X2: nat,Y3: nat] :
% 5.80/6.01 ( ( ( suc @ X2 )
% 5.80/6.01 = ( suc @ Y3 ) )
% 5.80/6.01 => ( X2 = Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_inject
% 5.80/6.01 thf(fact_192_linorder__neqE__nat,axiom,
% 5.80/6.01 ! [X2: nat,Y3: nat] :
% 5.80/6.01 ( ( X2 != Y3 )
% 5.80/6.01 => ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.80/6.01 => ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % linorder_neqE_nat
% 5.80/6.01 thf(fact_193_infinite__descent,axiom,
% 5.80/6.01 ! [P: nat > $o,N: nat] :
% 5.80/6.01 ( ! [N3: nat] :
% 5.80/6.01 ( ~ ( P @ N3 )
% 5.80/6.01 => ? [M3: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M3 @ N3 )
% 5.80/6.01 & ~ ( P @ M3 ) ) )
% 5.80/6.01 => ( P @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % infinite_descent
% 5.80/6.01 thf(fact_194_nat__less__induct,axiom,
% 5.80/6.01 ! [P: nat > $o,N: nat] :
% 5.80/6.01 ( ! [N3: nat] :
% 5.80/6.01 ( ! [M3: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M3 @ N3 )
% 5.80/6.01 => ( P @ M3 ) )
% 5.80/6.01 => ( P @ N3 ) )
% 5.80/6.01 => ( P @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_less_induct
% 5.80/6.01 thf(fact_195_less__irrefl__nat,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ~ ( ord_less_nat @ N @ N ) ).
% 5.80/6.01
% 5.80/6.01 % less_irrefl_nat
% 5.80/6.01 thf(fact_196_less__not__refl3,axiom,
% 5.80/6.01 ! [S2: nat,T: nat] :
% 5.80/6.01 ( ( ord_less_nat @ S2 @ T )
% 5.80/6.01 => ( S2 != T ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_not_refl3
% 5.80/6.01 thf(fact_197_less__not__refl2,axiom,
% 5.80/6.01 ! [N: nat,M: nat] :
% 5.80/6.01 ( ( ord_less_nat @ N @ M )
% 5.80/6.01 => ( M != N ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_not_refl2
% 5.80/6.01 thf(fact_198_less__not__refl,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ~ ( ord_less_nat @ N @ N ) ).
% 5.80/6.01
% 5.80/6.01 % less_not_refl
% 5.80/6.01 thf(fact_199_nat__neq__iff,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( M != N )
% 5.80/6.01 = ( ( ord_less_nat @ M @ N )
% 5.80/6.01 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % nat_neq_iff
% 5.80/6.01 thf(fact_200_size__neq__size__imp__neq,axiom,
% 5.80/6.01 ! [X2: list_VEBT_VEBT,Y3: list_VEBT_VEBT] :
% 5.80/6.01 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 5.80/6.01 != ( size_s6755466524823107622T_VEBT @ Y3 ) )
% 5.80/6.01 => ( X2 != Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % size_neq_size_imp_neq
% 5.80/6.01 thf(fact_201_size__neq__size__imp__neq,axiom,
% 5.80/6.01 ! [X2: list_real,Y3: list_real] :
% 5.80/6.01 ( ( ( size_size_list_real @ X2 )
% 5.80/6.01 != ( size_size_list_real @ Y3 ) )
% 5.80/6.01 => ( X2 != Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % size_neq_size_imp_neq
% 5.80/6.01 thf(fact_202_size__neq__size__imp__neq,axiom,
% 5.80/6.01 ! [X2: list_o,Y3: list_o] :
% 5.80/6.01 ( ( ( size_size_list_o @ X2 )
% 5.80/6.01 != ( size_size_list_o @ Y3 ) )
% 5.80/6.01 => ( X2 != Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % size_neq_size_imp_neq
% 5.80/6.01 thf(fact_203_size__neq__size__imp__neq,axiom,
% 5.80/6.01 ! [X2: list_nat,Y3: list_nat] :
% 5.80/6.01 ( ( ( size_size_list_nat @ X2 )
% 5.80/6.01 != ( size_size_list_nat @ Y3 ) )
% 5.80/6.01 => ( X2 != Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % size_neq_size_imp_neq
% 5.80/6.01 thf(fact_204_size__neq__size__imp__neq,axiom,
% 5.80/6.01 ! [X2: num,Y3: num] :
% 5.80/6.01 ( ( ( size_size_num @ X2 )
% 5.80/6.01 != ( size_size_num @ Y3 ) )
% 5.80/6.01 => ( X2 != Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % size_neq_size_imp_neq
% 5.80/6.01 thf(fact_205_size__neq__size__imp__neq,axiom,
% 5.80/6.01 ! [X2: list_VEBT_VEBTi,Y3: list_VEBT_VEBTi] :
% 5.80/6.01 ( ( ( size_s7982070591426661849_VEBTi @ X2 )
% 5.80/6.01 != ( size_s7982070591426661849_VEBTi @ Y3 ) )
% 5.80/6.01 => ( X2 != Y3 ) ) ).
% 5.80/6.01
% 5.80/6.01 % size_neq_size_imp_neq
% 5.80/6.01 thf(fact_206_neq__if__length__neq,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.80/6.01 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.80/6.01 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.80/6.01 => ( Xs != Ys ) ) ).
% 5.80/6.01
% 5.80/6.01 % neq_if_length_neq
% 5.80/6.01 thf(fact_207_neq__if__length__neq,axiom,
% 5.80/6.01 ! [Xs: list_real,Ys: list_real] :
% 5.80/6.01 ( ( ( size_size_list_real @ Xs )
% 5.80/6.01 != ( size_size_list_real @ Ys ) )
% 5.80/6.01 => ( Xs != Ys ) ) ).
% 5.80/6.01
% 5.80/6.01 % neq_if_length_neq
% 5.80/6.01 thf(fact_208_neq__if__length__neq,axiom,
% 5.80/6.01 ! [Xs: list_o,Ys: list_o] :
% 5.80/6.01 ( ( ( size_size_list_o @ Xs )
% 5.80/6.01 != ( size_size_list_o @ Ys ) )
% 5.80/6.01 => ( Xs != Ys ) ) ).
% 5.80/6.01
% 5.80/6.01 % neq_if_length_neq
% 5.80/6.01 thf(fact_209_neq__if__length__neq,axiom,
% 5.80/6.01 ! [Xs: list_nat,Ys: list_nat] :
% 5.80/6.01 ( ( ( size_size_list_nat @ Xs )
% 5.80/6.01 != ( size_size_list_nat @ Ys ) )
% 5.80/6.01 => ( Xs != Ys ) ) ).
% 5.80/6.01
% 5.80/6.01 % neq_if_length_neq
% 5.80/6.01 thf(fact_210_neq__if__length__neq,axiom,
% 5.80/6.01 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 5.80/6.01 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 5.80/6.01 != ( size_s7982070591426661849_VEBTi @ Ys ) )
% 5.80/6.01 => ( Xs != Ys ) ) ).
% 5.80/6.01
% 5.80/6.01 % neq_if_length_neq
% 5.80/6.01 thf(fact_211_Ex__list__of__length,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ? [Xs3: list_VEBT_VEBT] :
% 5.80/6.01 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.80/6.01 = N ) ).
% 5.80/6.01
% 5.80/6.01 % Ex_list_of_length
% 5.80/6.01 thf(fact_212_Ex__list__of__length,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ? [Xs3: list_real] :
% 5.80/6.01 ( ( size_size_list_real @ Xs3 )
% 5.80/6.01 = N ) ).
% 5.80/6.01
% 5.80/6.01 % Ex_list_of_length
% 5.80/6.01 thf(fact_213_Ex__list__of__length,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ? [Xs3: list_o] :
% 5.80/6.01 ( ( size_size_list_o @ Xs3 )
% 5.80/6.01 = N ) ).
% 5.80/6.01
% 5.80/6.01 % Ex_list_of_length
% 5.80/6.01 thf(fact_214_Ex__list__of__length,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ? [Xs3: list_nat] :
% 5.80/6.01 ( ( size_size_list_nat @ Xs3 )
% 5.80/6.01 = N ) ).
% 5.80/6.01
% 5.80/6.01 % Ex_list_of_length
% 5.80/6.01 thf(fact_215_Ex__list__of__length,axiom,
% 5.80/6.01 ! [N: nat] :
% 5.80/6.01 ? [Xs3: list_VEBT_VEBTi] :
% 5.80/6.01 ( ( size_s7982070591426661849_VEBTi @ Xs3 )
% 5.80/6.01 = N ) ).
% 5.80/6.01
% 5.80/6.01 % Ex_list_of_length
% 5.80/6.01 thf(fact_216_list__update__swap,axiom,
% 5.80/6.01 ! [I: nat,I3: nat,Xs: list_VEBT_VEBTi,X2: vEBT_VEBTi,X5: vEBT_VEBTi] :
% 5.80/6.01 ( ( I != I3 )
% 5.80/6.01 => ( ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) @ I3 @ X5 )
% 5.80/6.01 = ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I3 @ X5 ) @ I @ X2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_swap
% 5.80/6.01 thf(fact_217_list__update__swap,axiom,
% 5.80/6.01 ! [I: nat,I3: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT,X5: vEBT_VEBT] :
% 5.80/6.01 ( ( I != I3 )
% 5.80/6.01 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ I3 @ X5 )
% 5.80/6.01 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X5 ) @ I @ X2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_swap
% 5.80/6.01 thf(fact_218_list__update__swap,axiom,
% 5.80/6.01 ! [I: nat,I3: nat,Xs: list_nat,X2: nat,X5: nat] :
% 5.80/6.01 ( ( I != I3 )
% 5.80/6.01 => ( ( list_update_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ I3 @ X5 )
% 5.80/6.01 = ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X5 ) @ I @ X2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_swap
% 5.80/6.01 thf(fact_219_list__update__swap,axiom,
% 5.80/6.01 ! [I: nat,I3: nat,Xs: list_o,X2: $o,X5: $o] :
% 5.80/6.01 ( ( I != I3 )
% 5.80/6.01 => ( ( list_update_o @ ( list_update_o @ Xs @ I @ X2 ) @ I3 @ X5 )
% 5.80/6.01 = ( list_update_o @ ( list_update_o @ Xs @ I3 @ X5 ) @ I @ X2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_swap
% 5.80/6.01 thf(fact_220_list__update__swap,axiom,
% 5.80/6.01 ! [I: nat,I3: nat,Xs: list_real,X2: real,X5: real] :
% 5.80/6.01 ( ( I != I3 )
% 5.80/6.01 => ( ( list_update_real @ ( list_update_real @ Xs @ I @ X2 ) @ I3 @ X5 )
% 5.80/6.01 = ( list_update_real @ ( list_update_real @ Xs @ I3 @ X5 ) @ I @ X2 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_update_swap
% 5.80/6.01 thf(fact_221_not__less__less__Suc__eq,axiom,
% 5.80/6.01 ! [N: nat,M: nat] :
% 5.80/6.01 ( ~ ( ord_less_nat @ N @ M )
% 5.80/6.01 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.80/6.01 = ( N = M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_less_less_Suc_eq
% 5.80/6.01 thf(fact_222_strict__inc__induct,axiom,
% 5.80/6.01 ! [I: nat,J: nat,P: nat > $o] :
% 5.80/6.01 ( ( ord_less_nat @ I @ J )
% 5.80/6.01 => ( ! [I2: nat] :
% 5.80/6.01 ( ( J
% 5.80/6.01 = ( suc @ I2 ) )
% 5.80/6.01 => ( P @ I2 ) )
% 5.80/6.01 => ( ! [I2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ J )
% 5.80/6.01 => ( ( P @ ( suc @ I2 ) )
% 5.80/6.01 => ( P @ I2 ) ) )
% 5.80/6.01 => ( P @ I ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % strict_inc_induct
% 5.80/6.01 thf(fact_223_less__Suc__induct,axiom,
% 5.80/6.01 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.80/6.01 ( ( ord_less_nat @ I @ J )
% 5.80/6.01 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 5.80/6.01 => ( ! [I2: nat,J2: nat,K2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ J2 )
% 5.80/6.01 => ( ( ord_less_nat @ J2 @ K2 )
% 5.80/6.01 => ( ( P @ I2 @ J2 )
% 5.80/6.01 => ( ( P @ J2 @ K2 )
% 5.80/6.01 => ( P @ I2 @ K2 ) ) ) ) )
% 5.80/6.01 => ( P @ I @ J ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_Suc_induct
% 5.80/6.01 thf(fact_224_less__trans__Suc,axiom,
% 5.80/6.01 ! [I: nat,J: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I @ J )
% 5.80/6.01 => ( ( ord_less_nat @ J @ K )
% 5.80/6.01 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_trans_Suc
% 5.80/6.01 thf(fact_225_Suc__less__SucD,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.80/6.01 => ( ord_less_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_less_SucD
% 5.80/6.01 thf(fact_226_less__antisym,axiom,
% 5.80/6.01 ! [N: nat,M: nat] :
% 5.80/6.01 ( ~ ( ord_less_nat @ N @ M )
% 5.80/6.01 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.80/6.01 => ( M = N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_antisym
% 5.80/6.01 thf(fact_227_Suc__less__eq2,axiom,
% 5.80/6.01 ! [N: nat,M: nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.80/6.01 = ( ? [M7: nat] :
% 5.80/6.01 ( ( M
% 5.80/6.01 = ( suc @ M7 ) )
% 5.80/6.01 & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_less_eq2
% 5.80/6.01 thf(fact_228_Nat_OAll__less__Suc,axiom,
% 5.80/6.01 ! [N: nat,P: nat > $o] :
% 5.80/6.01 ( ( ! [I4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.80/6.01 => ( P @ I4 ) ) )
% 5.80/6.01 = ( ( P @ N )
% 5.80/6.01 & ! [I4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I4 @ N )
% 5.80/6.01 => ( P @ I4 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Nat.All_less_Suc
% 5.80/6.01 thf(fact_229_not__less__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.80/6.01 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % not_less_eq
% 5.80/6.01 thf(fact_230_less__Suc__eq,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.80/6.01 = ( ( ord_less_nat @ M @ N )
% 5.80/6.01 | ( M = N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_Suc_eq
% 5.80/6.01 thf(fact_231_Ex__less__Suc,axiom,
% 5.80/6.01 ! [N: nat,P: nat > $o] :
% 5.80/6.01 ( ( ? [I4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.80/6.01 & ( P @ I4 ) ) )
% 5.80/6.01 = ( ( P @ N )
% 5.80/6.01 | ? [I4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I4 @ N )
% 5.80/6.01 & ( P @ I4 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Ex_less_Suc
% 5.80/6.01 thf(fact_232_less__SucI,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ N )
% 5.80/6.01 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_SucI
% 5.80/6.01 thf(fact_233_less__SucE,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.80/6.01 => ( ~ ( ord_less_nat @ M @ N )
% 5.80/6.01 => ( M = N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % less_SucE
% 5.80/6.01 thf(fact_234_Suc__lessI,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ M @ N )
% 5.80/6.01 => ( ( ( suc @ M )
% 5.80/6.01 != N )
% 5.80/6.01 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_lessI
% 5.80/6.01 thf(fact_235_Suc__lessE,axiom,
% 5.80/6.01 ! [I: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.80/6.01 => ~ ! [J2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I @ J2 )
% 5.80/6.01 => ( K
% 5.80/6.01 != ( suc @ J2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_lessE
% 5.80/6.01 thf(fact_236_Suc__lessD,axiom,
% 5.80/6.01 ! [M: nat,N: nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.80/6.01 => ( ord_less_nat @ M @ N ) ) ).
% 5.80/6.01
% 5.80/6.01 % Suc_lessD
% 5.80/6.01 thf(fact_237_Nat_OlessE,axiom,
% 5.80/6.01 ! [I: nat,K: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I @ K )
% 5.80/6.01 => ( ( K
% 5.80/6.01 != ( suc @ I ) )
% 5.80/6.01 => ~ ! [J2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I @ J2 )
% 5.80/6.01 => ( K
% 5.80/6.01 != ( suc @ J2 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % Nat.lessE
% 5.80/6.01 thf(fact_238_length__induct,axiom,
% 5.80/6.01 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.80/6.01 ( ! [Xs3: list_VEBT_VEBT] :
% 5.80/6.01 ( ! [Ys2: list_VEBT_VEBT] :
% 5.80/6.01 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.80/6.01 => ( P @ Ys2 ) )
% 5.80/6.01 => ( P @ Xs3 ) )
% 5.80/6.01 => ( P @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_induct
% 5.80/6.01 thf(fact_239_length__induct,axiom,
% 5.80/6.01 ! [P: list_real > $o,Xs: list_real] :
% 5.80/6.01 ( ! [Xs3: list_real] :
% 5.80/6.01 ( ! [Ys2: list_real] :
% 5.80/6.01 ( ( ord_less_nat @ ( size_size_list_real @ Ys2 ) @ ( size_size_list_real @ Xs3 ) )
% 5.80/6.01 => ( P @ Ys2 ) )
% 5.80/6.01 => ( P @ Xs3 ) )
% 5.80/6.01 => ( P @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_induct
% 5.80/6.01 thf(fact_240_length__induct,axiom,
% 5.80/6.01 ! [P: list_o > $o,Xs: list_o] :
% 5.80/6.01 ( ! [Xs3: list_o] :
% 5.80/6.01 ( ! [Ys2: list_o] :
% 5.80/6.01 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.80/6.01 => ( P @ Ys2 ) )
% 5.80/6.01 => ( P @ Xs3 ) )
% 5.80/6.01 => ( P @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_induct
% 5.80/6.01 thf(fact_241_length__induct,axiom,
% 5.80/6.01 ! [P: list_nat > $o,Xs: list_nat] :
% 5.80/6.01 ( ! [Xs3: list_nat] :
% 5.80/6.01 ( ! [Ys2: list_nat] :
% 5.80/6.01 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.80/6.01 => ( P @ Ys2 ) )
% 5.80/6.01 => ( P @ Xs3 ) )
% 5.80/6.01 => ( P @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_induct
% 5.80/6.01 thf(fact_242_length__induct,axiom,
% 5.80/6.01 ! [P: list_VEBT_VEBTi > $o,Xs: list_VEBT_VEBTi] :
% 5.80/6.01 ( ! [Xs3: list_VEBT_VEBTi] :
% 5.80/6.01 ( ! [Ys2: list_VEBT_VEBTi] :
% 5.80/6.01 ( ( ord_less_nat @ ( size_s7982070591426661849_VEBTi @ Ys2 ) @ ( size_s7982070591426661849_VEBTi @ Xs3 ) )
% 5.80/6.01 => ( P @ Ys2 ) )
% 5.80/6.01 => ( P @ Xs3 ) )
% 5.80/6.01 => ( P @ Xs ) ) ).
% 5.80/6.01
% 5.80/6.01 % length_induct
% 5.80/6.01 thf(fact_243_combine__options__cases,axiom,
% 5.80/6.01 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 5.80/6.01 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.80/6.01 => ( ( Y3
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % combine_options_cases
% 5.80/6.01 thf(fact_244_combine__options__cases,axiom,
% 5.80/6.01 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y3: option_nat] :
% 5.80/6.01 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ( ( Y3 = none_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ! [A3: product_prod_nat_nat,B3: nat] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.80/6.01 => ( ( Y3
% 5.80/6.01 = ( some_nat @ B3 ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % combine_options_cases
% 5.80/6.01 thf(fact_245_combine__options__cases,axiom,
% 5.80/6.01 ! [X2: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 5.80/6.01 ( ( ( X2 = none_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ! [A3: nat,B3: product_prod_nat_nat] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_nat @ A3 ) )
% 5.80/6.01 => ( ( Y3
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % combine_options_cases
% 5.80/6.01 thf(fact_246_combine__options__cases,axiom,
% 5.80/6.01 ! [X2: option_nat,P: option_nat > option_nat > $o,Y3: option_nat] :
% 5.80/6.01 ( ( ( X2 = none_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ( ( Y3 = none_nat )
% 5.80/6.01 => ( P @ X2 @ Y3 ) )
% 5.80/6.01 => ( ! [A3: nat,B3: nat] :
% 5.80/6.01 ( ( X2
% 5.80/6.01 = ( some_nat @ A3 ) )
% 5.80/6.01 => ( ( Y3
% 5.80/6.01 = ( some_nat @ B3 ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) )
% 5.80/6.01 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % combine_options_cases
% 5.80/6.01 thf(fact_247_split__option__all,axiom,
% 5.80/6.01 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.80/6.01 ! [X6: option4927543243414619207at_nat] : ( P2 @ X6 ) )
% 5.80/6.01 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.80/6.01 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.80/6.01 & ! [X3: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % split_option_all
% 5.80/6.01 thf(fact_248_split__option__all,axiom,
% 5.80/6.01 ( ( ^ [P2: option_nat > $o] :
% 5.80/6.01 ! [X6: option_nat] : ( P2 @ X6 ) )
% 5.80/6.01 = ( ^ [P3: option_nat > $o] :
% 5.80/6.01 ( ( P3 @ none_nat )
% 5.80/6.01 & ! [X3: nat] : ( P3 @ ( some_nat @ X3 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % split_option_all
% 5.80/6.01 thf(fact_249_split__option__ex,axiom,
% 5.80/6.01 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.80/6.01 ? [X6: option4927543243414619207at_nat] : ( P2 @ X6 ) )
% 5.80/6.01 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.80/6.01 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.80/6.01 | ? [X3: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % split_option_ex
% 5.80/6.01 thf(fact_250_split__option__ex,axiom,
% 5.80/6.01 ( ( ^ [P2: option_nat > $o] :
% 5.80/6.01 ? [X6: option_nat] : ( P2 @ X6 ) )
% 5.80/6.01 = ( ^ [P3: option_nat > $o] :
% 5.80/6.01 ( ( P3 @ none_nat )
% 5.80/6.01 | ? [X3: nat] : ( P3 @ ( some_nat @ X3 ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % split_option_ex
% 5.80/6.01 thf(fact_251_option_Oexhaust,axiom,
% 5.80/6.01 ! [Y3: option4927543243414619207at_nat] :
% 5.80/6.01 ( ( Y3 != none_P5556105721700978146at_nat )
% 5.80/6.01 => ~ ! [X23: product_prod_nat_nat] :
% 5.80/6.01 ( Y3
% 5.80/6.01 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.exhaust
% 5.80/6.01 thf(fact_252_option_Oexhaust,axiom,
% 5.80/6.01 ! [Y3: option_nat] :
% 5.80/6.01 ( ( Y3 != none_nat )
% 5.80/6.01 => ~ ! [X23: nat] :
% 5.80/6.01 ( Y3
% 5.80/6.01 != ( some_nat @ X23 ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.exhaust
% 5.80/6.01 thf(fact_253_option_OdiscI,axiom,
% 5.80/6.01 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.80/6.01 ( ( Option
% 5.80/6.01 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.80/6.01 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.discI
% 5.80/6.01 thf(fact_254_option_OdiscI,axiom,
% 5.80/6.01 ! [Option: option_nat,X22: nat] :
% 5.80/6.01 ( ( Option
% 5.80/6.01 = ( some_nat @ X22 ) )
% 5.80/6.01 => ( Option != none_nat ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.discI
% 5.80/6.01 thf(fact_255_option_Odistinct_I1_J,axiom,
% 5.80/6.01 ! [X22: product_prod_nat_nat] :
% 5.80/6.01 ( none_P5556105721700978146at_nat
% 5.80/6.01 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.distinct(1)
% 5.80/6.01 thf(fact_256_option_Odistinct_I1_J,axiom,
% 5.80/6.01 ! [X22: nat] :
% 5.80/6.01 ( none_nat
% 5.80/6.01 != ( some_nat @ X22 ) ) ).
% 5.80/6.01
% 5.80/6.01 % option.distinct(1)
% 5.80/6.01 thf(fact_257_mult__numeral__1__right,axiom,
% 5.80/6.01 ! [A2: complex] :
% 5.80/6.01 ( ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1_right
% 5.80/6.01 thf(fact_258_mult__numeral__1__right,axiom,
% 5.80/6.01 ! [A2: real] :
% 5.80/6.01 ( ( times_times_real @ A2 @ ( numeral_numeral_real @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1_right
% 5.80/6.01 thf(fact_259_mult__numeral__1__right,axiom,
% 5.80/6.01 ! [A2: rat] :
% 5.80/6.01 ( ( times_times_rat @ A2 @ ( numeral_numeral_rat @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1_right
% 5.80/6.01 thf(fact_260_mult__numeral__1__right,axiom,
% 5.80/6.01 ! [A2: nat] :
% 5.80/6.01 ( ( times_times_nat @ A2 @ ( numeral_numeral_nat @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1_right
% 5.80/6.01 thf(fact_261_mult__numeral__1__right,axiom,
% 5.80/6.01 ! [A2: int] :
% 5.80/6.01 ( ( times_times_int @ A2 @ ( numeral_numeral_int @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1_right
% 5.80/6.01 thf(fact_262_mult__numeral__1,axiom,
% 5.80/6.01 ! [A2: complex] :
% 5.80/6.01 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A2 )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1
% 5.80/6.01 thf(fact_263_mult__numeral__1,axiom,
% 5.80/6.01 ! [A2: real] :
% 5.80/6.01 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A2 )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1
% 5.80/6.01 thf(fact_264_mult__numeral__1,axiom,
% 5.80/6.01 ! [A2: rat] :
% 5.80/6.01 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A2 )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1
% 5.80/6.01 thf(fact_265_mult__numeral__1,axiom,
% 5.80/6.01 ! [A2: nat] :
% 5.80/6.01 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A2 )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1
% 5.80/6.01 thf(fact_266_mult__numeral__1,axiom,
% 5.80/6.01 ! [A2: int] :
% 5.80/6.01 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A2 )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % mult_numeral_1
% 5.80/6.01 thf(fact_267_divide__numeral__1,axiom,
% 5.80/6.01 ! [A2: complex] :
% 5.80/6.01 ( ( divide1717551699836669952omplex @ A2 @ ( numera6690914467698888265omplex @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % divide_numeral_1
% 5.80/6.01 thf(fact_268_divide__numeral__1,axiom,
% 5.80/6.01 ! [A2: real] :
% 5.80/6.01 ( ( divide_divide_real @ A2 @ ( numeral_numeral_real @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % divide_numeral_1
% 5.80/6.01 thf(fact_269_divide__numeral__1,axiom,
% 5.80/6.01 ! [A2: rat] :
% 5.80/6.01 ( ( divide_divide_rat @ A2 @ ( numeral_numeral_rat @ one ) )
% 5.80/6.01 = A2 ) ).
% 5.80/6.01
% 5.80/6.01 % divide_numeral_1
% 5.80/6.01 thf(fact_270_lift__Suc__mono__less__iff,axiom,
% 5.80/6.01 ! [F: nat > real,N: nat,M: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.80/6.01 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less_iff
% 5.80/6.01 thf(fact_271_lift__Suc__mono__less__iff,axiom,
% 5.80/6.01 ! [F: nat > rat,N: nat,M: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.80/6.01 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less_iff
% 5.80/6.01 thf(fact_272_lift__Suc__mono__less__iff,axiom,
% 5.80/6.01 ! [F: nat > num,N: nat,M: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.80/6.01 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less_iff
% 5.80/6.01 thf(fact_273_lift__Suc__mono__less__iff,axiom,
% 5.80/6.01 ! [F: nat > nat,N: nat,M: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.80/6.01 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less_iff
% 5.80/6.01 thf(fact_274_lift__Suc__mono__less__iff,axiom,
% 5.80/6.01 ! [F: nat > int,N: nat,M: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.80/6.01 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less_iff
% 5.80/6.01 thf(fact_275_lift__Suc__mono__less,axiom,
% 5.80/6.01 ! [F: nat > real,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_real @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less
% 5.80/6.01 thf(fact_276_lift__Suc__mono__less,axiom,
% 5.80/6.01 ! [F: nat > rat,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_rat @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less
% 5.80/6.01 thf(fact_277_lift__Suc__mono__less,axiom,
% 5.80/6.01 ! [F: nat > num,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_num @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less
% 5.80/6.01 thf(fact_278_lift__Suc__mono__less,axiom,
% 5.80/6.01 ! [F: nat > nat,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_nat @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less
% 5.80/6.01 thf(fact_279_lift__Suc__mono__less,axiom,
% 5.80/6.01 ! [F: nat > int,N: nat,N2: nat] :
% 5.80/6.01 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.80/6.01 => ( ( ord_less_nat @ N @ N2 )
% 5.80/6.01 => ( ord_less_int @ ( F @ N ) @ ( F @ N2 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % lift_Suc_mono_less
% 5.80/6.01 thf(fact_280_obtain__list__from__elements,axiom,
% 5.80/6.01 ! [N: nat,P: vEBT_VEBT > nat > $o] :
% 5.80/6.01 ( ! [I2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ N )
% 5.80/6.01 => ? [Li: vEBT_VEBT] : ( P @ Li @ I2 ) )
% 5.80/6.01 => ~ ! [L2: list_VEBT_VEBT] :
% 5.80/6.01 ( ( ( size_s6755466524823107622T_VEBT @ L2 )
% 5.80/6.01 = N )
% 5.80/6.01 => ~ ! [I5: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I5 @ N )
% 5.80/6.01 => ( P @ ( nth_VEBT_VEBT @ L2 @ I5 ) @ I5 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % obtain_list_from_elements
% 5.80/6.01 thf(fact_281_obtain__list__from__elements,axiom,
% 5.80/6.01 ! [N: nat,P: real > nat > $o] :
% 5.80/6.01 ( ! [I2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ N )
% 5.80/6.01 => ? [Li: real] : ( P @ Li @ I2 ) )
% 5.80/6.01 => ~ ! [L2: list_real] :
% 5.80/6.01 ( ( ( size_size_list_real @ L2 )
% 5.80/6.01 = N )
% 5.80/6.01 => ~ ! [I5: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I5 @ N )
% 5.80/6.01 => ( P @ ( nth_real @ L2 @ I5 ) @ I5 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % obtain_list_from_elements
% 5.80/6.01 thf(fact_282_obtain__list__from__elements,axiom,
% 5.80/6.01 ! [N: nat,P: $o > nat > $o] :
% 5.80/6.01 ( ! [I2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ N )
% 5.80/6.01 => ? [Li: $o] : ( P @ Li @ I2 ) )
% 5.80/6.01 => ~ ! [L2: list_o] :
% 5.80/6.01 ( ( ( size_size_list_o @ L2 )
% 5.80/6.01 = N )
% 5.80/6.01 => ~ ! [I5: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I5 @ N )
% 5.80/6.01 => ( P @ ( nth_o @ L2 @ I5 ) @ I5 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % obtain_list_from_elements
% 5.80/6.01 thf(fact_283_obtain__list__from__elements,axiom,
% 5.80/6.01 ! [N: nat,P: nat > nat > $o] :
% 5.80/6.01 ( ! [I2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ N )
% 5.80/6.01 => ? [Li: nat] : ( P @ Li @ I2 ) )
% 5.80/6.01 => ~ ! [L2: list_nat] :
% 5.80/6.01 ( ( ( size_size_list_nat @ L2 )
% 5.80/6.01 = N )
% 5.80/6.01 => ~ ! [I5: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I5 @ N )
% 5.80/6.01 => ( P @ ( nth_nat @ L2 @ I5 ) @ I5 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % obtain_list_from_elements
% 5.80/6.01 thf(fact_284_obtain__list__from__elements,axiom,
% 5.80/6.01 ! [N: nat,P: vEBT_VEBTi > nat > $o] :
% 5.80/6.01 ( ! [I2: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I2 @ N )
% 5.80/6.01 => ? [Li: vEBT_VEBTi] : ( P @ Li @ I2 ) )
% 5.80/6.01 => ~ ! [L2: list_VEBT_VEBTi] :
% 5.80/6.01 ( ( ( size_s7982070591426661849_VEBTi @ L2 )
% 5.80/6.01 = N )
% 5.80/6.01 => ~ ! [I5: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I5 @ N )
% 5.80/6.01 => ( P @ ( nth_VEBT_VEBTi @ L2 @ I5 ) @ I5 ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % obtain_list_from_elements
% 5.80/6.01 thf(fact_285_list__eq__iff__nth__eq,axiom,
% 5.80/6.01 ( ( ^ [Y6: list_VEBT_VEBT,Z3: list_VEBT_VEBT] : ( Y6 = Z3 ) )
% 5.80/6.01 = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.80/6.01 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.80/6.01 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.80/6.01 & ! [I4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.80/6.01 => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.80/6.01 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.80/6.01
% 5.80/6.01 % list_eq_iff_nth_eq
% 5.80/6.01 thf(fact_286_list__eq__iff__nth__eq,axiom,
% 5.80/6.01 ( ( ^ [Y6: list_real,Z3: list_real] : ( Y6 = Z3 ) )
% 5.80/6.01 = ( ^ [Xs2: list_real,Ys3: list_real] :
% 5.80/6.01 ( ( ( size_size_list_real @ Xs2 )
% 5.80/6.01 = ( size_size_list_real @ Ys3 ) )
% 5.80/6.01 & ! [I4: nat] :
% 5.80/6.01 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.80/6.02 => ( ( nth_real @ Xs2 @ I4 )
% 5.80/6.02 = ( nth_real @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % list_eq_iff_nth_eq
% 5.80/6.02 thf(fact_287_list__eq__iff__nth__eq,axiom,
% 5.80/6.02 ( ( ^ [Y6: list_o,Z3: list_o] : ( Y6 = Z3 ) )
% 5.80/6.02 = ( ^ [Xs2: list_o,Ys3: list_o] :
% 5.80/6.02 ( ( ( size_size_list_o @ Xs2 )
% 5.80/6.02 = ( size_size_list_o @ Ys3 ) )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.80/6.02 => ( ( nth_o @ Xs2 @ I4 )
% 5.80/6.02 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % list_eq_iff_nth_eq
% 5.80/6.02 thf(fact_288_list__eq__iff__nth__eq,axiom,
% 5.80/6.02 ( ( ^ [Y6: list_nat,Z3: list_nat] : ( Y6 = Z3 ) )
% 5.80/6.02 = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 5.80/6.02 ( ( ( size_size_list_nat @ Xs2 )
% 5.80/6.02 = ( size_size_list_nat @ Ys3 ) )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.80/6.02 => ( ( nth_nat @ Xs2 @ I4 )
% 5.80/6.02 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % list_eq_iff_nth_eq
% 5.80/6.02 thf(fact_289_list__eq__iff__nth__eq,axiom,
% 5.80/6.02 ( ( ^ [Y6: list_VEBT_VEBTi,Z3: list_VEBT_VEBTi] : ( Y6 = Z3 ) )
% 5.80/6.02 = ( ^ [Xs2: list_VEBT_VEBTi,Ys3: list_VEBT_VEBTi] :
% 5.80/6.02 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 5.80/6.02 = ( size_s7982070591426661849_VEBTi @ Ys3 ) )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 5.80/6.02 => ( ( nth_VEBT_VEBTi @ Xs2 @ I4 )
% 5.80/6.02 = ( nth_VEBT_VEBTi @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % list_eq_iff_nth_eq
% 5.80/6.02 thf(fact_290_Skolem__list__nth,axiom,
% 5.80/6.02 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.80/6.02 ( ( ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ? [X7: vEBT_VEBT] : ( P @ I4 @ X7 ) ) )
% 5.80/6.02 = ( ? [Xs2: list_VEBT_VEBT] :
% 5.80/6.02 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.80/6.02 = K )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % Skolem_list_nth
% 5.80/6.02 thf(fact_291_Skolem__list__nth,axiom,
% 5.80/6.02 ! [K: nat,P: nat > real > $o] :
% 5.80/6.02 ( ( ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ? [X7: real] : ( P @ I4 @ X7 ) ) )
% 5.80/6.02 = ( ? [Xs2: list_real] :
% 5.80/6.02 ( ( ( size_size_list_real @ Xs2 )
% 5.80/6.02 = K )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ( P @ I4 @ ( nth_real @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % Skolem_list_nth
% 5.80/6.02 thf(fact_292_Skolem__list__nth,axiom,
% 5.80/6.02 ! [K: nat,P: nat > $o > $o] :
% 5.80/6.02 ( ( ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ? [X7: $o] : ( P @ I4 @ X7 ) ) )
% 5.80/6.02 = ( ? [Xs2: list_o] :
% 5.80/6.02 ( ( ( size_size_list_o @ Xs2 )
% 5.80/6.02 = K )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ( P @ I4 @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % Skolem_list_nth
% 5.80/6.02 thf(fact_293_Skolem__list__nth,axiom,
% 5.80/6.02 ! [K: nat,P: nat > nat > $o] :
% 5.80/6.02 ( ( ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ? [X7: nat] : ( P @ I4 @ X7 ) ) )
% 5.80/6.02 = ( ? [Xs2: list_nat] :
% 5.80/6.02 ( ( ( size_size_list_nat @ Xs2 )
% 5.80/6.02 = K )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ( P @ I4 @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % Skolem_list_nth
% 5.80/6.02 thf(fact_294_Skolem__list__nth,axiom,
% 5.80/6.02 ! [K: nat,P: nat > vEBT_VEBTi > $o] :
% 5.80/6.02 ( ( ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ? [X7: vEBT_VEBTi] : ( P @ I4 @ X7 ) ) )
% 5.80/6.02 = ( ? [Xs2: list_VEBT_VEBTi] :
% 5.80/6.02 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 5.80/6.02 = K )
% 5.80/6.02 & ! [I4: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I4 @ K )
% 5.80/6.02 => ( P @ I4 @ ( nth_VEBT_VEBTi @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % Skolem_list_nth
% 5.80/6.02 thf(fact_295_nth__equalityI,axiom,
% 5.80/6.02 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.80/6.02 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.80/6.02 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.80/6.02 => ( ! [I2: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.80/6.02 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.80/6.02 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 5.80/6.02 => ( Xs = Ys ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % nth_equalityI
% 5.80/6.02 thf(fact_296_nth__equalityI,axiom,
% 5.80/6.02 ! [Xs: list_real,Ys: list_real] :
% 5.80/6.02 ( ( ( size_size_list_real @ Xs )
% 5.80/6.02 = ( size_size_list_real @ Ys ) )
% 5.80/6.02 => ( ! [I2: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.80/6.02 => ( ( nth_real @ Xs @ I2 )
% 5.80/6.02 = ( nth_real @ Ys @ I2 ) ) )
% 5.80/6.02 => ( Xs = Ys ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % nth_equalityI
% 5.80/6.02 thf(fact_297_nth__equalityI,axiom,
% 5.80/6.02 ! [Xs: list_o,Ys: list_o] :
% 5.80/6.02 ( ( ( size_size_list_o @ Xs )
% 5.80/6.02 = ( size_size_list_o @ Ys ) )
% 5.80/6.02 => ( ! [I2: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.80/6.02 => ( ( nth_o @ Xs @ I2 )
% 5.80/6.02 = ( nth_o @ Ys @ I2 ) ) )
% 5.80/6.02 => ( Xs = Ys ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % nth_equalityI
% 5.80/6.02 thf(fact_298_nth__equalityI,axiom,
% 5.80/6.02 ! [Xs: list_nat,Ys: list_nat] :
% 5.80/6.02 ( ( ( size_size_list_nat @ Xs )
% 5.80/6.02 = ( size_size_list_nat @ Ys ) )
% 5.80/6.02 => ( ! [I2: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.80/6.02 => ( ( nth_nat @ Xs @ I2 )
% 5.80/6.02 = ( nth_nat @ Ys @ I2 ) ) )
% 5.80/6.02 => ( Xs = Ys ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % nth_equalityI
% 5.80/6.02 thf(fact_299_nth__equalityI,axiom,
% 5.80/6.02 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 5.80/6.02 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 5.80/6.02 = ( size_s7982070591426661849_VEBTi @ Ys ) )
% 5.80/6.02 => ( ! [I2: nat] :
% 5.80/6.02 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.80/6.02 => ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 5.80/6.02 = ( nth_VEBT_VEBTi @ Ys @ I2 ) ) )
% 5.80/6.02 => ( Xs = Ys ) ) ) ).
% 5.80/6.02
% 5.80/6.02 % nth_equalityI
% 5.80/6.02 thf(fact_300_numeral__Bit0__div__2,axiom,
% 5.80/6.02 ! [N: num] :
% 5.80/6.02 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.80/6.02 = ( numeral_numeral_nat @ N ) ) ).
% 5.80/6.02
% 5.80/6.02 % numeral_Bit0_div_2
% 5.80/6.02 thf(fact_301_numeral__Bit0__div__2,axiom,
% 5.80/6.02 ! [N: num] :
% 5.80/6.02 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( numeral_numeral_int @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_Bit0_div_2
% 5.82/6.02 thf(fact_302_list__update__same__conv,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 )
% 5.82/6.02 = Xs )
% 5.82/6.02 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 5.82/6.02 = X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_update_same_conv
% 5.82/6.02 thf(fact_303_list__update__same__conv,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_real,X2: real] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( ( ( list_update_real @ Xs @ I @ X2 )
% 5.82/6.02 = Xs )
% 5.82/6.02 = ( ( nth_real @ Xs @ I )
% 5.82/6.02 = X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_update_same_conv
% 5.82/6.02 thf(fact_304_list__update__same__conv,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_o,X2: $o] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( ( ( list_update_o @ Xs @ I @ X2 )
% 5.82/6.02 = Xs )
% 5.82/6.02 = ( ( nth_o @ Xs @ I )
% 5.82/6.02 = X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_update_same_conv
% 5.82/6.02 thf(fact_305_list__update__same__conv,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_nat,X2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( ( ( list_update_nat @ Xs @ I @ X2 )
% 5.82/6.02 = Xs )
% 5.82/6.02 = ( ( nth_nat @ Xs @ I )
% 5.82/6.02 = X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_update_same_conv
% 5.82/6.02 thf(fact_306_list__update__same__conv,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 )
% 5.82/6.02 = Xs )
% 5.82/6.02 = ( ( nth_VEBT_VEBTi @ Xs @ I )
% 5.82/6.02 = X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_update_same_conv
% 5.82/6.02 thf(fact_307_nth__list__update_H,axiom,
% 5.82/6.02 ! [I: nat,J: nat,L: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.02 ( ( ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 5.82/6.02 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ~ ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 5.82/6.02 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_VEBT_VEBT @ L @ J ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update'
% 5.82/6.02 thf(fact_308_nth__list__update_H,axiom,
% 5.82/6.02 ! [I: nat,J: nat,L: list_real,X2: real] :
% 5.82/6.02 ( ( ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 5.82/6.02 => ( ( nth_real @ ( list_update_real @ L @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ~ ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 5.82/6.02 => ( ( nth_real @ ( list_update_real @ L @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_real @ L @ J ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update'
% 5.82/6.02 thf(fact_309_nth__list__update_H,axiom,
% 5.82/6.02 ! [L: list_o,I: nat,X2: $o,J: nat] :
% 5.82/6.02 ( ( nth_o @ ( list_update_o @ L @ I @ X2 ) @ J )
% 5.82/6.02 = ( ( ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 5.82/6.02 => X2 )
% 5.82/6.02 & ( ~ ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 5.82/6.02 => ( nth_o @ L @ J ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update'
% 5.82/6.02 thf(fact_310_nth__list__update_H,axiom,
% 5.82/6.02 ! [I: nat,J: nat,L: list_nat,X2: nat] :
% 5.82/6.02 ( ( ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 5.82/6.02 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ~ ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 5.82/6.02 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_nat @ L @ J ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update'
% 5.82/6.02 thf(fact_311_nth__list__update_H,axiom,
% 5.82/6.02 ! [I: nat,J: nat,L: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.82/6.02 ( ( ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 5.82/6.02 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ~ ( ( I = J )
% 5.82/6.02 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 5.82/6.02 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_VEBT_VEBTi @ L @ J ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update'
% 5.82/6.02 thf(fact_312_nth__list__update,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( ( ( I = J )
% 5.82/6.02 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ( I != J )
% 5.82/6.02 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update
% 5.82/6.02 thf(fact_313_nth__list__update,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_real,J: nat,X2: real] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( ( ( I = J )
% 5.82/6.02 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ( I != J )
% 5.82/6.02 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_real @ Xs @ J ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update
% 5.82/6.02 thf(fact_314_nth__list__update,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_o,X2: $o,J: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = ( ( ( I = J )
% 5.82/6.02 => X2 )
% 5.82/6.02 & ( ( I != J )
% 5.82/6.02 => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update
% 5.82/6.02 thf(fact_315_nth__list__update,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_nat,J: nat,X2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( ( ( I = J )
% 5.82/6.02 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ( I != J )
% 5.82/6.02 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update
% 5.82/6.02 thf(fact_316_nth__list__update,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat,X2: vEBT_VEBTi] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( ( ( I = J )
% 5.82/6.02 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = X2 ) )
% 5.82/6.02 & ( ( I != J )
% 5.82/6.02 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) @ J )
% 5.82/6.02 = ( nth_VEBT_VEBTi @ Xs @ J ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_list_update
% 5.82/6.02 thf(fact_317_highbound,axiom,
% 5.82/6.02 ( ( ma != mi )
% 5.82/6.02 => ( ( ord_less_eq_nat @ xa @ ma )
% 5.82/6.02 => ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % highbound
% 5.82/6.02 thf(fact_318_xbound,axiom,
% 5.82/6.02 ( ( ord_less_eq_nat @ mi @ xa )
% 5.82/6.02 => ( ( ord_less_eq_nat @ xa @ ma )
% 5.82/6.02 => ( ord_less_eq_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % xbound
% 5.82/6.02 thf(fact_319_member__inv,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 & ( ( X2 = Mi )
% 5.82/6.02 | ( X2 = Ma )
% 5.82/6.02 | ( ( ord_less_nat @ X2 @ Ma )
% 5.82/6.02 & ( ord_less_nat @ Mi @ X2 )
% 5.82/6.02 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.02 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % member_inv
% 5.82/6.02 thf(fact_320_succ__list__to__short,axiom,
% 5.82/6.02 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.02 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = none_nat ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % succ_list_to_short
% 5.82/6.02 thf(fact_321_pred__list__to__short,axiom,
% 5.82/6.02 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.02 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = none_nat ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % pred_list_to_short
% 5.82/6.02 thf(fact_322_insert__simp__mima,axiom,
% 5.82/6.02 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ( X2 = Mi )
% 5.82/6.02 | ( X2 = Ma ) )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % insert_simp_mima
% 5.82/6.02 thf(fact_323_succ__min,axiom,
% 5.82/6.02 ! [Deg: nat,X2: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.02 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( some_nat @ Mi ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % succ_min
% 5.82/6.02 thf(fact_324_pred__max,axiom,
% 5.82/6.02 ! [Deg: nat,Ma: nat,X2: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( ord_less_nat @ Ma @ X2 )
% 5.82/6.02 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( some_nat @ Ma ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % pred_max
% 5.82/6.02 thf(fact_325_highboundn,axiom,
% 5.82/6.02 ( ( ma != mi )
% 5.82/6.02 => ( ( ord_less_eq_nat @ xa @ ma )
% 5.82/6.02 => ( ord_less_nat @ ( vEBT_VEBT_high @ xnew @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % highboundn
% 5.82/6.02 thf(fact_326_less__option__None__Some__code,axiom,
% 5.82/6.02 ! [X2: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_None_Some_code
% 5.82/6.02 thf(fact_327_enat__ord__number_I2_J,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.82/6.02 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % enat_ord_number(2)
% 5.82/6.02 thf(fact_328_less__option__Some,axiom,
% 5.82/6.02 ! [X2: real,Y3: real] :
% 5.82/6.02 ( ( ord_less_option_real @ ( some_real @ X2 ) @ ( some_real @ Y3 ) )
% 5.82/6.02 = ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_Some
% 5.82/6.02 thf(fact_329_less__option__Some,axiom,
% 5.82/6.02 ! [X2: rat,Y3: rat] :
% 5.82/6.02 ( ( ord_less_option_rat @ ( some_rat @ X2 ) @ ( some_rat @ Y3 ) )
% 5.82/6.02 = ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_Some
% 5.82/6.02 thf(fact_330_less__option__Some,axiom,
% 5.82/6.02 ! [X2: num,Y3: num] :
% 5.82/6.02 ( ( ord_less_option_num @ ( some_num @ X2 ) @ ( some_num @ Y3 ) )
% 5.82/6.02 = ( ord_less_num @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_Some
% 5.82/6.02 thf(fact_331_less__option__Some,axiom,
% 5.82/6.02 ! [X2: nat,Y3: nat] :
% 5.82/6.02 ( ( ord_less_option_nat @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.82/6.02 = ( ord_less_nat @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_Some
% 5.82/6.02 thf(fact_332_less__option__Some,axiom,
% 5.82/6.02 ! [X2: int,Y3: int] :
% 5.82/6.02 ( ( ord_less_option_int @ ( some_int @ X2 ) @ ( some_int @ Y3 ) )
% 5.82/6.02 = ( ord_less_int @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_Some
% 5.82/6.02 thf(fact_333_min__Null__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ( ( vEBT_VEBT_minNull @ T )
% 5.82/6.02 => ~ ( vEBT_vebt_member @ T @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % min_Null_member
% 5.82/6.02 thf(fact_334_less__eq__option__None__code,axiom,
% 5.82/6.02 ! [X2: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X2 ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_None_code
% 5.82/6.02 thf(fact_335_less__option__None,axiom,
% 5.82/6.02 ! [X2: option_nat] :
% 5.82/6.02 ~ ( ord_less_option_nat @ X2 @ none_nat ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_None
% 5.82/6.02 thf(fact_336_enat__ord__number_I1_J,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.82/6.02 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % enat_ord_number(1)
% 5.82/6.02 thf(fact_337_less__eq__option__Some,axiom,
% 5.82/6.02 ! [X2: set_int,Y3: set_int] :
% 5.82/6.02 ( ( ord_le353528952715127954et_int @ ( some_set_int @ X2 ) @ ( some_set_int @ Y3 ) )
% 5.82/6.02 = ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_Some
% 5.82/6.02 thf(fact_338_less__eq__option__Some,axiom,
% 5.82/6.02 ! [X2: rat,Y3: rat] :
% 5.82/6.02 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X2 ) @ ( some_rat @ Y3 ) )
% 5.82/6.02 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_Some
% 5.82/6.02 thf(fact_339_less__eq__option__Some,axiom,
% 5.82/6.02 ! [X2: num,Y3: num] :
% 5.82/6.02 ( ( ord_le6622620407824499402on_num @ ( some_num @ X2 ) @ ( some_num @ Y3 ) )
% 5.82/6.02 = ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_Some
% 5.82/6.02 thf(fact_340_less__eq__option__Some,axiom,
% 5.82/6.02 ! [X2: nat,Y3: nat] :
% 5.82/6.02 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.82/6.02 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_Some
% 5.82/6.02 thf(fact_341_less__eq__option__Some,axiom,
% 5.82/6.02 ! [X2: int,Y3: int] :
% 5.82/6.02 ( ( ord_le1736525451366464988on_int @ ( some_int @ X2 ) @ ( some_int @ Y3 ) )
% 5.82/6.02 = ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_Some
% 5.82/6.02 thf(fact_342_less__eq__option__Some__None,axiom,
% 5.82/6.02 ! [X2: nat] :
% 5.82/6.02 ~ ( ord_le5914376470875661696on_nat @ ( some_nat @ X2 ) @ none_nat ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_Some_None
% 5.82/6.02 thf(fact_343__C7_Oprems_C,axiom,
% 5.82/6.02 vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ treeList @ summary ) @ na ).
% 5.82/6.02
% 5.82/6.02 % "7.prems"
% 5.82/6.02 thf(fact_344_enat__less__induct,axiom,
% 5.82/6.02 ! [P: extended_enat > $o,N: extended_enat] :
% 5.82/6.02 ( ! [N3: extended_enat] :
% 5.82/6.02 ( ! [M3: extended_enat] :
% 5.82/6.02 ( ( ord_le72135733267957522d_enat @ M3 @ N3 )
% 5.82/6.02 => ( P @ M3 ) )
% 5.82/6.02 => ( P @ N3 ) )
% 5.82/6.02 => ( P @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % enat_less_induct
% 5.82/6.02 thf(fact_345_less__eq__option__None,axiom,
% 5.82/6.02 ! [X2: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X2 ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_None
% 5.82/6.02 thf(fact_346_less__eq__option__None__is__None,axiom,
% 5.82/6.02 ! [X2: option_nat] :
% 5.82/6.02 ( ( ord_le5914376470875661696on_nat @ X2 @ none_nat )
% 5.82/6.02 => ( X2 = none_nat ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_eq_option_None_is_None
% 5.82/6.02 thf(fact_347_le__num__One__iff,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_less_eq_num @ X2 @ one )
% 5.82/6.02 = ( X2 = one ) ) ).
% 5.82/6.02
% 5.82/6.02 % le_num_One_iff
% 5.82/6.02 thf(fact_348_less__option__None__Some,axiom,
% 5.82/6.02 ! [X2: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_None_Some
% 5.82/6.02 thf(fact_349_less__option__None__is__Some,axiom,
% 5.82/6.02 ! [X2: option_nat] :
% 5.82/6.02 ( ( ord_less_option_nat @ none_nat @ X2 )
% 5.82/6.02 => ? [Z2: nat] :
% 5.82/6.02 ( X2
% 5.82/6.02 = ( some_nat @ Z2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_option_None_is_Some
% 5.82/6.02 thf(fact_350_vebt__member_Osimps_I5_J,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( ( X2 != Mi )
% 5.82/6.02 => ( ( X2 != Ma )
% 5.82/6.02 => ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.82/6.02 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.82/6.02 => ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.82/6.02 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.82/6.02 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.02 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.02 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % vebt_member.simps(5)
% 5.82/6.02 thf(fact_351_insert__simp__excp,axiom,
% 5.82/6.02 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.02 => ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( X2 != Ma )
% 5.82/6.02 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % insert_simp_excp
% 5.82/6.02 thf(fact_352_insert__simp__norm,axiom,
% 5.82/6.02 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.02 => ( ( ord_less_nat @ Mi @ X2 )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.02 => ( ( X2 != Ma )
% 5.82/6.02 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X2 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % insert_simp_norm
% 5.82/6.02 thf(fact_353_semiring__norm_I69_J,axiom,
% 5.82/6.02 ! [M: num] :
% 5.82/6.02 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(69)
% 5.82/6.02 thf(fact_354_semiring__norm_I76_J,axiom,
% 5.82/6.02 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(76)
% 5.82/6.02 thf(fact_355_mimaxprop,axiom,
% 5.82/6.02 ( ( ord_less_eq_nat @ mi @ ma )
% 5.82/6.02 & ( ord_less_eq_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mimaxprop
% 5.82/6.02 thf(fact_356_vebt__insert_Osimps_I4_J,axiom,
% 5.82/6.02 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.82/6.02
% 5.82/6.02 % vebt_insert.simps(4)
% 5.82/6.02 thf(fact_357_semiring__norm_I68_J,axiom,
% 5.82/6.02 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(68)
% 5.82/6.02 thf(fact_358_semiring__norm_I75_J,axiom,
% 5.82/6.02 ! [M: num] :
% 5.82/6.02 ~ ( ord_less_num @ M @ one ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(75)
% 5.82/6.02 thf(fact_359_semiring__norm_I71_J,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.82/6.02 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(71)
% 5.82/6.02 thf(fact_360_semiring__norm_I78_J,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.82/6.02 = ( ord_less_num @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(78)
% 5.82/6.02 thf(fact_361_deg__deg__n,axiom,
% 5.82/6.02 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.02 => ( Deg = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % deg_deg_n
% 5.82/6.02 thf(fact_362_delete__pres__valid,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X2 ) @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % delete_pres_valid
% 5.82/6.02 thf(fact_363_deg__SUcn__Node,axiom,
% 5.82/6.02 ! [Tree: vEBT_VEBT,N: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.82/6.02 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.02 ( Tree
% 5.82/6.02 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S3 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % deg_SUcn_Node
% 5.82/6.02 thf(fact_364_dele__member__cont__corr,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X2 ) @ Y3 )
% 5.82/6.02 = ( ( X2 != Y3 )
% 5.82/6.02 & ( vEBT_vebt_member @ T @ Y3 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % dele_member_cont_corr
% 5.82/6.02 thf(fact_365_power__shift,axiom,
% 5.82/6.02 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.02 ( ( ( power_power_nat @ X2 @ Y3 )
% 5.82/6.02 = Z )
% 5.82/6.02 = ( ( vEBT_VEBT_power @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.82/6.02 = ( some_nat @ Z ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_shift
% 5.82/6.02 thf(fact_366_mint__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_mint @ T )
% 5.82/6.02 = ( some_nat @ Maxi ) )
% 5.82/6.02 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mint_member
% 5.82/6.02 thf(fact_367_semiring__norm_I87_J,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( ( bit0 @ M )
% 5.82/6.02 = ( bit0 @ N ) )
% 5.82/6.02 = ( M = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(87)
% 5.82/6.02 thf(fact_368_mint__corr__help,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,Mini: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_mint @ T )
% 5.82/6.02 = ( some_nat @ Mini ) )
% 5.82/6.02 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.82/6.02 => ( ord_less_eq_nat @ Mini @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mint_corr_help
% 5.82/6.02 thf(fact_369_mulcomm,axiom,
% 5.82/6.02 ! [I: nat,Va: nat] :
% 5.82/6.02 ( ( times_times_nat @ I @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.02 = ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ I ) ) ).
% 5.82/6.02
% 5.82/6.02 % mulcomm
% 5.82/6.02 thf(fact_370_high__def,axiom,
% 5.82/6.02 ( vEBT_VEBT_high
% 5.82/6.02 = ( ^ [X3: nat,N4: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % high_def
% 5.82/6.02 thf(fact_371_member__bound,axiom,
% 5.82/6.02 ! [Tree: vEBT_VEBT,X2: nat,N: nat] :
% 5.82/6.02 ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.82/6.02 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.82/6.02 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % member_bound
% 5.82/6.02 thf(fact_372_geqmaxNone,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.02 => ( ( ord_less_eq_nat @ Ma @ X2 )
% 5.82/6.02 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = none_nat ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % geqmaxNone
% 5.82/6.02 thf(fact_373_semiring__norm_I83_J,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( one
% 5.82/6.02 != ( bit0 @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(83)
% 5.82/6.02 thf(fact_374_semiring__norm_I85_J,axiom,
% 5.82/6.02 ! [M: num] :
% 5.82/6.02 ( ( bit0 @ M )
% 5.82/6.02 != one ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(85)
% 5.82/6.02 thf(fact_375_misiz,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( some_nat @ M )
% 5.82/6.02 = ( vEBT_vebt_mint @ T ) )
% 5.82/6.02 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % misiz
% 5.82/6.02 thf(fact_376_helpypredd,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.82/6.02 = ( some_nat @ Y3 ) )
% 5.82/6.02 => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % helpypredd
% 5.82/6.02 thf(fact_377_helpyd,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.82/6.02 = ( some_nat @ Y3 ) )
% 5.82/6.02 => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % helpyd
% 5.82/6.02 thf(fact_378_post__member__pre__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X2 ) @ Y3 )
% 5.82/6.02 => ( ( vEBT_vebt_member @ T @ Y3 )
% 5.82/6.02 | ( X2 = Y3 ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % post_member_pre_member
% 5.82/6.02 thf(fact_379_max__Suc__Suc,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.82/6.02 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_Suc_Suc
% 5.82/6.02 thf(fact_380_semiring__norm_I13_J,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.82/6.02 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(13)
% 5.82/6.02 thf(fact_381_semiring__norm_I11_J,axiom,
% 5.82/6.02 ! [M: num] :
% 5.82/6.02 ( ( times_times_num @ M @ one )
% 5.82/6.02 = M ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(11)
% 5.82/6.02 thf(fact_382_semiring__norm_I12_J,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( times_times_num @ one @ N )
% 5.82/6.02 = N ) ).
% 5.82/6.02
% 5.82/6.02 % semiring_norm(12)
% 5.82/6.02 thf(fact_383_mi__ma__2__deg,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.02 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.82/6.02 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mi_ma_2_deg
% 5.82/6.02 thf(fact_384_member__correct,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.82/6.02 = ( member_nat @ X2 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % member_correct
% 5.82/6.02 thf(fact_385_max__number__of_I1_J,axiom,
% 5.82/6.02 ! [U: num,V: num] :
% 5.82/6.02 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.82/6.02 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.82/6.02 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.82/6.02 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.82/6.02 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.82/6.02 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_number_of(1)
% 5.82/6.02 thf(fact_386_max__number__of_I1_J,axiom,
% 5.82/6.02 ! [U: num,V: num] :
% 5.82/6.02 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.82/6.02 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.82/6.02 = ( numeral_numeral_real @ V ) ) )
% 5.82/6.02 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.82/6.02 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.82/6.02 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_number_of(1)
% 5.82/6.02 thf(fact_387_max__number__of_I1_J,axiom,
% 5.82/6.02 ! [U: num,V: num] :
% 5.82/6.02 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.82/6.02 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.82/6.02 = ( numeral_numeral_rat @ V ) ) )
% 5.82/6.02 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.82/6.02 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.82/6.02 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_number_of(1)
% 5.82/6.02 thf(fact_388_max__number__of_I1_J,axiom,
% 5.82/6.02 ! [U: num,V: num] :
% 5.82/6.02 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.02 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.02 = ( numeral_numeral_nat @ V ) ) )
% 5.82/6.02 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.02 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.02 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_number_of(1)
% 5.82/6.02 thf(fact_389_max__number__of_I1_J,axiom,
% 5.82/6.02 ! [U: num,V: num] :
% 5.82/6.02 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.02 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.02 = ( numeral_numeral_int @ V ) ) )
% 5.82/6.02 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.02 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.02 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_number_of(1)
% 5.82/6.02 thf(fact_390_nat__mult__max__right,axiom,
% 5.82/6.02 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.02 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 5.82/6.02 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_mult_max_right
% 5.82/6.02 thf(fact_391_nat__mult__max__left,axiom,
% 5.82/6.02 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.02 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 5.82/6.02 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_mult_max_left
% 5.82/6.02 thf(fact_392_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.82/6.02 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.82/6.02 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.82/6.02
% 5.82/6.02 % VEBT_internal.minNull.simps(5)
% 5.82/6.02 thf(fact_393_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.82/6.02 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.82/6.02
% 5.82/6.02 % VEBT_internal.minNull.simps(4)
% 5.82/6.02 thf(fact_394_vebt__member_Osimps_I2_J,axiom,
% 5.82/6.02 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 ) ).
% 5.82/6.02
% 5.82/6.02 % vebt_member.simps(2)
% 5.82/6.02 thf(fact_395_vebt__insert_Osimps_I5_J,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 = ( if_VEBT_VEBT
% 5.82/6.02 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.02 & ~ ( ( X2 = Mi )
% 5.82/6.02 | ( X2 = Ma ) ) )
% 5.82/6.02 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ X2 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.82/6.02 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % vebt_insert.simps(5)
% 5.82/6.02 thf(fact_396_mint__corr,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_mint @ T )
% 5.82/6.02 = ( some_nat @ X2 ) )
% 5.82/6.02 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mint_corr
% 5.82/6.02 thf(fact_397_mint__sound,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.82/6.02 => ( ( vEBT_vebt_mint @ T )
% 5.82/6.02 = ( some_nat @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mint_sound
% 5.82/6.02 thf(fact_398_mintlistlength,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.02 => ( ( Mi != Ma )
% 5.82/6.02 => ( ( ord_less_nat @ Mi @ Ma )
% 5.82/6.02 & ? [M5: nat] :
% 5.82/6.02 ( ( ( some_nat @ M5 )
% 5.82/6.02 = ( vEBT_vebt_mint @ Summary ) )
% 5.82/6.02 & ( ord_less_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mintlistlength
% 5.82/6.02 thf(fact_399_power__mult__numeral,axiom,
% 5.82/6.02 ! [A2: nat,M: num,N: num] :
% 5.82/6.02 ( ( power_power_nat @ ( power_power_nat @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_numeral
% 5.82/6.02 thf(fact_400_power__mult__numeral,axiom,
% 5.82/6.02 ! [A2: real,M: num,N: num] :
% 5.82/6.02 ( ( power_power_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_numeral
% 5.82/6.02 thf(fact_401_power__mult__numeral,axiom,
% 5.82/6.02 ! [A2: int,M: num,N: num] :
% 5.82/6.02 ( ( power_power_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_numeral
% 5.82/6.02 thf(fact_402_power__mult__numeral,axiom,
% 5.82/6.02 ! [A2: complex,M: num,N: num] :
% 5.82/6.02 ( ( power_power_complex @ ( power_power_complex @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_numeral
% 5.82/6.02 thf(fact_403_power__mult__numeral,axiom,
% 5.82/6.02 ! [A2: code_integer,M: num,N: num] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_numeral
% 5.82/6.02 thf(fact_404_listlength,axiom,
% 5.82/6.02 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.82/6.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ na @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % listlength
% 5.82/6.02 thf(fact_405_two__pow__div__gt__le,axiom,
% 5.82/6.02 ! [V: nat,N: nat,M: nat] :
% 5.82/6.02 ( ( 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 ) ) )
% 5.82/6.02 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % two_pow_div_gt_le
% 5.82/6.02 thf(fact_406_sumprop,axiom,
% 5.82/6.02 vEBT_invar_vebt @ summary @ ( minus_minus_nat @ na @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % sumprop
% 5.82/6.02 thf(fact_407_power__odd__eq,axiom,
% 5.82/6.02 ! [A2: complex,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.02 = ( times_times_complex @ A2 @ ( power_power_complex @ ( power_power_complex @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_odd_eq
% 5.82/6.02 thf(fact_408_power__odd__eq,axiom,
% 5.82/6.02 ! [A2: code_integer,N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.02 = ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_odd_eq
% 5.82/6.02 thf(fact_409_power__odd__eq,axiom,
% 5.82/6.02 ! [A2: real,N: nat] :
% 5.82/6.02 ( ( power_power_real @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.02 = ( times_times_real @ A2 @ ( power_power_real @ ( power_power_real @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_odd_eq
% 5.82/6.02 thf(fact_410_power__odd__eq,axiom,
% 5.82/6.02 ! [A2: rat,N: nat] :
% 5.82/6.02 ( ( power_power_rat @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.02 = ( times_times_rat @ A2 @ ( power_power_rat @ ( power_power_rat @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_odd_eq
% 5.82/6.02 thf(fact_411_power__odd__eq,axiom,
% 5.82/6.02 ! [A2: nat,N: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.02 = ( times_times_nat @ A2 @ ( power_power_nat @ ( power_power_nat @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_odd_eq
% 5.82/6.02 thf(fact_412_power__odd__eq,axiom,
% 5.82/6.02 ! [A2: int,N: nat] :
% 5.82/6.02 ( ( power_power_int @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.02 = ( times_times_int @ A2 @ ( power_power_int @ ( power_power_int @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_odd_eq
% 5.82/6.02 thf(fact_413_two__powr__height__bound__deg,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % two_powr_height_bound_deg
% 5.82/6.02 thf(fact_414_both__member__options__ding,axiom,
% 5.82/6.02 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.02 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % both_member_options_ding
% 5.82/6.02 thf(fact_415_setprop,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.82/6.02 => ( vEBT_invar_vebt @ T @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % setprop
% 5.82/6.02 thf(fact_416_not__min__Null__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT] :
% 5.82/6.02 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.82/6.02 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.82/6.02
% 5.82/6.02 % not_min_Null_member
% 5.82/6.02 thf(fact_417_set__vebt_H__def,axiom,
% 5.82/6.02 ( vEBT_VEBT_set_vebt
% 5.82/6.02 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_vebt'_def
% 5.82/6.02 thf(fact_418_dele__bmo__cont__corr,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X2 ) @ Y3 )
% 5.82/6.02 = ( ( X2 != Y3 )
% 5.82/6.02 & ( vEBT_V8194947554948674370ptions @ T @ Y3 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % dele_bmo_cont_corr
% 5.82/6.02 thf(fact_419_valid__member__both__member__options,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.82/6.02 => ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % valid_member_both_member_options
% 5.82/6.02 thf(fact_420_both__member__options__equiv__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.82/6.02 = ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % both_member_options_equiv_member
% 5.82/6.02 thf(fact_421_set__vebt__set__vebt_H__valid,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( vEBT_set_vebt @ T )
% 5.82/6.02 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_vebt_set_vebt'_valid
% 5.82/6.02 thf(fact_422_inthall,axiom,
% 5.82/6.02 ! [Xs: list_int,P: int > $o,N: nat] :
% 5.82/6.02 ( ! [X4: int] :
% 5.82/6.02 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % inthall
% 5.82/6.02 thf(fact_423_inthall,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.82/6.02 ( ! [X4: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % inthall
% 5.82/6.02 thf(fact_424_inthall,axiom,
% 5.82/6.02 ! [Xs: list_real,P: real > $o,N: nat] :
% 5.82/6.02 ( ! [X4: real] :
% 5.82/6.02 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % inthall
% 5.82/6.02 thf(fact_425_inthall,axiom,
% 5.82/6.02 ! [Xs: list_o,P: $o > $o,N: nat] :
% 5.82/6.02 ( ! [X4: $o] :
% 5.82/6.02 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % inthall
% 5.82/6.02 thf(fact_426_inthall,axiom,
% 5.82/6.02 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 5.82/6.02 ( ! [X4: nat] :
% 5.82/6.02 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % inthall
% 5.82/6.02 thf(fact_427_inthall,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBTi,P: vEBT_VEBTi > $o,N: nat] :
% 5.82/6.02 ( ! [X4: vEBT_VEBTi] :
% 5.82/6.02 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % inthall
% 5.82/6.02 thf(fact_428_mi__eq__ma__no__ch,axiom,
% 5.82/6.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.82/6.02 => ( ( Mi = Ma )
% 5.82/6.02 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.02 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X8 @ X_12 ) )
% 5.82/6.02 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mi_eq_ma_no_ch
% 5.82/6.02 thf(fact_429_diff__Suc__Suc,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.82/6.02 = ( minus_minus_nat @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_Suc_Suc
% 5.82/6.02 thf(fact_430_Suc__diff__diff,axiom,
% 5.82/6.02 ! [M: nat,N: nat,K: nat] :
% 5.82/6.02 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.82/6.02 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.82/6.02
% 5.82/6.02 % Suc_diff_diff
% 5.82/6.02 thf(fact_431_valid__insert__both__member__options__add,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X2 ) @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % valid_insert_both_member_options_add
% 5.82/6.02 thf(fact_432_valid__insert__both__member__options__pres,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.82/6.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y3 ) @ X2 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % valid_insert_both_member_options_pres
% 5.82/6.02 thf(fact_433_diff__diff__cancel,axiom,
% 5.82/6.02 ! [I: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ I @ N )
% 5.82/6.02 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.82/6.02 = I ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_diff_cancel
% 5.82/6.02 thf(fact_434_left__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [A2: complex,B2: complex,V: num] :
% 5.82/6.02 ( ( times_times_complex @ ( minus_minus_complex @ A2 @ B2 ) @ ( numera6690914467698888265omplex @ V ) )
% 5.82/6.02 = ( minus_minus_complex @ ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B2 @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % left_diff_distrib_numeral
% 5.82/6.02 thf(fact_435_left__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [A2: real,B2: real,V: num] :
% 5.82/6.02 ( ( times_times_real @ ( minus_minus_real @ A2 @ B2 ) @ ( numeral_numeral_real @ V ) )
% 5.82/6.02 = ( minus_minus_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B2 @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % left_diff_distrib_numeral
% 5.82/6.02 thf(fact_436_left__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [A2: rat,B2: rat,V: num] :
% 5.82/6.02 ( ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ ( numeral_numeral_rat @ V ) )
% 5.82/6.02 = ( minus_minus_rat @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B2 @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % left_diff_distrib_numeral
% 5.82/6.02 thf(fact_437_left__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [A2: int,B2: int,V: num] :
% 5.82/6.02 ( ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.02 = ( minus_minus_int @ ( times_times_int @ A2 @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B2 @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % left_diff_distrib_numeral
% 5.82/6.02 thf(fact_438_right__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: complex,C2: complex] :
% 5.82/6.02 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B2 @ C2 ) )
% 5.82/6.02 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % right_diff_distrib_numeral
% 5.82/6.02 thf(fact_439_right__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: real,C2: real] :
% 5.82/6.02 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B2 @ C2 ) )
% 5.82/6.02 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B2 ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % right_diff_distrib_numeral
% 5.82/6.02 thf(fact_440_right__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: rat,C2: rat] :
% 5.82/6.02 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B2 @ C2 ) )
% 5.82/6.02 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % right_diff_distrib_numeral
% 5.82/6.02 thf(fact_441_right__diff__distrib__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: int,C2: int] :
% 5.82/6.02 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B2 @ C2 ) )
% 5.82/6.02 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % right_diff_distrib_numeral
% 5.82/6.02 thf(fact_442_set__swap,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 5.82/6.02 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_swap
% 5.82/6.02 thf(fact_443_set__swap,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_real,J: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( ( set_real2 @ ( list_update_real @ ( list_update_real @ Xs @ I @ ( nth_real @ Xs @ J ) ) @ J @ ( nth_real @ Xs @ I ) ) )
% 5.82/6.02 = ( set_real2 @ Xs ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_swap
% 5.82/6.02 thf(fact_444_set__swap,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_o,J: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 5.82/6.02 = ( set_o2 @ Xs ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_swap
% 5.82/6.02 thf(fact_445_set__swap,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_nat,J: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 5.82/6.02 = ( set_nat2 @ Xs ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_swap
% 5.82/6.02 thf(fact_446_set__swap,axiom,
% 5.82/6.02 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ ( nth_VEBT_VEBTi @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBTi @ Xs @ I ) ) )
% 5.82/6.02 = ( set_VEBT_VEBTi2 @ Xs ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_swap
% 5.82/6.02 thf(fact_447_succ__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y3 )
% 5.82/6.02 = ( ( vEBT_vebt_member @ T @ Y3 )
% 5.82/6.02 & ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.02 & ! [Z4: nat] :
% 5.82/6.02 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.82/6.02 & ( ord_less_nat @ X2 @ Z4 ) )
% 5.82/6.02 => ( ord_less_eq_nat @ Y3 @ Z4 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % succ_member
% 5.82/6.02 thf(fact_448_pred__member,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y3 )
% 5.82/6.02 = ( ( vEBT_vebt_member @ T @ Y3 )
% 5.82/6.02 & ( ord_less_nat @ Y3 @ X2 )
% 5.82/6.02 & ! [Z4: nat] :
% 5.82/6.02 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.82/6.02 & ( ord_less_nat @ Z4 @ X2 ) )
% 5.82/6.02 => ( ord_less_eq_nat @ Z4 @ Y3 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % pred_member
% 5.82/6.02 thf(fact_449_pred__corr,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Px: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.82/6.02 = ( some_nat @ Px ) )
% 5.82/6.02 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Px ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % pred_corr
% 5.82/6.02 thf(fact_450_succ__corr,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.82/6.02 = ( some_nat @ Sx ) )
% 5.82/6.02 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % succ_corr
% 5.82/6.02 thf(fact_451_pred__correct,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.82/6.02 = ( some_nat @ Sx ) )
% 5.82/6.02 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % pred_correct
% 5.82/6.02 thf(fact_452_succ__correct,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.82/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.02 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.82/6.02 = ( some_nat @ Sx ) )
% 5.82/6.02 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % succ_correct
% 5.82/6.02 thf(fact_453_local_Opower__def,axiom,
% 5.82/6.02 ( vEBT_VEBT_power
% 5.82/6.02 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.82/6.02
% 5.82/6.02 % local.power_def
% 5.82/6.02 thf(fact_454_subset__code_I1_J,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.02 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B )
% 5.82/6.02 = ( ! [X3: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.02 => ( member_VEBT_VEBT @ X3 @ B ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % subset_code(1)
% 5.82/6.02 thf(fact_455_subset__code_I1_J,axiom,
% 5.82/6.02 ! [Xs: list_real,B: set_real] :
% 5.82/6.02 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B )
% 5.82/6.02 = ( ! [X3: real] :
% 5.82/6.02 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.82/6.02 => ( member_real @ X3 @ B ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % subset_code(1)
% 5.82/6.02 thf(fact_456_subset__code_I1_J,axiom,
% 5.82/6.02 ! [Xs: list_nat,B: set_nat] :
% 5.82/6.02 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B )
% 5.82/6.02 = ( ! [X3: nat] :
% 5.82/6.02 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.82/6.02 => ( member_nat @ X3 @ B ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % subset_code(1)
% 5.82/6.02 thf(fact_457_subset__code_I1_J,axiom,
% 5.82/6.02 ! [Xs: list_int,B: set_int] :
% 5.82/6.02 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B )
% 5.82/6.02 = ( ! [X3: int] :
% 5.82/6.02 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.82/6.02 => ( member_int @ X3 @ B ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % subset_code(1)
% 5.82/6.02 thf(fact_458_diff__commute,axiom,
% 5.82/6.02 ! [I: nat,J: nat,K: nat] :
% 5.82/6.02 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.82/6.02 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_commute
% 5.82/6.02 thf(fact_459_zero__induct__lemma,axiom,
% 5.82/6.02 ! [P: nat > $o,K: nat,I: nat] :
% 5.82/6.02 ( ( P @ K )
% 5.82/6.02 => ( ! [N3: nat] :
% 5.82/6.02 ( ( P @ ( suc @ N3 ) )
% 5.82/6.02 => ( P @ N3 ) )
% 5.82/6.02 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % zero_induct_lemma
% 5.82/6.02 thf(fact_460_diff__less__mono2,axiom,
% 5.82/6.02 ! [M: nat,N: nat,L: nat] :
% 5.82/6.02 ( ( ord_less_nat @ M @ N )
% 5.82/6.02 => ( ( ord_less_nat @ M @ L )
% 5.82/6.02 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_less_mono2
% 5.82/6.02 thf(fact_461_less__imp__diff__less,axiom,
% 5.82/6.02 ! [J: nat,K: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_nat @ J @ K )
% 5.82/6.02 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_imp_diff_less
% 5.82/6.02 thf(fact_462_diff__le__mono2,axiom,
% 5.82/6.02 ! [M: nat,N: nat,L: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.02 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_le_mono2
% 5.82/6.02 thf(fact_463_le__diff__iff_H,axiom,
% 5.82/6.02 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ A2 @ C2 )
% 5.82/6.02 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A2 ) @ ( minus_minus_nat @ C2 @ B2 ) )
% 5.82/6.02 = ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % le_diff_iff'
% 5.82/6.02 thf(fact_464_diff__le__self,axiom,
% 5.82/6.02 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.82/6.02
% 5.82/6.02 % diff_le_self
% 5.82/6.02 thf(fact_465_diff__le__mono,axiom,
% 5.82/6.02 ! [M: nat,N: nat,L: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.02 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_le_mono
% 5.82/6.02 thf(fact_466_Nat_Odiff__diff__eq,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.02 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.82/6.02 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % Nat.diff_diff_eq
% 5.82/6.02 thf(fact_467_le__diff__iff,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.02 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.82/6.02 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % le_diff_iff
% 5.82/6.02 thf(fact_468_eq__diff__iff,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.02 => ( ( ( minus_minus_nat @ M @ K )
% 5.82/6.02 = ( minus_minus_nat @ N @ K ) )
% 5.82/6.02 = ( M = N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % eq_diff_iff
% 5.82/6.02 thf(fact_469_diff__mult__distrib,axiom,
% 5.82/6.02 ! [M: nat,N: nat,K: nat] :
% 5.82/6.02 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.82/6.02 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_mult_distrib
% 5.82/6.02 thf(fact_470_diff__mult__distrib2,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.02 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_mult_distrib2
% 5.82/6.02 thf(fact_471_set__update__subsetI,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBTi,A: set_VEBT_VEBTi,X2: vEBT_VEBTi,I: nat] :
% 5.82/6.02 ( ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ A )
% 5.82/6.02 => ( ( member_VEBT_VEBTi @ X2 @ A )
% 5.82/6.02 => ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) ) @ A ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_subsetI
% 5.82/6.02 thf(fact_472_set__update__subsetI,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBT,A: set_VEBT_VEBT,X2: vEBT_VEBT,I: nat] :
% 5.82/6.02 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A )
% 5.82/6.02 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.02 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) ) @ A ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_subsetI
% 5.82/6.02 thf(fact_473_set__update__subsetI,axiom,
% 5.82/6.02 ! [Xs: list_nat,A: set_nat,X2: nat,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A )
% 5.82/6.02 => ( ( member_nat @ X2 @ A )
% 5.82/6.02 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X2 ) ) @ A ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_subsetI
% 5.82/6.02 thf(fact_474_set__update__subsetI,axiom,
% 5.82/6.02 ! [Xs: list_o,A: set_o,X2: $o,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A )
% 5.82/6.02 => ( ( member_o @ X2 @ A )
% 5.82/6.02 => ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X2 ) ) @ A ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_subsetI
% 5.82/6.02 thf(fact_475_set__update__subsetI,axiom,
% 5.82/6.02 ! [Xs: list_real,A: set_real,X2: real,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A )
% 5.82/6.02 => ( ( member_real @ X2 @ A )
% 5.82/6.02 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X2 ) ) @ A ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_subsetI
% 5.82/6.02 thf(fact_476_set__update__subsetI,axiom,
% 5.82/6.02 ! [Xs: list_int,A: set_int,X2: int,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A )
% 5.82/6.02 => ( ( member_int @ X2 @ A )
% 5.82/6.02 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X2 ) ) @ A ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_subsetI
% 5.82/6.02 thf(fact_477_Suc__diff__Suc,axiom,
% 5.82/6.02 ! [N: nat,M: nat] :
% 5.82/6.02 ( ( ord_less_nat @ N @ M )
% 5.82/6.02 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.82/6.02 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % Suc_diff_Suc
% 5.82/6.02 thf(fact_478_diff__less__Suc,axiom,
% 5.82/6.02 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_less_Suc
% 5.82/6.02 thf(fact_479_Suc__diff__le,axiom,
% 5.82/6.02 ! [N: nat,M: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.02 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.82/6.02 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % Suc_diff_le
% 5.82/6.02 thf(fact_480_diff__less__mono,axiom,
% 5.82/6.02 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.02 => ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.02 => ( ord_less_nat @ ( minus_minus_nat @ A2 @ C2 ) @ ( minus_minus_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_less_mono
% 5.82/6.02 thf(fact_481_less__diff__iff,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.02 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.82/6.02 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_diff_iff
% 5.82/6.02 thf(fact_482_power2__commute,axiom,
% 5.82/6.02 ! [X2: complex,Y3: complex] :
% 5.82/6.02 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( power_power_complex @ ( minus_minus_complex @ Y3 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_commute
% 5.82/6.02 thf(fact_483_power2__commute,axiom,
% 5.82/6.02 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ Y3 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_commute
% 5.82/6.02 thf(fact_484_power2__commute,axiom,
% 5.82/6.02 ! [X2: real,Y3: real] :
% 5.82/6.02 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( power_power_real @ ( minus_minus_real @ Y3 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_commute
% 5.82/6.02 thf(fact_485_power2__commute,axiom,
% 5.82/6.02 ! [X2: rat,Y3: rat] :
% 5.82/6.02 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( power_power_rat @ ( minus_minus_rat @ Y3 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_commute
% 5.82/6.02 thf(fact_486_power2__commute,axiom,
% 5.82/6.02 ! [X2: int,Y3: int] :
% 5.82/6.02 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( power_power_int @ ( minus_minus_int @ Y3 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_commute
% 5.82/6.02 thf(fact_487_nth__mem,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_int] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.82/6.02 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_mem
% 5.82/6.02 thf(fact_488_nth__mem,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_mem
% 5.82/6.02 thf(fact_489_nth__mem,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_real] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_mem
% 5.82/6.02 thf(fact_490_nth__mem,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_mem
% 5.82/6.02 thf(fact_491_nth__mem,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_nat] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_mem
% 5.82/6.02 thf(fact_492_nth__mem,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_VEBT_VEBTi] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( member_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ ( set_VEBT_VEBTi2 @ Xs ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nth_mem
% 5.82/6.02 thf(fact_493_list__ball__nth,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_ball_nth
% 5.82/6.02 thf(fact_494_list__ball__nth,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_real,P: real > $o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( ! [X4: real] :
% 5.82/6.02 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_ball_nth
% 5.82/6.02 thf(fact_495_list__ball__nth,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_o,P: $o > $o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( ! [X4: $o] :
% 5.82/6.02 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_ball_nth
% 5.82/6.02 thf(fact_496_list__ball__nth,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( ! [X4: nat] :
% 5.82/6.02 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_ball_nth
% 5.82/6.02 thf(fact_497_list__ball__nth,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_VEBT_VEBTi,P: vEBT_VEBTi > $o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( ! [X4: vEBT_VEBTi] :
% 5.82/6.02 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.02 => ( P @ X4 ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % list_ball_nth
% 5.82/6.02 thf(fact_498_in__set__conv__nth,axiom,
% 5.82/6.02 ! [X2: int,Xs: list_int] :
% 5.82/6.02 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.82/6.02 = ( ? [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.82/6.02 & ( ( nth_int @ Xs @ I4 )
% 5.82/6.02 = X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_conv_nth
% 5.82/6.02 thf(fact_499_in__set__conv__nth,axiom,
% 5.82/6.02 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.02 = ( ? [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 & ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.82/6.02 = X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_conv_nth
% 5.82/6.02 thf(fact_500_in__set__conv__nth,axiom,
% 5.82/6.02 ! [X2: real,Xs: list_real] :
% 5.82/6.02 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.82/6.02 = ( ? [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 & ( ( nth_real @ Xs @ I4 )
% 5.82/6.02 = X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_conv_nth
% 5.82/6.02 thf(fact_501_in__set__conv__nth,axiom,
% 5.82/6.02 ! [X2: $o,Xs: list_o] :
% 5.82/6.02 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.82/6.02 = ( ? [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 & ( ( nth_o @ Xs @ I4 )
% 5.82/6.02 = X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_conv_nth
% 5.82/6.02 thf(fact_502_in__set__conv__nth,axiom,
% 5.82/6.02 ! [X2: nat,Xs: list_nat] :
% 5.82/6.02 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.82/6.02 = ( ? [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 & ( ( nth_nat @ Xs @ I4 )
% 5.82/6.02 = X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_conv_nth
% 5.82/6.02 thf(fact_503_in__set__conv__nth,axiom,
% 5.82/6.02 ! [X2: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 5.82/6.02 ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.02 = ( ? [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 & ( ( nth_VEBT_VEBTi @ Xs @ I4 )
% 5.82/6.02 = X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_conv_nth
% 5.82/6.02 thf(fact_504_all__set__conv__nth,axiom,
% 5.82/6.02 ! [L: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.02 ( ( ! [X3: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ L ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBT @ L @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_nth
% 5.82/6.02 thf(fact_505_all__set__conv__nth,axiom,
% 5.82/6.02 ! [L: list_real,P: real > $o] :
% 5.82/6.02 ( ( ! [X3: real] :
% 5.82/6.02 ( ( member_real @ X3 @ ( set_real2 @ L ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ L ) )
% 5.82/6.02 => ( P @ ( nth_real @ L @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_nth
% 5.82/6.02 thf(fact_506_all__set__conv__nth,axiom,
% 5.82/6.02 ! [L: list_o,P: $o > $o] :
% 5.82/6.02 ( ( ! [X3: $o] :
% 5.82/6.02 ( ( member_o @ X3 @ ( set_o2 @ L ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ L ) )
% 5.82/6.02 => ( P @ ( nth_o @ L @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_nth
% 5.82/6.02 thf(fact_507_all__set__conv__nth,axiom,
% 5.82/6.02 ! [L: list_nat,P: nat > $o] :
% 5.82/6.02 ( ( ! [X3: nat] :
% 5.82/6.02 ( ( member_nat @ X3 @ ( set_nat2 @ L ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ L ) )
% 5.82/6.02 => ( P @ ( nth_nat @ L @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_nth
% 5.82/6.02 thf(fact_508_all__set__conv__nth,axiom,
% 5.82/6.02 ! [L: list_VEBT_VEBTi,P: vEBT_VEBTi > $o] :
% 5.82/6.02 ( ( ! [X3: vEBT_VEBTi] :
% 5.82/6.02 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ L ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBTi @ L @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_nth
% 5.82/6.02 thf(fact_509_all__nth__imp__all__set,axiom,
% 5.82/6.02 ! [Xs: list_int,P: int > $o,X2: int] :
% 5.82/6.02 ( ! [I2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_int @ Xs @ I2 ) ) )
% 5.82/6.02 => ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.82/6.02 => ( P @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_nth_imp_all_set
% 5.82/6.02 thf(fact_510_all__nth__imp__all__set,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.82/6.02 ( ! [I2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 5.82/6.02 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.02 => ( P @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_nth_imp_all_set
% 5.82/6.02 thf(fact_511_all__nth__imp__all__set,axiom,
% 5.82/6.02 ! [Xs: list_real,P: real > $o,X2: real] :
% 5.82/6.02 ( ! [I2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_real @ Xs @ I2 ) ) )
% 5.82/6.02 => ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.82/6.02 => ( P @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_nth_imp_all_set
% 5.82/6.02 thf(fact_512_all__nth__imp__all__set,axiom,
% 5.82/6.02 ! [Xs: list_o,P: $o > $o,X2: $o] :
% 5.82/6.02 ( ! [I2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_o @ Xs @ I2 ) ) )
% 5.82/6.02 => ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.82/6.02 => ( P @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_nth_imp_all_set
% 5.82/6.02 thf(fact_513_all__nth__imp__all__set,axiom,
% 5.82/6.02 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 5.82/6.02 ( ! [I2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_nat @ Xs @ I2 ) ) )
% 5.82/6.02 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.82/6.02 => ( P @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_nth_imp_all_set
% 5.82/6.02 thf(fact_514_all__nth__imp__all__set,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBTi,P: vEBT_VEBTi > $o,X2: vEBT_VEBTi] :
% 5.82/6.02 ( ! [I2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBTi @ Xs @ I2 ) ) )
% 5.82/6.02 => ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.02 => ( P @ X2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_nth_imp_all_set
% 5.82/6.02 thf(fact_515_all__set__conv__all__nth,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.02 ( ( ! [X3: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_all_nth
% 5.82/6.02 thf(fact_516_all__set__conv__all__nth,axiom,
% 5.82/6.02 ! [Xs: list_real,P: real > $o] :
% 5.82/6.02 ( ( ! [X3: real] :
% 5.82/6.02 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_real @ Xs @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_all_nth
% 5.82/6.02 thf(fact_517_all__set__conv__all__nth,axiom,
% 5.82/6.02 ! [Xs: list_o,P: $o > $o] :
% 5.82/6.02 ( ( ! [X3: $o] :
% 5.82/6.02 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_o @ Xs @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_all_nth
% 5.82/6.02 thf(fact_518_all__set__conv__all__nth,axiom,
% 5.82/6.02 ! [Xs: list_nat,P: nat > $o] :
% 5.82/6.02 ( ( ! [X3: nat] :
% 5.82/6.02 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_all_nth
% 5.82/6.02 thf(fact_519_all__set__conv__all__nth,axiom,
% 5.82/6.02 ! [Xs: list_VEBT_VEBTi,P: vEBT_VEBTi > $o] :
% 5.82/6.02 ( ( ! [X3: vEBT_VEBTi] :
% 5.82/6.02 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.02 => ( P @ X3 ) ) )
% 5.82/6.02 = ( ! [I4: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I4 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( P @ ( nth_VEBT_VEBTi @ Xs @ I4 ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % all_set_conv_all_nth
% 5.82/6.02 thf(fact_520_in__set__upd__eq,axiom,
% 5.82/6.02 ! [I: nat,L: list_int,X2: int,Y3: int] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 5.82/6.02 => ( ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ( ( member_int @ X2 @ ( set_int2 @ L ) )
% 5.82/6.02 & ! [Y: int] : ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq
% 5.82/6.02 thf(fact_521_in__set__upd__eq,axiom,
% 5.82/6.02 ! [I: nat,L: list_VEBT_VEBT,X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.02 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ L ) )
% 5.82/6.02 & ! [Y: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq
% 5.82/6.02 thf(fact_522_in__set__upd__eq,axiom,
% 5.82/6.02 ! [I: nat,L: list_real,X2: real,Y3: real] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 5.82/6.02 => ( ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ( ( member_real @ X2 @ ( set_real2 @ L ) )
% 5.82/6.02 & ! [Y: real] : ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq
% 5.82/6.02 thf(fact_523_in__set__upd__eq,axiom,
% 5.82/6.02 ! [I: nat,L: list_o,X2: $o,Y3: $o] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 5.82/6.02 => ( ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ( ( member_o @ X2 @ ( set_o2 @ L ) )
% 5.82/6.02 & ! [Y: $o] : ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq
% 5.82/6.02 thf(fact_524_in__set__upd__eq,axiom,
% 5.82/6.02 ! [I: nat,L: list_nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 5.82/6.02 => ( ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ( ( member_nat @ X2 @ ( set_nat2 @ L ) )
% 5.82/6.02 & ! [Y: nat] : ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq
% 5.82/6.02 thf(fact_525_in__set__upd__eq,axiom,
% 5.82/6.02 ! [I: nat,L: list_VEBT_VEBTi,X2: vEBT_VEBTi,Y3: vEBT_VEBTi] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 5.82/6.02 => ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ L ) )
% 5.82/6.02 & ! [Y: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq
% 5.82/6.02 thf(fact_526_set__update__memI,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_int,X2: int] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.82/6.02 => ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ Xs @ N @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_memI
% 5.82/6.02 thf(fact_527_set__update__memI,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.02 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_memI
% 5.82/6.02 thf(fact_528_set__update__memI,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_real,X2: real] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.02 => ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ Xs @ N @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_memI
% 5.82/6.02 thf(fact_529_set__update__memI,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_o,X2: $o] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.82/6.02 => ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ Xs @ N @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_memI
% 5.82/6.02 thf(fact_530_set__update__memI,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_nat,X2: nat] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.82/6.02 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_memI
% 5.82/6.02 thf(fact_531_set__update__memI,axiom,
% 5.82/6.02 ! [N: nat,Xs: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.02 => ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ N @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_update_memI
% 5.82/6.02 thf(fact_532_in__set__upd__cases,axiom,
% 5.82/6.02 ! [X2: int,L: list_int,I: nat,Y3: int] :
% 5.82/6.02 ( ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ L @ I @ Y3 ) ) )
% 5.82/6.02 => ( ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 5.82/6.02 => ( X2 != Y3 ) )
% 5.82/6.02 => ( member_int @ X2 @ ( set_int2 @ L ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_cases
% 5.82/6.02 thf(fact_533_in__set__upd__cases,axiom,
% 5.82/6.02 ! [X2: vEBT_VEBT,L: list_VEBT_VEBT,I: nat,Y3: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y3 ) ) )
% 5.82/6.02 => ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.02 => ( X2 != Y3 ) )
% 5.82/6.02 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_cases
% 5.82/6.02 thf(fact_534_in__set__upd__cases,axiom,
% 5.82/6.02 ! [X2: real,L: list_real,I: nat,Y3: real] :
% 5.82/6.02 ( ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ L @ I @ Y3 ) ) )
% 5.82/6.02 => ( ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 5.82/6.02 => ( X2 != Y3 ) )
% 5.82/6.02 => ( member_real @ X2 @ ( set_real2 @ L ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_cases
% 5.82/6.02 thf(fact_535_in__set__upd__cases,axiom,
% 5.82/6.02 ! [X2: $o,L: list_o,I: nat,Y3: $o] :
% 5.82/6.02 ( ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ L @ I @ Y3 ) ) )
% 5.82/6.02 => ( ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 5.82/6.02 => ( X2 = ~ Y3 ) )
% 5.82/6.02 => ( member_o @ X2 @ ( set_o2 @ L ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_cases
% 5.82/6.02 thf(fact_536_in__set__upd__cases,axiom,
% 5.82/6.02 ! [X2: nat,L: list_nat,I: nat,Y3: nat] :
% 5.82/6.02 ( ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y3 ) ) )
% 5.82/6.02 => ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 5.82/6.02 => ( X2 != Y3 ) )
% 5.82/6.02 => ( member_nat @ X2 @ ( set_nat2 @ L ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_cases
% 5.82/6.02 thf(fact_537_in__set__upd__cases,axiom,
% 5.82/6.02 ! [X2: vEBT_VEBTi,L: list_VEBT_VEBTi,I: nat,Y3: vEBT_VEBTi] :
% 5.82/6.02 ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y3 ) ) )
% 5.82/6.02 => ( ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 5.82/6.02 => ( X2 != Y3 ) )
% 5.82/6.02 => ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_cases
% 5.82/6.02 thf(fact_538_in__set__upd__eq__aux,axiom,
% 5.82/6.02 ! [I: nat,L: list_int,X2: int,Y3: int] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 5.82/6.02 => ( ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ! [Y: int] : ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq_aux
% 5.82/6.02 thf(fact_539_in__set__upd__eq__aux,axiom,
% 5.82/6.02 ! [I: nat,L: list_VEBT_VEBT,X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.02 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ! [Y: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq_aux
% 5.82/6.02 thf(fact_540_in__set__upd__eq__aux,axiom,
% 5.82/6.02 ! [I: nat,L: list_real,X2: real,Y3: real] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 5.82/6.02 => ( ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ! [Y: real] : ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq_aux
% 5.82/6.02 thf(fact_541_in__set__upd__eq__aux,axiom,
% 5.82/6.02 ! [I: nat,L: list_o,X2: $o,Y3: $o] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 5.82/6.02 => ( ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ! [Y: $o] : ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq_aux
% 5.82/6.02 thf(fact_542_in__set__upd__eq__aux,axiom,
% 5.82/6.02 ! [I: nat,L: list_nat,X2: nat,Y3: nat] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 5.82/6.02 => ( ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ! [Y: nat] : ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq_aux
% 5.82/6.02 thf(fact_543_in__set__upd__eq__aux,axiom,
% 5.82/6.02 ! [I: nat,L: list_VEBT_VEBTi,X2: vEBT_VEBTi,Y3: vEBT_VEBTi] :
% 5.82/6.02 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 5.82/6.02 => ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y3 ) ) )
% 5.82/6.02 = ( ( X2 = Y3 )
% 5.82/6.02 | ! [Y: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_set_upd_eq_aux
% 5.82/6.02 thf(fact_544_diff__le__diff__pow,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.82/6.02 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_le_diff_pow
% 5.82/6.02 thf(fact_545_power__minus__is__div,axiom,
% 5.82/6.02 ! [B2: nat,A2: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.02 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.02 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_minus_is_div
% 5.82/6.02 thf(fact_546_less__two__pow__divD,axiom,
% 5.82/6.02 ! [X2: nat,N: nat,M: nat] :
% 5.82/6.02 ( ( ord_less_nat @ X2 @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 5.82/6.02 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.02 & ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_two_pow_divD
% 5.82/6.02 thf(fact_547_less__two__pow__divI,axiom,
% 5.82/6.02 ! [X2: nat,N: nat,M: nat] :
% 5.82/6.02 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) )
% 5.82/6.02 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.02 => ( ord_less_nat @ X2 @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % less_two_pow_divI
% 5.82/6.02 thf(fact_548_power__commutes,axiom,
% 5.82/6.02 ! [A2: complex,N: nat] :
% 5.82/6.02 ( ( times_times_complex @ ( power_power_complex @ A2 @ N ) @ A2 )
% 5.82/6.02 = ( times_times_complex @ A2 @ ( power_power_complex @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commutes
% 5.82/6.02 thf(fact_549_power__commutes,axiom,
% 5.82/6.02 ! [A2: code_integer,N: nat] :
% 5.82/6.02 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ A2 )
% 5.82/6.02 = ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commutes
% 5.82/6.02 thf(fact_550_power__commutes,axiom,
% 5.82/6.02 ! [A2: real,N: nat] :
% 5.82/6.02 ( ( times_times_real @ ( power_power_real @ A2 @ N ) @ A2 )
% 5.82/6.02 = ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commutes
% 5.82/6.02 thf(fact_551_power__commutes,axiom,
% 5.82/6.02 ! [A2: rat,N: nat] :
% 5.82/6.02 ( ( times_times_rat @ ( power_power_rat @ A2 @ N ) @ A2 )
% 5.82/6.02 = ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commutes
% 5.82/6.02 thf(fact_552_power__commutes,axiom,
% 5.82/6.02 ! [A2: nat,N: nat] :
% 5.82/6.02 ( ( times_times_nat @ ( power_power_nat @ A2 @ N ) @ A2 )
% 5.82/6.02 = ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commutes
% 5.82/6.02 thf(fact_553_power__commutes,axiom,
% 5.82/6.02 ! [A2: int,N: nat] :
% 5.82/6.02 ( ( times_times_int @ ( power_power_int @ A2 @ N ) @ A2 )
% 5.82/6.02 = ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commutes
% 5.82/6.02 thf(fact_554_power__mult__distrib,axiom,
% 5.82/6.02 ! [A2: complex,B2: complex,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ ( times_times_complex @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( times_times_complex @ ( power_power_complex @ A2 @ N ) @ ( power_power_complex @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_distrib
% 5.82/6.02 thf(fact_555_power__mult__distrib,axiom,
% 5.82/6.02 ! [A2: code_integer,B2: code_integer,N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_distrib
% 5.82/6.02 thf(fact_556_power__mult__distrib,axiom,
% 5.82/6.02 ! [A2: real,B2: real,N: nat] :
% 5.82/6.02 ( ( power_power_real @ ( times_times_real @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( times_times_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_distrib
% 5.82/6.02 thf(fact_557_power__mult__distrib,axiom,
% 5.82/6.02 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.02 ( ( power_power_rat @ ( times_times_rat @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( times_times_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_distrib
% 5.82/6.02 thf(fact_558_power__mult__distrib,axiom,
% 5.82/6.02 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.02 ( ( power_power_nat @ ( times_times_nat @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( times_times_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_distrib
% 5.82/6.02 thf(fact_559_power__mult__distrib,axiom,
% 5.82/6.02 ! [A2: int,B2: int,N: nat] :
% 5.82/6.02 ( ( power_power_int @ ( times_times_int @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( times_times_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult_distrib
% 5.82/6.02 thf(fact_560_power__commuting__commutes,axiom,
% 5.82/6.02 ! [X2: complex,Y3: complex,N: nat] :
% 5.82/6.02 ( ( ( times_times_complex @ X2 @ Y3 )
% 5.82/6.02 = ( times_times_complex @ Y3 @ X2 ) )
% 5.82/6.02 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ Y3 )
% 5.82/6.02 = ( times_times_complex @ Y3 @ ( power_power_complex @ X2 @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commuting_commutes
% 5.82/6.02 thf(fact_561_power__commuting__commutes,axiom,
% 5.82/6.02 ! [X2: code_integer,Y3: code_integer,N: nat] :
% 5.82/6.02 ( ( ( times_3573771949741848930nteger @ X2 @ Y3 )
% 5.82/6.02 = ( times_3573771949741848930nteger @ Y3 @ X2 ) )
% 5.82/6.02 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ N ) @ Y3 )
% 5.82/6.02 = ( times_3573771949741848930nteger @ Y3 @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commuting_commutes
% 5.82/6.02 thf(fact_562_power__commuting__commutes,axiom,
% 5.82/6.02 ! [X2: real,Y3: real,N: nat] :
% 5.82/6.02 ( ( ( times_times_real @ X2 @ Y3 )
% 5.82/6.02 = ( times_times_real @ Y3 @ X2 ) )
% 5.82/6.02 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ Y3 )
% 5.82/6.02 = ( times_times_real @ Y3 @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commuting_commutes
% 5.82/6.02 thf(fact_563_power__commuting__commutes,axiom,
% 5.82/6.02 ! [X2: rat,Y3: rat,N: nat] :
% 5.82/6.02 ( ( ( times_times_rat @ X2 @ Y3 )
% 5.82/6.02 = ( times_times_rat @ Y3 @ X2 ) )
% 5.82/6.02 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ Y3 )
% 5.82/6.02 = ( times_times_rat @ Y3 @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commuting_commutes
% 5.82/6.02 thf(fact_564_power__commuting__commutes,axiom,
% 5.82/6.02 ! [X2: nat,Y3: nat,N: nat] :
% 5.82/6.02 ( ( ( times_times_nat @ X2 @ Y3 )
% 5.82/6.02 = ( times_times_nat @ Y3 @ X2 ) )
% 5.82/6.02 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ Y3 )
% 5.82/6.02 = ( times_times_nat @ Y3 @ ( power_power_nat @ X2 @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commuting_commutes
% 5.82/6.02 thf(fact_565_power__commuting__commutes,axiom,
% 5.82/6.02 ! [X2: int,Y3: int,N: nat] :
% 5.82/6.02 ( ( ( times_times_int @ X2 @ Y3 )
% 5.82/6.02 = ( times_times_int @ Y3 @ X2 ) )
% 5.82/6.02 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ Y3 )
% 5.82/6.02 = ( times_times_int @ Y3 @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_commuting_commutes
% 5.82/6.02 thf(fact_566_power__divide,axiom,
% 5.82/6.02 ! [A2: complex,B2: complex,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( divide1717551699836669952omplex @ ( power_power_complex @ A2 @ N ) @ ( power_power_complex @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_divide
% 5.82/6.02 thf(fact_567_power__divide,axiom,
% 5.82/6.02 ! [A2: real,B2: real,N: nat] :
% 5.82/6.02 ( ( power_power_real @ ( divide_divide_real @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( divide_divide_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_divide
% 5.82/6.02 thf(fact_568_power__divide,axiom,
% 5.82/6.02 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.02 ( ( power_power_rat @ ( divide_divide_rat @ A2 @ B2 ) @ N )
% 5.82/6.02 = ( divide_divide_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_divide
% 5.82/6.02 thf(fact_569_power__mult,axiom,
% 5.82/6.02 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ ( times_times_nat @ M @ N ) )
% 5.82/6.02 = ( power_power_nat @ ( power_power_nat @ A2 @ M ) @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult
% 5.82/6.02 thf(fact_570_power__mult,axiom,
% 5.82/6.02 ! [A2: real,M: nat,N: nat] :
% 5.82/6.02 ( ( power_power_real @ A2 @ ( times_times_nat @ M @ N ) )
% 5.82/6.02 = ( power_power_real @ ( power_power_real @ A2 @ M ) @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult
% 5.82/6.02 thf(fact_571_power__mult,axiom,
% 5.82/6.02 ! [A2: int,M: nat,N: nat] :
% 5.82/6.02 ( ( power_power_int @ A2 @ ( times_times_nat @ M @ N ) )
% 5.82/6.02 = ( power_power_int @ ( power_power_int @ A2 @ M ) @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult
% 5.82/6.02 thf(fact_572_power__mult,axiom,
% 5.82/6.02 ! [A2: complex,M: nat,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ ( times_times_nat @ M @ N ) )
% 5.82/6.02 = ( power_power_complex @ ( power_power_complex @ A2 @ M ) @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult
% 5.82/6.02 thf(fact_573_power__mult,axiom,
% 5.82/6.02 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ ( times_times_nat @ M @ N ) )
% 5.82/6.02 = ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_mult
% 5.82/6.02 thf(fact_574_power__Suc,axiom,
% 5.82/6.02 ! [A2: complex,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_complex @ A2 @ ( power_power_complex @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc
% 5.82/6.02 thf(fact_575_power__Suc,axiom,
% 5.82/6.02 ! [A2: code_integer,N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc
% 5.82/6.02 thf(fact_576_power__Suc,axiom,
% 5.82/6.02 ! [A2: real,N: nat] :
% 5.82/6.02 ( ( power_power_real @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc
% 5.82/6.02 thf(fact_577_power__Suc,axiom,
% 5.82/6.02 ! [A2: rat,N: nat] :
% 5.82/6.02 ( ( power_power_rat @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc
% 5.82/6.02 thf(fact_578_power__Suc,axiom,
% 5.82/6.02 ! [A2: nat,N: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc
% 5.82/6.02 thf(fact_579_power__Suc,axiom,
% 5.82/6.02 ! [A2: int,N: nat] :
% 5.82/6.02 ( ( power_power_int @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc
% 5.82/6.02 thf(fact_580_power__Suc2,axiom,
% 5.82/6.02 ! [A2: complex,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_complex @ ( power_power_complex @ A2 @ N ) @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc2
% 5.82/6.02 thf(fact_581_power__Suc2,axiom,
% 5.82/6.02 ! [A2: code_integer,N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc2
% 5.82/6.02 thf(fact_582_power__Suc2,axiom,
% 5.82/6.02 ! [A2: real,N: nat] :
% 5.82/6.02 ( ( power_power_real @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_real @ ( power_power_real @ A2 @ N ) @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc2
% 5.82/6.02 thf(fact_583_power__Suc2,axiom,
% 5.82/6.02 ! [A2: rat,N: nat] :
% 5.82/6.02 ( ( power_power_rat @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_rat @ ( power_power_rat @ A2 @ N ) @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc2
% 5.82/6.02 thf(fact_584_power__Suc2,axiom,
% 5.82/6.02 ! [A2: nat,N: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_nat @ ( power_power_nat @ A2 @ N ) @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc2
% 5.82/6.02 thf(fact_585_power__Suc2,axiom,
% 5.82/6.02 ! [A2: int,N: nat] :
% 5.82/6.02 ( ( power_power_int @ A2 @ ( suc @ N ) )
% 5.82/6.02 = ( times_times_int @ ( power_power_int @ A2 @ N ) @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_Suc2
% 5.82/6.02 thf(fact_586_div__mult__le,axiom,
% 5.82/6.02 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) @ A2 ) ).
% 5.82/6.02
% 5.82/6.02 % div_mult_le
% 5.82/6.02 thf(fact_587_power__numeral__even,axiom,
% 5.82/6.02 ! [Z: complex,W: num] :
% 5.82/6.02 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.82/6.02 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_numeral_even
% 5.82/6.02 thf(fact_588_power__numeral__even,axiom,
% 5.82/6.02 ! [Z: code_integer,W: num] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.82/6.02 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_numeral_even
% 5.82/6.02 thf(fact_589_power__numeral__even,axiom,
% 5.82/6.02 ! [Z: real,W: num] :
% 5.82/6.02 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.82/6.02 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_numeral_even
% 5.82/6.02 thf(fact_590_power__numeral__even,axiom,
% 5.82/6.02 ! [Z: rat,W: num] :
% 5.82/6.02 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.82/6.02 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_numeral_even
% 5.82/6.02 thf(fact_591_power__numeral__even,axiom,
% 5.82/6.02 ! [Z: nat,W: num] :
% 5.82/6.02 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.82/6.02 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_numeral_even
% 5.82/6.02 thf(fact_592_power__numeral__even,axiom,
% 5.82/6.02 ! [Z: int,W: num] :
% 5.82/6.02 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.82/6.02 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_numeral_even
% 5.82/6.02 thf(fact_593_power4__eq__xxxx,axiom,
% 5.82/6.02 ! [X2: complex] :
% 5.82/6.02 ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power4_eq_xxxx
% 5.82/6.02 thf(fact_594_power4__eq__xxxx,axiom,
% 5.82/6.02 ! [X2: code_integer] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power4_eq_xxxx
% 5.82/6.02 thf(fact_595_power4__eq__xxxx,axiom,
% 5.82/6.02 ! [X2: real] :
% 5.82/6.02 ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power4_eq_xxxx
% 5.82/6.02 thf(fact_596_power4__eq__xxxx,axiom,
% 5.82/6.02 ! [X2: rat] :
% 5.82/6.02 ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power4_eq_xxxx
% 5.82/6.02 thf(fact_597_power4__eq__xxxx,axiom,
% 5.82/6.02 ! [X2: nat] :
% 5.82/6.02 ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power4_eq_xxxx
% 5.82/6.02 thf(fact_598_power4__eq__xxxx,axiom,
% 5.82/6.02 ! [X2: int] :
% 5.82/6.02 ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power4_eq_xxxx
% 5.82/6.02 thf(fact_599_power2__eq__square,axiom,
% 5.82/6.02 ! [A2: complex] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( times_times_complex @ A2 @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_eq_square
% 5.82/6.02 thf(fact_600_power2__eq__square,axiom,
% 5.82/6.02 ! [A2: code_integer] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( times_3573771949741848930nteger @ A2 @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_eq_square
% 5.82/6.02 thf(fact_601_power2__eq__square,axiom,
% 5.82/6.02 ! [A2: real] :
% 5.82/6.02 ( ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( times_times_real @ A2 @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_eq_square
% 5.82/6.02 thf(fact_602_power2__eq__square,axiom,
% 5.82/6.02 ! [A2: rat] :
% 5.82/6.02 ( ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( times_times_rat @ A2 @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_eq_square
% 5.82/6.02 thf(fact_603_power2__eq__square,axiom,
% 5.82/6.02 ! [A2: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( times_times_nat @ A2 @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_eq_square
% 5.82/6.02 thf(fact_604_power2__eq__square,axiom,
% 5.82/6.02 ! [A2: int] :
% 5.82/6.02 ( ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.02 = ( times_times_int @ A2 @ A2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_eq_square
% 5.82/6.02 thf(fact_605_power__even__eq,axiom,
% 5.82/6.02 ! [A2: nat,N: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 = ( power_power_nat @ ( power_power_nat @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_even_eq
% 5.82/6.02 thf(fact_606_power__even__eq,axiom,
% 5.82/6.02 ! [A2: real,N: nat] :
% 5.82/6.02 ( ( power_power_real @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 = ( power_power_real @ ( power_power_real @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_even_eq
% 5.82/6.02 thf(fact_607_power__even__eq,axiom,
% 5.82/6.02 ! [A2: int,N: nat] :
% 5.82/6.02 ( ( power_power_int @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 = ( power_power_int @ ( power_power_int @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_even_eq
% 5.82/6.02 thf(fact_608_power__even__eq,axiom,
% 5.82/6.02 ! [A2: complex,N: nat] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 = ( power_power_complex @ ( power_power_complex @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_even_eq
% 5.82/6.02 thf(fact_609_power__even__eq,axiom,
% 5.82/6.02 ! [A2: code_integer,N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 = ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_even_eq
% 5.82/6.02 thf(fact_610_self__le__ge2__pow,axiom,
% 5.82/6.02 ! [K: nat,M: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.82/6.02 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % self_le_ge2_pow
% 5.82/6.02 thf(fact_611_power2__nat__le__eq__le,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.02 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_nat_le_eq_le
% 5.82/6.02 thf(fact_612_power2__nat__le__imp__le,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.82/6.02 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % power2_nat_le_imp_le
% 5.82/6.02 thf(fact_613_in__children__def,axiom,
% 5.82/6.02 ( vEBT_V5917875025757280293ildren
% 5.82/6.02 = ( ^ [N4: nat,TreeList3: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X3 @ N4 ) ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % in_children_def
% 5.82/6.02 thf(fact_614_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.82/6.02 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.02 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % both_member_options_from_chilf_to_complete_tree
% 5.82/6.02 thf(fact_615_both__member__options__from__complete__tree__to__child,axiom,
% 5.82/6.02 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.02 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.02 | ( X2 = Mi )
% 5.82/6.02 | ( X2 = Ma ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % both_member_options_from_complete_tree_to_child
% 5.82/6.02 thf(fact_616_nat__less__power__trans,axiom,
% 5.82/6.02 ! [N: nat,M: nat,K: nat] :
% 5.82/6.02 ( ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 5.82/6.02 => ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.02 => ( 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 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_less_power_trans
% 5.82/6.02 thf(fact_617_set__n__deg__not__0,axiom,
% 5.82/6.02 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 5.82/6.02 ( ! [X4: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.02 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.82/6.02 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.02 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % set_n_deg_not_0
% 5.82/6.02 thf(fact_618_nat__le__power__trans,axiom,
% 5.82/6.02 ! [N: nat,M: nat,K: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 5.82/6.02 => ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.02 => ( 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 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_le_power_trans
% 5.82/6.02 thf(fact_619_nat__power__less__diff,axiom,
% 5.82/6.02 ! [N: nat,Q3: nat,M: nat] :
% 5.82/6.02 ( ( 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 ) )
% 5.82/6.02 => ( ord_less_nat @ Q3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_power_less_diff
% 5.82/6.02 thf(fact_620_xndef,axiom,
% 5.82/6.02 ( xnew
% 5.82/6.02 = ( 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 @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % xndef
% 5.82/6.02 thf(fact_621_bit__concat__def,axiom,
% 5.82/6.02 ( vEBT_VEBT_bit_concat
% 5.82/6.02 = ( ^ [H: nat,L3: nat,D3: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D3 ) ) @ L3 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % bit_concat_def
% 5.82/6.02 thf(fact_622_low__inv,axiom,
% 5.82/6.02 ! [X2: nat,N: nat,Y3: nat] :
% 5.82/6.02 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.82/6.02 = X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % low_inv
% 5.82/6.02 thf(fact_623_high__inv,axiom,
% 5.82/6.02 ! [X2: nat,N: nat,Y3: nat] :
% 5.82/6.02 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.02 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.82/6.02 = Y3 ) ) ).
% 5.82/6.02
% 5.82/6.02 % high_inv
% 5.82/6.02 thf(fact_624_even__odd__cases,axiom,
% 5.82/6.02 ! [X2: nat] :
% 5.82/6.02 ( ! [N3: nat] :
% 5.82/6.02 ( X2
% 5.82/6.02 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.82/6.02 => ~ ! [N3: nat] :
% 5.82/6.02 ( X2
% 5.82/6.02 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % even_odd_cases
% 5.82/6.02 thf(fact_625_height__compose__summary,axiom,
% 5.82/6.02 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % height_compose_summary
% 5.82/6.02 thf(fact_626_pow__sum,axiom,
% 5.82/6.02 ! [A2: nat,B2: nat] :
% 5.82/6.02 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A2 @ B2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % pow_sum
% 5.82/6.02 thf(fact_627_height__compose__child,axiom,
% 5.82/6.02 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 5.82/6.02 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.02 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % height_compose_child
% 5.82/6.02 thf(fact_628_high__bound__aux,axiom,
% 5.82/6.02 ! [Ma: nat,N: nat,M: nat] :
% 5.82/6.02 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.82/6.02 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % high_bound_aux
% 5.82/6.02 thf(fact_629_numeral__plus__numeral,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.82/6.02 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_plus_numeral
% 5.82/6.02 thf(fact_630_numeral__plus__numeral,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.82/6.02 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_plus_numeral
% 5.82/6.02 thf(fact_631_numeral__plus__numeral,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.82/6.02 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_plus_numeral
% 5.82/6.02 thf(fact_632_numeral__plus__numeral,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_plus_numeral
% 5.82/6.02 thf(fact_633_numeral__plus__numeral,axiom,
% 5.82/6.02 ! [M: num,N: num] :
% 5.82/6.02 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.82/6.02 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_plus_numeral
% 5.82/6.02 thf(fact_634_add__numeral__left,axiom,
% 5.82/6.02 ! [V: num,W: num,Z: complex] :
% 5.82/6.02 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.82/6.02 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.82/6.02
% 5.82/6.02 % add_numeral_left
% 5.82/6.02 thf(fact_635_add__numeral__left,axiom,
% 5.82/6.02 ! [V: num,W: num,Z: real] :
% 5.82/6.02 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.82/6.02 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.82/6.02
% 5.82/6.02 % add_numeral_left
% 5.82/6.02 thf(fact_636_add__numeral__left,axiom,
% 5.82/6.02 ! [V: num,W: num,Z: rat] :
% 5.82/6.02 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.82/6.02 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.82/6.02
% 5.82/6.02 % add_numeral_left
% 5.82/6.02 thf(fact_637_add__numeral__left,axiom,
% 5.82/6.02 ! [V: num,W: num,Z: nat] :
% 5.82/6.02 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.82/6.02 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.82/6.02
% 5.82/6.02 % add_numeral_left
% 5.82/6.02 thf(fact_638_add__numeral__left,axiom,
% 5.82/6.02 ! [V: num,W: num,Z: int] :
% 5.82/6.02 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.82/6.02 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.82/6.02
% 5.82/6.02 % add_numeral_left
% 5.82/6.02 thf(fact_639_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_power_assn @ one_one_assn @ N )
% 5.82/6.02 = one_one_assn ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_640_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_power_rat @ one_one_rat @ N )
% 5.82/6.02 = one_one_rat ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_641_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_power_nat @ one_one_nat @ N )
% 5.82/6.02 = one_one_nat ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_642_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_power_real @ one_one_real @ N )
% 5.82/6.02 = one_one_real ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_643_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_power_int @ one_one_int @ N )
% 5.82/6.02 = one_one_int ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_644_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_power_complex @ one_one_complex @ N )
% 5.82/6.02 = one_one_complex ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_645_power__one,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 5.82/6.02 = one_one_Code_integer ) ).
% 5.82/6.02
% 5.82/6.02 % power_one
% 5.82/6.02 thf(fact_646_add__Suc__right,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.82/6.02 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % add_Suc_right
% 5.82/6.02 thf(fact_647_nat__add__left__cancel__less,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.82/6.02 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_add_left_cancel_less
% 5.82/6.02 thf(fact_648_power__one__right,axiom,
% 5.82/6.02 ! [A2: nat] :
% 5.82/6.02 ( ( power_power_nat @ A2 @ one_one_nat )
% 5.82/6.02 = A2 ) ).
% 5.82/6.02
% 5.82/6.02 % power_one_right
% 5.82/6.02 thf(fact_649_power__one__right,axiom,
% 5.82/6.02 ! [A2: real] :
% 5.82/6.02 ( ( power_power_real @ A2 @ one_one_nat )
% 5.82/6.02 = A2 ) ).
% 5.82/6.02
% 5.82/6.02 % power_one_right
% 5.82/6.02 thf(fact_650_power__one__right,axiom,
% 5.82/6.02 ! [A2: int] :
% 5.82/6.02 ( ( power_power_int @ A2 @ one_one_nat )
% 5.82/6.02 = A2 ) ).
% 5.82/6.02
% 5.82/6.02 % power_one_right
% 5.82/6.02 thf(fact_651_power__one__right,axiom,
% 5.82/6.02 ! [A2: complex] :
% 5.82/6.02 ( ( power_power_complex @ A2 @ one_one_nat )
% 5.82/6.02 = A2 ) ).
% 5.82/6.02
% 5.82/6.02 % power_one_right
% 5.82/6.02 thf(fact_652_power__one__right,axiom,
% 5.82/6.02 ! [A2: code_integer] :
% 5.82/6.02 ( ( power_8256067586552552935nteger @ A2 @ one_one_nat )
% 5.82/6.02 = A2 ) ).
% 5.82/6.02
% 5.82/6.02 % power_one_right
% 5.82/6.02 thf(fact_653_nat__add__left__cancel__le,axiom,
% 5.82/6.02 ! [K: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.82/6.02 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_add_left_cancel_le
% 5.82/6.02 thf(fact_654_diff__diff__left,axiom,
% 5.82/6.02 ! [I: nat,J: nat,K: nat] :
% 5.82/6.02 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.82/6.02 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % diff_diff_left
% 5.82/6.02 thf(fact_655_nat__mult__eq__1__iff,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( ( times_times_nat @ M @ N )
% 5.82/6.02 = one_one_nat )
% 5.82/6.02 = ( ( M = one_one_nat )
% 5.82/6.02 & ( N = one_one_nat ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_mult_eq_1_iff
% 5.82/6.02 thf(fact_656_nat__1__eq__mult__iff,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( one_one_nat
% 5.82/6.02 = ( times_times_nat @ M @ N ) )
% 5.82/6.02 = ( ( M = one_one_nat )
% 5.82/6.02 & ( N = one_one_nat ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % nat_1_eq_mult_iff
% 5.82/6.02 thf(fact_657_minewdef,axiom,
% 5.82/6.02 ( minew
% 5.82/6.02 = ( 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 @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % minewdef
% 5.82/6.02 thf(fact_658_one__eq__numeral__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( one_one_complex
% 5.82/6.02 = ( numera6690914467698888265omplex @ N ) )
% 5.82/6.02 = ( one = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_eq_numeral_iff
% 5.82/6.02 thf(fact_659_one__eq__numeral__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( one_one_real
% 5.82/6.02 = ( numeral_numeral_real @ N ) )
% 5.82/6.02 = ( one = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_eq_numeral_iff
% 5.82/6.02 thf(fact_660_one__eq__numeral__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( one_one_rat
% 5.82/6.02 = ( numeral_numeral_rat @ N ) )
% 5.82/6.02 = ( one = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_eq_numeral_iff
% 5.82/6.02 thf(fact_661_one__eq__numeral__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( one_one_nat
% 5.82/6.02 = ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( one = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_eq_numeral_iff
% 5.82/6.02 thf(fact_662_one__eq__numeral__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( one_one_int
% 5.82/6.02 = ( numeral_numeral_int @ N ) )
% 5.82/6.02 = ( one = N ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_eq_numeral_iff
% 5.82/6.02 thf(fact_663_numeral__eq__one__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( ( numera6690914467698888265omplex @ N )
% 5.82/6.02 = one_one_complex )
% 5.82/6.02 = ( N = one ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_eq_one_iff
% 5.82/6.02 thf(fact_664_numeral__eq__one__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( ( numeral_numeral_real @ N )
% 5.82/6.02 = one_one_real )
% 5.82/6.02 = ( N = one ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_eq_one_iff
% 5.82/6.02 thf(fact_665_numeral__eq__one__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( ( numeral_numeral_rat @ N )
% 5.82/6.02 = one_one_rat )
% 5.82/6.02 = ( N = one ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_eq_one_iff
% 5.82/6.02 thf(fact_666_numeral__eq__one__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( ( numeral_numeral_nat @ N )
% 5.82/6.02 = one_one_nat )
% 5.82/6.02 = ( N = one ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_eq_one_iff
% 5.82/6.02 thf(fact_667_numeral__eq__one__iff,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( ( numeral_numeral_int @ N )
% 5.82/6.02 = one_one_int )
% 5.82/6.02 = ( N = one ) ) ).
% 5.82/6.02
% 5.82/6.02 % numeral_eq_one_iff
% 5.82/6.02 thf(fact_668_distrib__right__numeral,axiom,
% 5.82/6.02 ! [A2: complex,B2: complex,V: num] :
% 5.82/6.02 ( ( times_times_complex @ ( plus_plus_complex @ A2 @ B2 ) @ ( numera6690914467698888265omplex @ V ) )
% 5.82/6.02 = ( plus_plus_complex @ ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B2 @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_right_numeral
% 5.82/6.02 thf(fact_669_distrib__right__numeral,axiom,
% 5.82/6.02 ! [A2: real,B2: real,V: num] :
% 5.82/6.02 ( ( times_times_real @ ( plus_plus_real @ A2 @ B2 ) @ ( numeral_numeral_real @ V ) )
% 5.82/6.02 = ( plus_plus_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B2 @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_right_numeral
% 5.82/6.02 thf(fact_670_distrib__right__numeral,axiom,
% 5.82/6.02 ! [A2: rat,B2: rat,V: num] :
% 5.82/6.02 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ ( numeral_numeral_rat @ V ) )
% 5.82/6.02 = ( plus_plus_rat @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B2 @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_right_numeral
% 5.82/6.02 thf(fact_671_distrib__right__numeral,axiom,
% 5.82/6.02 ! [A2: nat,B2: nat,V: num] :
% 5.82/6.02 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.02 = ( plus_plus_nat @ ( times_times_nat @ A2 @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B2 @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_right_numeral
% 5.82/6.02 thf(fact_672_distrib__right__numeral,axiom,
% 5.82/6.02 ! [A2: int,B2: int,V: num] :
% 5.82/6.02 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.02 = ( plus_plus_int @ ( times_times_int @ A2 @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B2 @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_right_numeral
% 5.82/6.02 thf(fact_673_distrib__left__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: complex,C2: complex] :
% 5.82/6.02 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B2 @ C2 ) )
% 5.82/6.02 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_left_numeral
% 5.82/6.02 thf(fact_674_distrib__left__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: real,C2: real] :
% 5.82/6.02 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.02 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B2 ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_left_numeral
% 5.82/6.02 thf(fact_675_distrib__left__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: rat,C2: rat] :
% 5.82/6.02 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.02 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_left_numeral
% 5.82/6.02 thf(fact_676_distrib__left__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: nat,C2: nat] :
% 5.82/6.02 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.02 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_left_numeral
% 5.82/6.02 thf(fact_677_distrib__left__numeral,axiom,
% 5.82/6.02 ! [V: num,B2: int,C2: int] :
% 5.82/6.02 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.02 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C2 ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % distrib_left_numeral
% 5.82/6.02 thf(fact_678_power__inject__exp,axiom,
% 5.82/6.02 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.02 => ( ( ( power_8256067586552552935nteger @ A2 @ M )
% 5.82/6.02 = ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.02 = ( M = N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_inject_exp
% 5.82/6.02 thf(fact_679_power__inject__exp,axiom,
% 5.82/6.02 ! [A2: real,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.02 => ( ( ( power_power_real @ A2 @ M )
% 5.82/6.02 = ( power_power_real @ A2 @ N ) )
% 5.82/6.02 = ( M = N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_inject_exp
% 5.82/6.02 thf(fact_680_power__inject__exp,axiom,
% 5.82/6.02 ! [A2: rat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.02 => ( ( ( power_power_rat @ A2 @ M )
% 5.82/6.02 = ( power_power_rat @ A2 @ N ) )
% 5.82/6.02 = ( M = N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_inject_exp
% 5.82/6.02 thf(fact_681_power__inject__exp,axiom,
% 5.82/6.02 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.02 => ( ( ( power_power_nat @ A2 @ M )
% 5.82/6.02 = ( power_power_nat @ A2 @ N ) )
% 5.82/6.02 = ( M = N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_inject_exp
% 5.82/6.02 thf(fact_682_power__inject__exp,axiom,
% 5.82/6.02 ! [A2: int,M: nat,N: nat] :
% 5.82/6.02 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.02 => ( ( ( power_power_int @ A2 @ M )
% 5.82/6.02 = ( power_power_int @ A2 @ N ) )
% 5.82/6.02 = ( M = N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % power_inject_exp
% 5.82/6.02 thf(fact_683_diff__Suc__1,axiom,
% 5.82/6.02 ! [N: nat] :
% 5.82/6.02 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.82/6.02 = N ) ).
% 5.82/6.02
% 5.82/6.02 % diff_Suc_1
% 5.82/6.02 thf(fact_684_mult__Suc__right,axiom,
% 5.82/6.02 ! [M: nat,N: nat] :
% 5.82/6.02 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.82/6.02 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % mult_Suc_right
% 5.82/6.02 thf(fact_685_max__0__1_I6_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ one_on7984719198319812577d_enat )
% 5.82/6.02 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(6)
% 5.82/6.02 thf(fact_686_max__0__1_I6_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ one_one_real )
% 5.82/6.02 = ( numeral_numeral_real @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(6)
% 5.82/6.02 thf(fact_687_max__0__1_I6_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat )
% 5.82/6.02 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(6)
% 5.82/6.02 thf(fact_688_max__0__1_I6_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat )
% 5.82/6.02 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(6)
% 5.82/6.02 thf(fact_689_max__0__1_I6_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ one_one_int )
% 5.82/6.02 = ( numeral_numeral_int @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(6)
% 5.82/6.02 thf(fact_690_max__0__1_I5_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.82/6.02 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(5)
% 5.82/6.02 thf(fact_691_max__0__1_I5_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.82/6.02 = ( numeral_numeral_real @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(5)
% 5.82/6.02 thf(fact_692_max__0__1_I5_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.82/6.02 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(5)
% 5.82/6.02 thf(fact_693_max__0__1_I5_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.82/6.02 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(5)
% 5.82/6.02 thf(fact_694_max__0__1_I5_J,axiom,
% 5.82/6.02 ! [X2: num] :
% 5.82/6.02 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.82/6.02 = ( numeral_numeral_int @ X2 ) ) ).
% 5.82/6.02
% 5.82/6.02 % max_0_1(5)
% 5.82/6.02 thf(fact_695_Nat_Oadd__diff__assoc,axiom,
% 5.82/6.02 ! [K: nat,J: nat,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.02 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.82/6.02 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % Nat.add_diff_assoc
% 5.82/6.02 thf(fact_696_Nat_Oadd__diff__assoc2,axiom,
% 5.82/6.02 ! [K: nat,J: nat,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.02 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.82/6.02 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % Nat.add_diff_assoc2
% 5.82/6.02 thf(fact_697_Nat_Odiff__diff__right,axiom,
% 5.82/6.02 ! [K: nat,J: nat,I: nat] :
% 5.82/6.02 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.02 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.82/6.02 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % Nat.diff_diff_right
% 5.82/6.02 thf(fact_698_option_Ocollapse,axiom,
% 5.82/6.02 ! [Option: option4927543243414619207at_nat] :
% 5.82/6.02 ( ( Option != none_P5556105721700978146at_nat )
% 5.82/6.02 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.82/6.02 = Option ) ) ).
% 5.82/6.02
% 5.82/6.02 % option.collapse
% 5.82/6.02 thf(fact_699_option_Ocollapse,axiom,
% 5.82/6.02 ! [Option: option_nat] :
% 5.82/6.02 ( ( Option != none_nat )
% 5.82/6.02 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.82/6.02 = Option ) ) ).
% 5.82/6.02
% 5.82/6.02 % option.collapse
% 5.82/6.02 thf(fact_700_newnodedef,axiom,
% 5.82/6.02 ( newnode
% 5.82/6.02 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( 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 @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % newnodedef
% 5.82/6.02 thf(fact_701_one__plus__numeral,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.82/6.02 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_plus_numeral
% 5.82/6.02 thf(fact_702_one__plus__numeral,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.82/6.02 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_plus_numeral
% 5.82/6.02 thf(fact_703_one__plus__numeral,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.82/6.02 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_plus_numeral
% 5.82/6.02 thf(fact_704_one__plus__numeral,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.82/6.02 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_plus_numeral
% 5.82/6.02 thf(fact_705_one__plus__numeral,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.82/6.02 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.82/6.02
% 5.82/6.02 % one_plus_numeral
% 5.82/6.02 thf(fact_706_numeral__plus__one,axiom,
% 5.82/6.02 ! [N: num] :
% 5.82/6.02 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.82/6.03 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_plus_one
% 5.82/6.03 thf(fact_707_numeral__plus__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.82/6.03 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_plus_one
% 5.82/6.03 thf(fact_708_numeral__plus__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.82/6.03 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_plus_one
% 5.82/6.03 thf(fact_709_numeral__plus__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.82/6.03 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_plus_one
% 5.82/6.03 thf(fact_710_numeral__plus__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.82/6.03 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_plus_one
% 5.82/6.03 thf(fact_711_aktnodedef,axiom,
% 5.82/6.03 ( ( ma != mi )
% 5.82/6.03 => ( ( ord_less_eq_nat @ xa @ ma )
% 5.82/6.03 => ( aktnode
% 5.82/6.03 = ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % aktnodedef
% 5.82/6.03 thf(fact_712_power__strict__increasing__iff,axiom,
% 5.82/6.03 ! [B2: code_integer,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B2 )
% 5.82/6.03 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B2 @ X2 ) @ ( power_8256067586552552935nteger @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing_iff
% 5.82/6.03 thf(fact_713_power__strict__increasing__iff,axiom,
% 5.82/6.03 ! [B2: real,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.03 => ( ( ord_less_real @ ( power_power_real @ B2 @ X2 ) @ ( power_power_real @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing_iff
% 5.82/6.03 thf(fact_714_power__strict__increasing__iff,axiom,
% 5.82/6.03 ! [B2: rat,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ B2 )
% 5.82/6.03 => ( ( ord_less_rat @ ( power_power_rat @ B2 @ X2 ) @ ( power_power_rat @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing_iff
% 5.82/6.03 thf(fact_715_power__strict__increasing__iff,axiom,
% 5.82/6.03 ! [B2: nat,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ B2 )
% 5.82/6.03 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ X2 ) @ ( power_power_nat @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing_iff
% 5.82/6.03 thf(fact_716_power__strict__increasing__iff,axiom,
% 5.82/6.03 ! [B2: int,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ B2 )
% 5.82/6.03 => ( ( ord_less_int @ ( power_power_int @ B2 @ X2 ) @ ( power_power_int @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing_iff
% 5.82/6.03 thf(fact_717_diff__Suc__diff__eq1,axiom,
% 5.82/6.03 ! [K: nat,J: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.03 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.82/6.03 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % diff_Suc_diff_eq1
% 5.82/6.03 thf(fact_718_diff__Suc__diff__eq2,axiom,
% 5.82/6.03 ! [K: nat,J: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.03 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.82/6.03 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % diff_Suc_diff_eq2
% 5.82/6.03 thf(fact_719_Suc__diff,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.03 => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.82/6.03 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.03 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_diff
% 5.82/6.03 thf(fact_720_nested__mint,axiom,
% 5.82/6.03 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.03 => ( ( N
% 5.82/6.03 = ( suc @ ( suc @ Va ) ) )
% 5.82/6.03 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.82/6.03 => ( ( Ma != Mi )
% 5.82/6.03 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nested_mint
% 5.82/6.03 thf(fact_721_one__add__one,axiom,
% 5.82/6.03 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.82/6.03 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_add_one
% 5.82/6.03 thf(fact_722_one__add__one,axiom,
% 5.82/6.03 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.82/6.03 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_add_one
% 5.82/6.03 thf(fact_723_one__add__one,axiom,
% 5.82/6.03 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.82/6.03 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_add_one
% 5.82/6.03 thf(fact_724_one__add__one,axiom,
% 5.82/6.03 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.82/6.03 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_add_one
% 5.82/6.03 thf(fact_725_one__add__one,axiom,
% 5.82/6.03 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.82/6.03 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_add_one
% 5.82/6.03 thf(fact_726_power__increasing__iff,axiom,
% 5.82/6.03 ! [B2: code_integer,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B2 )
% 5.82/6.03 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B2 @ X2 ) @ ( power_8256067586552552935nteger @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing_iff
% 5.82/6.03 thf(fact_727_power__increasing__iff,axiom,
% 5.82/6.03 ! [B2: real,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.03 => ( ( ord_less_eq_real @ ( power_power_real @ B2 @ X2 ) @ ( power_power_real @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing_iff
% 5.82/6.03 thf(fact_728_power__increasing__iff,axiom,
% 5.82/6.03 ! [B2: rat,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ B2 )
% 5.82/6.03 => ( ( ord_less_eq_rat @ ( power_power_rat @ B2 @ X2 ) @ ( power_power_rat @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing_iff
% 5.82/6.03 thf(fact_729_power__increasing__iff,axiom,
% 5.82/6.03 ! [B2: nat,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ B2 )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ X2 ) @ ( power_power_nat @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing_iff
% 5.82/6.03 thf(fact_730_power__increasing__iff,axiom,
% 5.82/6.03 ! [B2: int,X2: nat,Y3: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ B2 )
% 5.82/6.03 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ X2 ) @ ( power_power_int @ B2 @ Y3 ) )
% 5.82/6.03 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing_iff
% 5.82/6.03 thf(fact_731_add__2__eq__Suc_H,axiom,
% 5.82/6.03 ! [N: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( suc @ ( suc @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_2_eq_Suc'
% 5.82/6.03 thf(fact_732_add__2__eq__Suc,axiom,
% 5.82/6.03 ! [N: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.03 = ( suc @ ( suc @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_2_eq_Suc
% 5.82/6.03 thf(fact_733_Suc__1,axiom,
% 5.82/6.03 ( ( suc @ one_one_nat )
% 5.82/6.03 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_1
% 5.82/6.03 thf(fact_734_add__self__div__2,axiom,
% 5.82/6.03 ! [M: nat] :
% 5.82/6.03 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = M ) ).
% 5.82/6.03
% 5.82/6.03 % add_self_div_2
% 5.82/6.03 thf(fact_735_numeral__le__one__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.82/6.03 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_le_one_iff
% 5.82/6.03 thf(fact_736_numeral__le__one__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.82/6.03 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_le_one_iff
% 5.82/6.03 thf(fact_737_numeral__le__one__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.82/6.03 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_le_one_iff
% 5.82/6.03 thf(fact_738_numeral__le__one__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.82/6.03 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_le_one_iff
% 5.82/6.03 thf(fact_739_one__less__numeral__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.82/6.03 = ( ord_less_num @ one @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_less_numeral_iff
% 5.82/6.03 thf(fact_740_one__less__numeral__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.82/6.03 = ( ord_less_num @ one @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_less_numeral_iff
% 5.82/6.03 thf(fact_741_one__less__numeral__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.82/6.03 = ( ord_less_num @ one @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_less_numeral_iff
% 5.82/6.03 thf(fact_742_one__less__numeral__iff,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.82/6.03 = ( ord_less_num @ one @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_less_numeral_iff
% 5.82/6.03 thf(fact_743__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062aktnode_O_A_I_092_060lbrakk_062ma_A_092_060noteq_062_Ami_059_Ax_A_092_060le_062_Ama_092_060rbrakk_062_A_092_060Longrightarrow_062_Aaktnode_A_061_AtreeList_A_B_Ahigh_A_I2_A_K_A2_A_094_A_Iva_Adiv_A2_J_A_K_Athe_A_Ivebt__mint_Asummary_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_J_A_ISuc_A_Iva_Adiv_A2_J_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.82/6.03 ~ ! [Aktnode: vEBT_VEBT] :
% 5.82/6.03 ~ ( ( ma != mi )
% 5.82/6.03 => ( ( ord_less_eq_nat @ xa @ ma )
% 5.82/6.03 => ( Aktnode
% 5.82/6.03 = ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % \<open>\<And>thesis. (\<And>aktnode. (\<lbrakk>ma \<noteq> mi; x \<le> ma\<rbrakk> \<Longrightarrow> aktnode = treeList ! high (2 * 2 ^ (va div 2) * the (vebt_mint summary) + the (vebt_mint (treeList ! the (vebt_mint summary)))) (Suc (va div 2))) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.82/6.03 thf(fact_744_is__num__normalize_I1_J,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( plus_plus_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % is_num_normalize(1)
% 5.82/6.03 thf(fact_745_is__num__normalize_I1_J,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( plus_plus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % is_num_normalize(1)
% 5.82/6.03 thf(fact_746_is__num__normalize_I1_J,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( plus_plus_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % is_num_normalize(1)
% 5.82/6.03 thf(fact_747_subset__Collect__conv,axiom,
% 5.82/6.03 ! [S: set_nat,P: nat > $o] :
% 5.82/6.03 ( ( ord_less_eq_set_nat @ S @ ( collect_nat @ P ) )
% 5.82/6.03 = ( ! [X3: nat] :
% 5.82/6.03 ( ( member_nat @ X3 @ S )
% 5.82/6.03 => ( P @ X3 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % subset_Collect_conv
% 5.82/6.03 thf(fact_748_subset__Collect__conv,axiom,
% 5.82/6.03 ! [S: set_complex,P: complex > $o] :
% 5.82/6.03 ( ( ord_le211207098394363844omplex @ S @ ( collect_complex @ P ) )
% 5.82/6.03 = ( ! [X3: complex] :
% 5.82/6.03 ( ( member_complex @ X3 @ S )
% 5.82/6.03 => ( P @ X3 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % subset_Collect_conv
% 5.82/6.03 thf(fact_749_subset__Collect__conv,axiom,
% 5.82/6.03 ! [S: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.82/6.03 ( ( ord_le2843351958646193337nt_int @ S @ ( collec213857154873943460nt_int @ P ) )
% 5.82/6.03 = ( ! [X3: product_prod_int_int] :
% 5.82/6.03 ( ( member5262025264175285858nt_int @ X3 @ S )
% 5.82/6.03 => ( P @ X3 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % subset_Collect_conv
% 5.82/6.03 thf(fact_750_subset__Collect__conv,axiom,
% 5.82/6.03 ! [S: set_int,P: int > $o] :
% 5.82/6.03 ( ( ord_less_eq_set_int @ S @ ( collect_int @ P ) )
% 5.82/6.03 = ( ! [X3: int] :
% 5.82/6.03 ( ( member_int @ X3 @ S )
% 5.82/6.03 => ( P @ X3 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % subset_Collect_conv
% 5.82/6.03 thf(fact_751_one__plus__numeral__commute,axiom,
% 5.82/6.03 ! [X2: num] :
% 5.82/6.03 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X2 ) )
% 5.82/6.03 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_plus_numeral_commute
% 5.82/6.03 thf(fact_752_one__plus__numeral__commute,axiom,
% 5.82/6.03 ! [X2: num] :
% 5.82/6.03 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.82/6.03 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_plus_numeral_commute
% 5.82/6.03 thf(fact_753_one__plus__numeral__commute,axiom,
% 5.82/6.03 ! [X2: num] :
% 5.82/6.03 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.82/6.03 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_plus_numeral_commute
% 5.82/6.03 thf(fact_754_one__plus__numeral__commute,axiom,
% 5.82/6.03 ! [X2: num] :
% 5.82/6.03 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.82/6.03 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_plus_numeral_commute
% 5.82/6.03 thf(fact_755_one__plus__numeral__commute,axiom,
% 5.82/6.03 ! [X2: num] :
% 5.82/6.03 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.82/6.03 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_plus_numeral_commute
% 5.82/6.03 thf(fact_756_Suc__eq__plus1,axiom,
% 5.82/6.03 ( suc
% 5.82/6.03 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_eq_plus1
% 5.82/6.03 thf(fact_757_plus__1__eq__Suc,axiom,
% 5.82/6.03 ( ( plus_plus_nat @ one_one_nat )
% 5.82/6.03 = suc ) ).
% 5.82/6.03
% 5.82/6.03 % plus_1_eq_Suc
% 5.82/6.03 thf(fact_758_Suc__eq__plus1__left,axiom,
% 5.82/6.03 ( suc
% 5.82/6.03 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_eq_plus1_left
% 5.82/6.03 thf(fact_759_add__Suc__shift,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.82/6.03 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_Suc_shift
% 5.82/6.03 thf(fact_760_add__Suc,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.82/6.03 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_Suc
% 5.82/6.03 thf(fact_761_nat__arith_Osuc1,axiom,
% 5.82/6.03 ! [A: nat,K: nat,A2: nat] :
% 5.82/6.03 ( ( A
% 5.82/6.03 = ( plus_plus_nat @ K @ A2 ) )
% 5.82/6.03 => ( ( suc @ A )
% 5.82/6.03 = ( plus_plus_nat @ K @ ( suc @ A2 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_arith.suc1
% 5.82/6.03 thf(fact_762_less__add__eq__less,axiom,
% 5.82/6.03 ! [K: nat,L: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ K @ L )
% 5.82/6.03 => ( ( ( plus_plus_nat @ M @ L )
% 5.82/6.03 = ( plus_plus_nat @ K @ N ) )
% 5.82/6.03 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_eq_less
% 5.82/6.03 thf(fact_763_trans__less__add2,axiom,
% 5.82/6.03 ! [I: nat,J: nat,M: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I @ J )
% 5.82/6.03 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % trans_less_add2
% 5.82/6.03 thf(fact_764_trans__less__add1,axiom,
% 5.82/6.03 ! [I: nat,J: nat,M: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I @ J )
% 5.82/6.03 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % trans_less_add1
% 5.82/6.03 thf(fact_765_add__less__mono1,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I @ J )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_less_mono1
% 5.82/6.03 thf(fact_766_not__add__less2,axiom,
% 5.82/6.03 ! [J: nat,I: nat] :
% 5.82/6.03 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.82/6.03
% 5.82/6.03 % not_add_less2
% 5.82/6.03 thf(fact_767_not__add__less1,axiom,
% 5.82/6.03 ! [I: nat,J: nat] :
% 5.82/6.03 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.82/6.03
% 5.82/6.03 % not_add_less1
% 5.82/6.03 thf(fact_768_add__less__mono,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I @ J )
% 5.82/6.03 => ( ( ord_less_nat @ K @ L )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_less_mono
% 5.82/6.03 thf(fact_769_add__lessD1,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.82/6.03 => ( ord_less_nat @ I @ K ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_lessD1
% 5.82/6.03 thf(fact_770_le__numeral__extra_I4_J,axiom,
% 5.82/6.03 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.82/6.03
% 5.82/6.03 % le_numeral_extra(4)
% 5.82/6.03 thf(fact_771_le__numeral__extra_I4_J,axiom,
% 5.82/6.03 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.82/6.03
% 5.82/6.03 % le_numeral_extra(4)
% 5.82/6.03 thf(fact_772_le__numeral__extra_I4_J,axiom,
% 5.82/6.03 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.82/6.03
% 5.82/6.03 % le_numeral_extra(4)
% 5.82/6.03 thf(fact_773_le__numeral__extra_I4_J,axiom,
% 5.82/6.03 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.82/6.03
% 5.82/6.03 % le_numeral_extra(4)
% 5.82/6.03 thf(fact_774_less__numeral__extra_I4_J,axiom,
% 5.82/6.03 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.82/6.03
% 5.82/6.03 % less_numeral_extra(4)
% 5.82/6.03 thf(fact_775_less__numeral__extra_I4_J,axiom,
% 5.82/6.03 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.82/6.03
% 5.82/6.03 % less_numeral_extra(4)
% 5.82/6.03 thf(fact_776_less__numeral__extra_I4_J,axiom,
% 5.82/6.03 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.82/6.03
% 5.82/6.03 % less_numeral_extra(4)
% 5.82/6.03 thf(fact_777_less__numeral__extra_I4_J,axiom,
% 5.82/6.03 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.82/6.03
% 5.82/6.03 % less_numeral_extra(4)
% 5.82/6.03 thf(fact_778_add__leE,axiom,
% 5.82/6.03 ! [M: nat,K: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.82/6.03 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.03 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_leE
% 5.82/6.03 thf(fact_779_le__add1,axiom,
% 5.82/6.03 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add1
% 5.82/6.03 thf(fact_780_le__add2,axiom,
% 5.82/6.03 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add2
% 5.82/6.03 thf(fact_781_add__leD1,axiom,
% 5.82/6.03 ! [M: nat,K: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.82/6.03 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_leD1
% 5.82/6.03 thf(fact_782_add__leD2,axiom,
% 5.82/6.03 ! [M: nat,K: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.82/6.03 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_leD2
% 5.82/6.03 thf(fact_783_le__Suc__ex,axiom,
% 5.82/6.03 ! [K: nat,L: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ L )
% 5.82/6.03 => ? [N3: nat] :
% 5.82/6.03 ( L
% 5.82/6.03 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_Suc_ex
% 5.82/6.03 thf(fact_784_add__le__mono,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ( ord_less_eq_nat @ K @ L )
% 5.82/6.03 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_mono
% 5.82/6.03 thf(fact_785_add__le__mono1,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_mono1
% 5.82/6.03 thf(fact_786_trans__le__add1,axiom,
% 5.82/6.03 ! [I: nat,J: nat,M: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % trans_le_add1
% 5.82/6.03 thf(fact_787_trans__le__add2,axiom,
% 5.82/6.03 ! [I: nat,J: nat,M: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % trans_le_add2
% 5.82/6.03 thf(fact_788_nat__le__iff__add,axiom,
% 5.82/6.03 ( ord_less_eq_nat
% 5.82/6.03 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.03 ? [K3: nat] :
% 5.82/6.03 ( N4
% 5.82/6.03 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_le_iff_add
% 5.82/6.03 thf(fact_789_diff__add__inverse2,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.82/6.03 = M ) ).
% 5.82/6.03
% 5.82/6.03 % diff_add_inverse2
% 5.82/6.03 thf(fact_790_diff__add__inverse,axiom,
% 5.82/6.03 ! [N: nat,M: nat] :
% 5.82/6.03 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.82/6.03 = M ) ).
% 5.82/6.03
% 5.82/6.03 % diff_add_inverse
% 5.82/6.03 thf(fact_791_diff__cancel2,axiom,
% 5.82/6.03 ! [M: nat,K: nat,N: nat] :
% 5.82/6.03 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.82/6.03 = ( minus_minus_nat @ M @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % diff_cancel2
% 5.82/6.03 thf(fact_792_Nat_Odiff__cancel,axiom,
% 5.82/6.03 ! [K: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.82/6.03 = ( minus_minus_nat @ M @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % Nat.diff_cancel
% 5.82/6.03 thf(fact_793_left__add__mult__distrib,axiom,
% 5.82/6.03 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_add_mult_distrib
% 5.82/6.03 thf(fact_794_add__mult__distrib2,axiom,
% 5.82/6.03 ! [K: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_mult_distrib2
% 5.82/6.03 thf(fact_795_add__mult__distrib,axiom,
% 5.82/6.03 ! [M: nat,N: nat,K: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_mult_distrib
% 5.82/6.03 thf(fact_796_nat__mult__1__right,axiom,
% 5.82/6.03 ! [N: nat] :
% 5.82/6.03 ( ( times_times_nat @ N @ one_one_nat )
% 5.82/6.03 = N ) ).
% 5.82/6.03
% 5.82/6.03 % nat_mult_1_right
% 5.82/6.03 thf(fact_797_nat__mult__1,axiom,
% 5.82/6.03 ! [N: nat] :
% 5.82/6.03 ( ( times_times_nat @ one_one_nat @ N )
% 5.82/6.03 = N ) ).
% 5.82/6.03
% 5.82/6.03 % nat_mult_1
% 5.82/6.03 thf(fact_798_option_Osel,axiom,
% 5.82/6.03 ! [X22: product_prod_nat_nat] :
% 5.82/6.03 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.82/6.03 = X22 ) ).
% 5.82/6.03
% 5.82/6.03 % option.sel
% 5.82/6.03 thf(fact_799_option_Osel,axiom,
% 5.82/6.03 ! [X22: nat] :
% 5.82/6.03 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.82/6.03 = X22 ) ).
% 5.82/6.03
% 5.82/6.03 % option.sel
% 5.82/6.03 thf(fact_800_option_Oexpand,axiom,
% 5.82/6.03 ! [Option: option_nat,Option2: option_nat] :
% 5.82/6.03 ( ( ( Option = none_nat )
% 5.82/6.03 = ( Option2 = none_nat ) )
% 5.82/6.03 => ( ( ( Option != none_nat )
% 5.82/6.03 => ( ( Option2 != none_nat )
% 5.82/6.03 => ( ( the_nat @ Option )
% 5.82/6.03 = ( the_nat @ Option2 ) ) ) )
% 5.82/6.03 => ( Option = Option2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % option.expand
% 5.82/6.03 thf(fact_801_option_Oexpand,axiom,
% 5.82/6.03 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.82/6.03 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.82/6.03 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.82/6.03 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.82/6.03 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.82/6.03 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.82/6.03 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.82/6.03 => ( Option = Option2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % option.expand
% 5.82/6.03 thf(fact_802_nat__add__max__right,axiom,
% 5.82/6.03 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 5.82/6.03 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_add_max_right
% 5.82/6.03 thf(fact_803_nat__add__max__left,axiom,
% 5.82/6.03 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 5.82/6.03 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_add_max_left
% 5.82/6.03 thf(fact_804_nat__1__add__1,axiom,
% 5.82/6.03 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.82/6.03 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_1_add_1
% 5.82/6.03 thf(fact_805_numeral__Bit0,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_Bit0
% 5.82/6.03 thf(fact_806_numeral__Bit0,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_Bit0
% 5.82/6.03 thf(fact_807_numeral__Bit0,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_Bit0
% 5.82/6.03 thf(fact_808_numeral__Bit0,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_Bit0
% 5.82/6.03 thf(fact_809_numeral__Bit0,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_Bit0
% 5.82/6.03 thf(fact_810_power__add,axiom,
% 5.82/6.03 ! [A2: complex,M: nat,N: nat] :
% 5.82/6.03 ( ( power_power_complex @ A2 @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( times_times_complex @ ( power_power_complex @ A2 @ M ) @ ( power_power_complex @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add
% 5.82/6.03 thf(fact_811_power__add,axiom,
% 5.82/6.03 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.03 ( ( power_8256067586552552935nteger @ A2 @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add
% 5.82/6.03 thf(fact_812_power__add,axiom,
% 5.82/6.03 ! [A2: real,M: nat,N: nat] :
% 5.82/6.03 ( ( power_power_real @ A2 @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( times_times_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add
% 5.82/6.03 thf(fact_813_power__add,axiom,
% 5.82/6.03 ! [A2: rat,M: nat,N: nat] :
% 5.82/6.03 ( ( power_power_rat @ A2 @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( times_times_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add
% 5.82/6.03 thf(fact_814_power__add,axiom,
% 5.82/6.03 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( power_power_nat @ A2 @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( times_times_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add
% 5.82/6.03 thf(fact_815_power__add,axiom,
% 5.82/6.03 ! [A2: int,M: nat,N: nat] :
% 5.82/6.03 ( ( power_power_int @ A2 @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 = ( times_times_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add
% 5.82/6.03 thf(fact_816_less__imp__Suc__add,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ M @ N )
% 5.82/6.03 => ? [K2: nat] :
% 5.82/6.03 ( N
% 5.82/6.03 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_imp_Suc_add
% 5.82/6.03 thf(fact_817_less__iff__Suc__add,axiom,
% 5.82/6.03 ( ord_less_nat
% 5.82/6.03 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.03 ? [K3: nat] :
% 5.82/6.03 ( N4
% 5.82/6.03 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_iff_Suc_add
% 5.82/6.03 thf(fact_818_less__add__Suc2,axiom,
% 5.82/6.03 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_Suc2
% 5.82/6.03 thf(fact_819_less__add__Suc1,axiom,
% 5.82/6.03 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_Suc1
% 5.82/6.03 thf(fact_820_less__natE,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ M @ N )
% 5.82/6.03 => ~ ! [Q4: nat] :
% 5.82/6.03 ( N
% 5.82/6.03 != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_natE
% 5.82/6.03 thf(fact_821_one__le__numeral,axiom,
% 5.82/6.03 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_numeral
% 5.82/6.03 thf(fact_822_one__le__numeral,axiom,
% 5.82/6.03 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_numeral
% 5.82/6.03 thf(fact_823_one__le__numeral,axiom,
% 5.82/6.03 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_numeral
% 5.82/6.03 thf(fact_824_one__le__numeral,axiom,
% 5.82/6.03 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_numeral
% 5.82/6.03 thf(fact_825_not__numeral__less__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.82/6.03
% 5.82/6.03 % not_numeral_less_one
% 5.82/6.03 thf(fact_826_not__numeral__less__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.82/6.03
% 5.82/6.03 % not_numeral_less_one
% 5.82/6.03 thf(fact_827_not__numeral__less__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.82/6.03
% 5.82/6.03 % not_numeral_less_one
% 5.82/6.03 thf(fact_828_not__numeral__less__one,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.82/6.03
% 5.82/6.03 % not_numeral_less_one
% 5.82/6.03 thf(fact_829_mono__nat__linear__lb,axiom,
% 5.82/6.03 ! [F: nat > nat,M: nat,K: nat] :
% 5.82/6.03 ( ! [M5: nat,N3: nat] :
% 5.82/6.03 ( ( ord_less_nat @ M5 @ N3 )
% 5.82/6.03 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N3 ) ) )
% 5.82/6.03 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % mono_nat_linear_lb
% 5.82/6.03 thf(fact_830_numeral__One,axiom,
% 5.82/6.03 ( ( numera6690914467698888265omplex @ one )
% 5.82/6.03 = one_one_complex ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_One
% 5.82/6.03 thf(fact_831_numeral__One,axiom,
% 5.82/6.03 ( ( numeral_numeral_real @ one )
% 5.82/6.03 = one_one_real ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_One
% 5.82/6.03 thf(fact_832_numeral__One,axiom,
% 5.82/6.03 ( ( numeral_numeral_rat @ one )
% 5.82/6.03 = one_one_rat ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_One
% 5.82/6.03 thf(fact_833_numeral__One,axiom,
% 5.82/6.03 ( ( numeral_numeral_nat @ one )
% 5.82/6.03 = one_one_nat ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_One
% 5.82/6.03 thf(fact_834_numeral__One,axiom,
% 5.82/6.03 ( ( numeral_numeral_int @ one )
% 5.82/6.03 = one_one_int ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_One
% 5.82/6.03 thf(fact_835_mult__Suc,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.82/6.03 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_Suc
% 5.82/6.03 thf(fact_836_less__diff__conv,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.82/6.03 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_diff_conv
% 5.82/6.03 thf(fact_837_add__diff__inverse__nat,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ~ ( ord_less_nat @ M @ N )
% 5.82/6.03 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.03 = M ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_diff_inverse_nat
% 5.82/6.03 thf(fact_838_one__le__power,axiom,
% 5.82/6.03 ! [A2: real,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_power
% 5.82/6.03 thf(fact_839_one__le__power,axiom,
% 5.82/6.03 ! [A2: code_integer,N: nat] :
% 5.82/6.03 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_power
% 5.82/6.03 thf(fact_840_one__le__power,axiom,
% 5.82/6.03 ! [A2: rat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_power
% 5.82/6.03 thf(fact_841_one__le__power,axiom,
% 5.82/6.03 ! [A2: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_power
% 5.82/6.03 thf(fact_842_one__le__power,axiom,
% 5.82/6.03 ! [A2: int,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % one_le_power
% 5.82/6.03 thf(fact_843_mlex__bound,axiom,
% 5.82/6.03 ! [A2: nat,A: nat,B2: nat,N7: nat] :
% 5.82/6.03 ( ( ord_less_nat @ A2 @ A )
% 5.82/6.03 => ( ( ord_less_nat @ B2 @ N7 )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( times_times_nat @ A @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % mlex_bound
% 5.82/6.03 thf(fact_844_mlex__fst__decrI,axiom,
% 5.82/6.03 ! [A2: nat,A4: nat,B2: nat,N7: nat,B4: nat] :
% 5.82/6.03 ( ( ord_less_nat @ A2 @ A4 )
% 5.82/6.03 => ( ( ord_less_nat @ B2 @ N7 )
% 5.82/6.03 => ( ( ord_less_nat @ B4 @ N7 )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N7 ) @ B4 ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % mlex_fst_decrI
% 5.82/6.03 thf(fact_845_mlex__snd__decrI,axiom,
% 5.82/6.03 ! [A2: nat,A4: nat,B2: nat,B4: nat,N7: nat] :
% 5.82/6.03 ( ( A2 = A4 )
% 5.82/6.03 => ( ( ord_less_nat @ B2 @ B4 )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N7 ) @ B4 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % mlex_snd_decrI
% 5.82/6.03 thf(fact_846_le__diff__conv,axiom,
% 5.82/6.03 ! [J: nat,K: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.82/6.03 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_diff_conv
% 5.82/6.03 thf(fact_847_Nat_Ole__diff__conv2,axiom,
% 5.82/6.03 ! [K: nat,J: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.03 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.82/6.03 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Nat.le_diff_conv2
% 5.82/6.03 thf(fact_848_Nat_Odiff__add__assoc,axiom,
% 5.82/6.03 ! [K: nat,J: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.03 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.82/6.03 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Nat.diff_add_assoc
% 5.82/6.03 thf(fact_849_Nat_Odiff__add__assoc2,axiom,
% 5.82/6.03 ! [K: nat,J: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.03 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.82/6.03 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Nat.diff_add_assoc2
% 5.82/6.03 thf(fact_850_Nat_Ole__imp__diff__is__add,axiom,
% 5.82/6.03 ! [I: nat,J: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ( ( minus_minus_nat @ J @ I )
% 5.82/6.03 = K )
% 5.82/6.03 = ( J
% 5.82/6.03 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Nat.le_imp_diff_is_add
% 5.82/6.03 thf(fact_851_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: assn,Y3: assn,N: nat] :
% 5.82/6.03 ( ( ( times_times_assn @ X2 @ Y3 )
% 5.82/6.03 = one_one_assn )
% 5.82/6.03 => ( ( times_times_assn @ ( power_power_assn @ X2 @ N ) @ ( power_power_assn @ Y3 @ N ) )
% 5.82/6.03 = one_one_assn ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_852_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: complex,Y3: complex,N: nat] :
% 5.82/6.03 ( ( ( times_times_complex @ X2 @ Y3 )
% 5.82/6.03 = one_one_complex )
% 5.82/6.03 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 5.82/6.03 = one_one_complex ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_853_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: code_integer,Y3: code_integer,N: nat] :
% 5.82/6.03 ( ( ( times_3573771949741848930nteger @ X2 @ Y3 )
% 5.82/6.03 = one_one_Code_integer )
% 5.82/6.03 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ N ) )
% 5.82/6.03 = one_one_Code_integer ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_854_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: real,Y3: real,N: nat] :
% 5.82/6.03 ( ( ( times_times_real @ X2 @ Y3 )
% 5.82/6.03 = one_one_real )
% 5.82/6.03 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 5.82/6.03 = one_one_real ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_855_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: rat,Y3: rat,N: nat] :
% 5.82/6.03 ( ( ( times_times_rat @ X2 @ Y3 )
% 5.82/6.03 = one_one_rat )
% 5.82/6.03 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 5.82/6.03 = one_one_rat ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_856_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: nat,Y3: nat,N: nat] :
% 5.82/6.03 ( ( ( times_times_nat @ X2 @ Y3 )
% 5.82/6.03 = one_one_nat )
% 5.82/6.03 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y3 @ N ) )
% 5.82/6.03 = one_one_nat ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_857_left__right__inverse__power,axiom,
% 5.82/6.03 ! [X2: int,Y3: int,N: nat] :
% 5.82/6.03 ( ( ( times_times_int @ X2 @ Y3 )
% 5.82/6.03 = one_one_int )
% 5.82/6.03 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 5.82/6.03 = one_one_int ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_right_inverse_power
% 5.82/6.03 thf(fact_858_mlex__leI,axiom,
% 5.82/6.03 ! [A2: nat,A4: nat,B2: nat,B4: nat,N7: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ A2 @ A4 )
% 5.82/6.03 => ( ( ord_less_eq_nat @ B2 @ B4 )
% 5.82/6.03 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N7 ) @ B4 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % mlex_leI
% 5.82/6.03 thf(fact_859_power__one__over,axiom,
% 5.82/6.03 ! [A2: complex,N: nat] :
% 5.82/6.03 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A2 ) @ N )
% 5.82/6.03 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_one_over
% 5.82/6.03 thf(fact_860_power__one__over,axiom,
% 5.82/6.03 ! [A2: real,N: nat] :
% 5.82/6.03 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A2 ) @ N )
% 5.82/6.03 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_one_over
% 5.82/6.03 thf(fact_861_power__one__over,axiom,
% 5.82/6.03 ! [A2: rat,N: nat] :
% 5.82/6.03 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) @ N )
% 5.82/6.03 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_one_over
% 5.82/6.03 thf(fact_862_numerals_I1_J,axiom,
% 5.82/6.03 ( ( numeral_numeral_nat @ one )
% 5.82/6.03 = one_one_nat ) ).
% 5.82/6.03
% 5.82/6.03 % numerals(1)
% 5.82/6.03 thf(fact_863_diff__Suc__eq__diff__pred,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.82/6.03 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % diff_Suc_eq_diff_pred
% 5.82/6.03 thf(fact_864_nat__minus__add__max,axiom,
% 5.82/6.03 ! [N: nat,M: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.82/6.03 = ( ord_max_nat @ N @ M ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_minus_add_max
% 5.82/6.03 thf(fact_865_option_Oexhaust__sel,axiom,
% 5.82/6.03 ! [Option: option4927543243414619207at_nat] :
% 5.82/6.03 ( ( Option != none_P5556105721700978146at_nat )
% 5.82/6.03 => ( Option
% 5.82/6.03 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % option.exhaust_sel
% 5.82/6.03 thf(fact_866_option_Oexhaust__sel,axiom,
% 5.82/6.03 ! [Option: option_nat] :
% 5.82/6.03 ( ( Option != none_nat )
% 5.82/6.03 => ( Option
% 5.82/6.03 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % option.exhaust_sel
% 5.82/6.03 thf(fact_867_numeral__code_I2_J,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_code(2)
% 5.82/6.03 thf(fact_868_numeral__code_I2_J,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_code(2)
% 5.82/6.03 thf(fact_869_numeral__code_I2_J,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_code(2)
% 5.82/6.03 thf(fact_870_numeral__code_I2_J,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_code(2)
% 5.82/6.03 thf(fact_871_numeral__code_I2_J,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.82/6.03 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % numeral_code(2)
% 5.82/6.03 thf(fact_872_power__2__mult__step__le,axiom,
% 5.82/6.03 ! [N2: nat,N: nat,K4: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ N2 @ N )
% 5.82/6.03 => ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K4 ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) )
% 5.82/6.03 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_nat @ K4 @ one_one_nat ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_2_mult_step_le
% 5.82/6.03 thf(fact_873_ex__power__ivl2,axiom,
% 5.82/6.03 ! [B2: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.82/6.03 => ? [N3: nat] :
% 5.82/6.03 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N3 ) @ K )
% 5.82/6.03 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ex_power_ivl2
% 5.82/6.03 thf(fact_874_ex__power__ivl1,axiom,
% 5.82/6.03 ! [B2: nat,K: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.03 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.82/6.03 => ? [N3: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N3 ) @ K )
% 5.82/6.03 & ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ex_power_ivl1
% 5.82/6.03 thf(fact_875_less__diff__conv2,axiom,
% 5.82/6.03 ! [K: nat,J: nat,I: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ K @ J )
% 5.82/6.03 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.82/6.03 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_diff_conv2
% 5.82/6.03 thf(fact_876_power__less__power__Suc,axiom,
% 5.82/6.03 ! [A2: code_integer,N: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_power_Suc
% 5.82/6.03 thf(fact_877_power__less__power__Suc,axiom,
% 5.82/6.03 ! [A2: real,N: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_power_Suc
% 5.82/6.03 thf(fact_878_power__less__power__Suc,axiom,
% 5.82/6.03 ! [A2: rat,N: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_power_Suc
% 5.82/6.03 thf(fact_879_power__less__power__Suc,axiom,
% 5.82/6.03 ! [A2: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_power_Suc
% 5.82/6.03 thf(fact_880_power__less__power__Suc,axiom,
% 5.82/6.03 ! [A2: int,N: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_power_Suc
% 5.82/6.03 thf(fact_881_power__gt1__lemma,axiom,
% 5.82/6.03 ! [A2: code_integer,N: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1_lemma
% 5.82/6.03 thf(fact_882_power__gt1__lemma,axiom,
% 5.82/6.03 ! [A2: real,N: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ord_less_real @ one_one_real @ ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1_lemma
% 5.82/6.03 thf(fact_883_power__gt1__lemma,axiom,
% 5.82/6.03 ! [A2: rat,N: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1_lemma
% 5.82/6.03 thf(fact_884_power__gt1__lemma,axiom,
% 5.82/6.03 ! [A2: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1_lemma
% 5.82/6.03 thf(fact_885_power__gt1__lemma,axiom,
% 5.82/6.03 ! [A2: int,N: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ord_less_int @ one_one_int @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1_lemma
% 5.82/6.03 thf(fact_886_power__gt1,axiom,
% 5.82/6.03 ! [A2: code_integer,N: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1
% 5.82/6.03 thf(fact_887_power__gt1,axiom,
% 5.82/6.03 ! [A2: real,N: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ord_less_real @ one_one_real @ ( power_power_real @ A2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1
% 5.82/6.03 thf(fact_888_power__gt1,axiom,
% 5.82/6.03 ! [A2: rat,N: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1
% 5.82/6.03 thf(fact_889_power__gt1,axiom,
% 5.82/6.03 ! [A2: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1
% 5.82/6.03 thf(fact_890_power__gt1,axiom,
% 5.82/6.03 ! [A2: int,N: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ord_less_int @ one_one_int @ ( power_power_int @ A2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_gt1
% 5.82/6.03 thf(fact_891_power__strict__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: code_integer] :
% 5.82/6.03 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing
% 5.82/6.03 thf(fact_892_power__strict__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: real] :
% 5.82/6.03 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing
% 5.82/6.03 thf(fact_893_power__strict__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: rat] :
% 5.82/6.03 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing
% 5.82/6.03 thf(fact_894_power__strict__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: nat] :
% 5.82/6.03 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing
% 5.82/6.03 thf(fact_895_power__strict__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: int] :
% 5.82/6.03 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_strict_increasing
% 5.82/6.03 thf(fact_896_power__less__imp__less__exp,axiom,
% 5.82/6.03 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_imp_less_exp
% 5.82/6.03 thf(fact_897_power__less__imp__less__exp,axiom,
% 5.82/6.03 ! [A2: real,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ( ord_less_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_imp_less_exp
% 5.82/6.03 thf(fact_898_power__less__imp__less__exp,axiom,
% 5.82/6.03 ! [A2: rat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ( ord_less_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_imp_less_exp
% 5.82/6.03 thf(fact_899_power__less__imp__less__exp,axiom,
% 5.82/6.03 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ( ord_less_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_imp_less_exp
% 5.82/6.03 thf(fact_900_power__less__imp__less__exp,axiom,
% 5.82/6.03 ! [A2: int,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ( ord_less_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_less_imp_less_exp
% 5.82/6.03 thf(fact_901_power__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: real] :
% 5.82/6.03 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_eq_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing
% 5.82/6.03 thf(fact_902_power__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: code_integer] :
% 5.82/6.03 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing
% 5.82/6.03 thf(fact_903_power__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: rat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing
% 5.82/6.03 thf(fact_904_power__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing
% 5.82/6.03 thf(fact_905_power__increasing,axiom,
% 5.82/6.03 ! [N: nat,N7: nat,A2: int] :
% 5.82/6.03 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.03 => ( ( ord_less_eq_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ N7 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_increasing
% 5.82/6.03 thf(fact_906_nat__diff__add__eq2,axiom,
% 5.82/6.03 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_diff_add_eq2
% 5.82/6.03 thf(fact_907_nat__diff__add__eq1,axiom,
% 5.82/6.03 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ J @ I )
% 5.82/6.03 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_diff_add_eq1
% 5.82/6.03 thf(fact_908_nat__le__add__iff2,axiom,
% 5.82/6.03 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_le_add_iff2
% 5.82/6.03 thf(fact_909_nat__le__add__iff1,axiom,
% 5.82/6.03 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ J @ I )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_le_add_iff1
% 5.82/6.03 thf(fact_910_nat__eq__add__iff2,axiom,
% 5.82/6.03 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( M
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_eq_add_iff2
% 5.82/6.03 thf(fact_911_nat__eq__add__iff1,axiom,
% 5.82/6.03 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ J @ I )
% 5.82/6.03 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.82/6.03 = N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_eq_add_iff1
% 5.82/6.03 thf(fact_912_left__add__twice,axiom,
% 5.82/6.03 ! [A2: complex,B2: complex] :
% 5.82/6.03 ( ( plus_plus_complex @ A2 @ ( plus_plus_complex @ A2 @ B2 ) )
% 5.82/6.03 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A2 ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_add_twice
% 5.82/6.03 thf(fact_913_left__add__twice,axiom,
% 5.82/6.03 ! [A2: real,B2: real] :
% 5.82/6.03 ( ( plus_plus_real @ A2 @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A2 ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_add_twice
% 5.82/6.03 thf(fact_914_left__add__twice,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat] :
% 5.82/6.03 ( ( plus_plus_rat @ A2 @ ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A2 ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_add_twice
% 5.82/6.03 thf(fact_915_left__add__twice,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_add_twice
% 5.82/6.03 thf(fact_916_left__add__twice,axiom,
% 5.82/6.03 ! [A2: int,B2: int] :
% 5.82/6.03 ( ( plus_plus_int @ A2 @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_add_twice
% 5.82/6.03 thf(fact_917_mult__2__right,axiom,
% 5.82/6.03 ! [Z: complex] :
% 5.82/6.03 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2_right
% 5.82/6.03 thf(fact_918_mult__2__right,axiom,
% 5.82/6.03 ! [Z: real] :
% 5.82/6.03 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2_right
% 5.82/6.03 thf(fact_919_mult__2__right,axiom,
% 5.82/6.03 ! [Z: rat] :
% 5.82/6.03 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2_right
% 5.82/6.03 thf(fact_920_mult__2__right,axiom,
% 5.82/6.03 ! [Z: nat] :
% 5.82/6.03 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2_right
% 5.82/6.03 thf(fact_921_mult__2__right,axiom,
% 5.82/6.03 ! [Z: int] :
% 5.82/6.03 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2_right
% 5.82/6.03 thf(fact_922_mult__2,axiom,
% 5.82/6.03 ! [Z: complex] :
% 5.82/6.03 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.82/6.03 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2
% 5.82/6.03 thf(fact_923_mult__2,axiom,
% 5.82/6.03 ! [Z: real] :
% 5.82/6.03 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.82/6.03 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2
% 5.82/6.03 thf(fact_924_mult__2,axiom,
% 5.82/6.03 ! [Z: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.82/6.03 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2
% 5.82/6.03 thf(fact_925_mult__2,axiom,
% 5.82/6.03 ! [Z: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.82/6.03 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2
% 5.82/6.03 thf(fact_926_mult__2,axiom,
% 5.82/6.03 ! [Z: int] :
% 5.82/6.03 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.82/6.03 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.82/6.03
% 5.82/6.03 % mult_2
% 5.82/6.03 thf(fact_927_one__power2,axiom,
% 5.82/6.03 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = one_one_rat ) ).
% 5.82/6.03
% 5.82/6.03 % one_power2
% 5.82/6.03 thf(fact_928_one__power2,axiom,
% 5.82/6.03 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = one_one_nat ) ).
% 5.82/6.03
% 5.82/6.03 % one_power2
% 5.82/6.03 thf(fact_929_one__power2,axiom,
% 5.82/6.03 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = one_one_real ) ).
% 5.82/6.03
% 5.82/6.03 % one_power2
% 5.82/6.03 thf(fact_930_one__power2,axiom,
% 5.82/6.03 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = one_one_int ) ).
% 5.82/6.03
% 5.82/6.03 % one_power2
% 5.82/6.03 thf(fact_931_one__power2,axiom,
% 5.82/6.03 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = one_one_complex ) ).
% 5.82/6.03
% 5.82/6.03 % one_power2
% 5.82/6.03 thf(fact_932_one__power2,axiom,
% 5.82/6.03 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = one_one_Code_integer ) ).
% 5.82/6.03
% 5.82/6.03 % one_power2
% 5.82/6.03 thf(fact_933_power__le__imp__le__exp,axiom,
% 5.82/6.03 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.03 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_le_imp_le_exp
% 5.82/6.03 thf(fact_934_power__le__imp__le__exp,axiom,
% 5.82/6.03 ! [A2: real,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.03 => ( ( ord_less_eq_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_le_imp_le_exp
% 5.82/6.03 thf(fact_935_power__le__imp__le__exp,axiom,
% 5.82/6.03 ! [A2: rat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.03 => ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_le_imp_le_exp
% 5.82/6.03 thf(fact_936_power__le__imp__le__exp,axiom,
% 5.82/6.03 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_le_imp_le_exp
% 5.82/6.03 thf(fact_937_power__le__imp__le__exp,axiom,
% 5.82/6.03 ! [A2: int,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.03 => ( ( ord_less_eq_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.82/6.03 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_le_imp_le_exp
% 5.82/6.03 thf(fact_938_nat__less__add__iff1,axiom,
% 5.82/6.03 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ J @ I )
% 5.82/6.03 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_less_add_iff1
% 5.82/6.03 thf(fact_939_nat__less__add__iff2,axiom,
% 5.82/6.03 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.03 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.82/6.03 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_less_add_iff2
% 5.82/6.03 thf(fact_940_Suc__n__minus__m__eq,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.03 => ( ( ord_less_nat @ one_one_nat @ M )
% 5.82/6.03 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.03 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_n_minus_m_eq
% 5.82/6.03 thf(fact_941_nat__add__offset__less,axiom,
% 5.82/6.03 ! [Y3: nat,N: nat,X2: nat,M: nat,Sz: nat] :
% 5.82/6.03 ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.03 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( Sz
% 5.82/6.03 = ( plus_plus_nat @ M @ N ) )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ Y3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Sz ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % nat_add_offset_less
% 5.82/6.03 thf(fact_942_power2__sum,axiom,
% 5.82/6.03 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.03 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_sum
% 5.82/6.03 thf(fact_943_power2__sum,axiom,
% 5.82/6.03 ! [X2: complex,Y3: complex] :
% 5.82/6.03 ( ( power_power_complex @ ( plus_plus_complex @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_sum
% 5.82/6.03 thf(fact_944_power2__sum,axiom,
% 5.82/6.03 ! [X2: real,Y3: real] :
% 5.82/6.03 ( ( power_power_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_sum
% 5.82/6.03 thf(fact_945_power2__sum,axiom,
% 5.82/6.03 ! [X2: rat,Y3: rat] :
% 5.82/6.03 ( ( power_power_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_sum
% 5.82/6.03 thf(fact_946_power2__sum,axiom,
% 5.82/6.03 ! [X2: nat,Y3: nat] :
% 5.82/6.03 ( ( power_power_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_sum
% 5.82/6.03 thf(fact_947_power2__sum,axiom,
% 5.82/6.03 ! [X2: int,Y3: int] :
% 5.82/6.03 ( ( power_power_int @ ( plus_plus_int @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_sum
% 5.82/6.03 thf(fact_948_diff__diff__less,axiom,
% 5.82/6.03 ! [I: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I @ ( minus_minus_nat @ M @ ( minus_minus_nat @ M @ N ) ) )
% 5.82/6.03 = ( ( ord_less_nat @ I @ M )
% 5.82/6.03 & ( ord_less_nat @ I @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % diff_diff_less
% 5.82/6.03 thf(fact_949_power2__diff,axiom,
% 5.82/6.03 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.03 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_diff
% 5.82/6.03 thf(fact_950_power2__diff,axiom,
% 5.82/6.03 ! [X2: complex,Y3: complex] :
% 5.82/6.03 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_diff
% 5.82/6.03 thf(fact_951_power2__diff,axiom,
% 5.82/6.03 ! [X2: real,Y3: real] :
% 5.82/6.03 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_diff
% 5.82/6.03 thf(fact_952_power2__diff,axiom,
% 5.82/6.03 ! [X2: rat,Y3: rat] :
% 5.82/6.03 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_diff
% 5.82/6.03 thf(fact_953_power2__diff,axiom,
% 5.82/6.03 ! [X2: int,Y3: int] :
% 5.82/6.03 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.03 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power2_diff
% 5.82/6.03 thf(fact_954_n__less__equal__power__2,axiom,
% 5.82/6.03 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % n_less_equal_power_2
% 5.82/6.03 thf(fact_955_tdeletemimi_H,axiom,
% 5.82/6.03 ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X2 ) @ one_one_nat ) ) ).
% 5.82/6.03
% 5.82/6.03 % tdeletemimi'
% 5.82/6.03 thf(fact_956_invar__vebt_Ointros_I5_J,axiom,
% 5.82/6.03 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.82/6.03 ( ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.82/6.03 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.82/6.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( M
% 5.82/6.03 = ( suc @ N ) )
% 5.82/6.03 => ( ( Deg
% 5.82/6.03 = ( plus_plus_nat @ N @ M ) )
% 5.82/6.03 => ( ! [I2: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X7 ) )
% 5.82/6.03 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.82/6.03 => ( ( ( Mi = Ma )
% 5.82/6.03 => ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 5.82/6.03 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.82/6.03 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.82/6.03 => ( ( ( Mi != Ma )
% 5.82/6.03 => ! [I2: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.82/6.03 = I2 )
% 5.82/6.03 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.82/6.03 & ! [X4: nat] :
% 5.82/6.03 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.82/6.03 = I2 )
% 5.82/6.03 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.82/6.03 => ( ( ord_less_nat @ Mi @ X4 )
% 5.82/6.03 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % invar_vebt.intros(5)
% 5.82/6.03 thf(fact_957_invar__vebt_Ointros_I4_J,axiom,
% 5.82/6.03 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.82/6.03 ( ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.82/6.03 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.82/6.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( M = N )
% 5.82/6.03 => ( ( Deg
% 5.82/6.03 = ( plus_plus_nat @ N @ M ) )
% 5.82/6.03 => ( ! [I2: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X7 ) )
% 5.82/6.03 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.82/6.03 => ( ( ( Mi = Ma )
% 5.82/6.03 => ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 5.82/6.03 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.82/6.03 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.82/6.03 => ( ( ( Mi != Ma )
% 5.82/6.03 => ! [I2: nat] :
% 5.82/6.03 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.82/6.03 = I2 )
% 5.82/6.03 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.82/6.03 & ! [X4: nat] :
% 5.82/6.03 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.82/6.03 = I2 )
% 5.82/6.03 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.82/6.03 => ( ( ord_less_nat @ Mi @ X4 )
% 5.82/6.03 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % invar_vebt.intros(4)
% 5.82/6.03 thf(fact_958_minNull__delete__time__bound_H,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X2 ) )
% 5.82/6.03 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X2 ) @ one_one_nat ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % minNull_delete_time_bound'
% 5.82/6.03 thf(fact_959_delete__bound__height_H,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % delete_bound_height'
% 5.82/6.03 thf(fact_960_del__x__mia,axiom,
% 5.82/6.03 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( X2 = Mi )
% 5.82/6.03 & ( ord_less_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( 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 ) )
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( 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 ) ) ) ) ) )
% 5.82/6.03 = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( 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 ) ) ) ) ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( 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 ) ) ) ) ) )
% 5.82/6.03 = Ma )
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ ( 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 ) ) ) ) ) )
% 5.82/6.03 @ Summary ) )
% 5.82/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_mia
% 5.82/6.03 thf(fact_961_del__x__mi__lets__in__minNull,axiom,
% 5.82/6.03 ! [X2: nat,Mi: 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] :
% 5.82/6.03 ( ( ( X2 = Mi )
% 5.82/6.03 & ( ord_less_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( Xn
% 5.82/6.03 = ( 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 ) ) ) ) ) ) )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( Newnode
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 => ( ( Newlist
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.82/6.03 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( Sn
% 5.82/6.03 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ Xn
% 5.82/6.03 @ ( if_nat @ ( Xn = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ Xn
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ Newlist
% 5.82/6.03 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_mi_lets_in_minNull
% 5.82/6.03 thf(fact_962_del__x__mi__lets__in,axiom,
% 5.82/6.03 ! [X2: nat,Mi: 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] :
% 5.82/6.03 ( ( ( X2 = Mi )
% 5.82/6.03 & ( ord_less_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( Xn
% 5.82/6.03 = ( 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 ) ) ) ) ) ) )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( Newnode
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 => ( ( Newlist
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.82/6.03 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ Xn
% 5.82/6.03 @ ( if_nat @ ( Xn = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ Xn
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ Newlist
% 5.82/6.03 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.82/6.03 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_mi_lets_in
% 5.82/6.03 thf(fact_963_del__x__mi,axiom,
% 5.82/6.03 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat] :
% 5.82/6.03 ( ( ( X2 = Mi )
% 5.82/6.03 & ( ord_less_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( Xn
% 5.82/6.03 = ( 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 ) ) ) ) ) ) )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ Xn
% 5.82/6.03 @ ( if_nat @ ( Xn = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ Xn
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_mi
% 5.82/6.03 thf(fact_964_del__in__range,axiom,
% 5.82/6.03 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.82/6.03 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( X2 = Mi ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( ( X2 = Mi )
% 5.82/6.03 => ( ( 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 ) ) ) ) ) )
% 5.82/6.03 = Ma ) )
% 5.82/6.03 & ( ( X2 != Mi )
% 5.82/6.03 => ( X2 = Ma ) ) )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ ( if_nat @ ( X2 = Mi ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.82/6.03 @ ( 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 @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( 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 @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( X2 = Mi ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( ( X2 = Mi )
% 5.82/6.03 => ( ( 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 ) ) ) ) ) )
% 5.82/6.03 = Ma ) )
% 5.82/6.03 & ( ( X2 != Mi )
% 5.82/6.03 => ( X2 = Ma ) ) )
% 5.82/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( 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 @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ Summary ) )
% 5.82/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_in_range
% 5.82/6.03 thf(fact_965_del__x__not__mia,axiom,
% 5.82/6.03 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.82/6.03 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ Mi
% 5.82/6.03 @ ( if_nat @ ( X2 = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ Mi
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X2 = 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 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_not_mia
% 5.82/6.03 thf(fact_966_maxbmo,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,X2: nat] :
% 5.82/6.03 ( ( ( vEBT_vebt_maxt @ T )
% 5.82/6.03 = ( some_nat @ X2 ) )
% 5.82/6.03 => ( vEBT_V8194947554948674370ptions @ T @ X2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % maxbmo
% 5.82/6.03 thf(fact_967_maxt__member,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( ( ( vEBT_vebt_maxt @ T )
% 5.82/6.03 = ( some_nat @ Maxi ) )
% 5.82/6.03 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % maxt_member
% 5.82/6.03 thf(fact_968_VEBT_Oinject_I1_J,axiom,
% 5.82/6.03 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.82/6.03 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.82/6.03 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.82/6.03 = ( ( X11 = Y11 )
% 5.82/6.03 & ( X12 = Y12 )
% 5.82/6.03 & ( X13 = Y13 )
% 5.82/6.03 & ( X14 = Y14 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % VEBT.inject(1)
% 5.82/6.03 thf(fact_969_maxt__corr__help,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X2: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( ( ( vEBT_vebt_maxt @ T )
% 5.82/6.03 = ( some_nat @ Maxi ) )
% 5.82/6.03 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.82/6.03 => ( ord_less_eq_nat @ X2 @ Maxi ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % maxt_corr_help
% 5.82/6.03 thf(fact_970_maxt__corr,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( ( ( vEBT_vebt_maxt @ T )
% 5.82/6.03 = ( some_nat @ X2 ) )
% 5.82/6.03 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % maxt_corr
% 5.82/6.03 thf(fact_971_maxt__sound,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.82/6.03 => ( ( vEBT_vebt_maxt @ T )
% 5.82/6.03 = ( some_nat @ X2 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % maxt_sound
% 5.82/6.03 thf(fact_972_semiring__norm_I6_J,axiom,
% 5.82/6.03 ! [M: num,N: num] :
% 5.82/6.03 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.82/6.03 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % semiring_norm(6)
% 5.82/6.03 thf(fact_973_summaxma,axiom,
% 5.82/6.03 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.82/6.03 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % summaxma
% 5.82/6.03 thf(fact_974_semiring__norm_I2_J,axiom,
% 5.82/6.03 ( ( plus_plus_num @ one @ one )
% 5.82/6.03 = ( bit0 @ one ) ) ).
% 5.82/6.03
% 5.82/6.03 % semiring_norm(2)
% 5.82/6.03 thf(fact_975_Suc__numeral,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.82/6.03 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_numeral
% 5.82/6.03 thf(fact_976_power__add__numeral,axiom,
% 5.82/6.03 ! [A2: complex,M: num,N: num] :
% 5.82/6.03 ( ( times_times_complex @ ( power_power_complex @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A2 @ ( numeral_numeral_nat @ N ) ) )
% 5.82/6.03 = ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral
% 5.82/6.03 thf(fact_977_power__add__numeral,axiom,
% 5.82/6.03 ! [A2: code_integer,M: num,N: num] :
% 5.82/6.03 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ N ) ) )
% 5.82/6.03 = ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral
% 5.82/6.03 thf(fact_978_power__add__numeral,axiom,
% 5.82/6.03 ! [A2: real,M: num,N: num] :
% 5.82/6.03 ( ( times_times_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ N ) ) )
% 5.82/6.03 = ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral
% 5.82/6.03 thf(fact_979_power__add__numeral,axiom,
% 5.82/6.03 ! [A2: rat,M: num,N: num] :
% 5.82/6.03 ( ( times_times_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ N ) ) )
% 5.82/6.03 = ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral
% 5.82/6.03 thf(fact_980_power__add__numeral,axiom,
% 5.82/6.03 ! [A2: nat,M: num,N: num] :
% 5.82/6.03 ( ( times_times_nat @ ( power_power_nat @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A2 @ ( numeral_numeral_nat @ N ) ) )
% 5.82/6.03 = ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral
% 5.82/6.03 thf(fact_981_power__add__numeral,axiom,
% 5.82/6.03 ! [A2: int,M: num,N: num] :
% 5.82/6.03 ( ( times_times_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ N ) ) )
% 5.82/6.03 = ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral
% 5.82/6.03 thf(fact_982_power__add__numeral2,axiom,
% 5.82/6.03 ! [A2: complex,M: num,N: num,B2: complex] :
% 5.82/6.03 ( ( times_times_complex @ ( power_power_complex @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A2 @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.82/6.03 = ( times_times_complex @ ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral2
% 5.82/6.03 thf(fact_983_power__add__numeral2,axiom,
% 5.82/6.03 ! [A2: code_integer,M: num,N: num,B2: code_integer] :
% 5.82/6.03 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.82/6.03 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral2
% 5.82/6.03 thf(fact_984_power__add__numeral2,axiom,
% 5.82/6.03 ! [A2: real,M: num,N: num,B2: real] :
% 5.82/6.03 ( ( times_times_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.82/6.03 = ( times_times_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral2
% 5.82/6.03 thf(fact_985_power__add__numeral2,axiom,
% 5.82/6.03 ! [A2: rat,M: num,N: num,B2: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.82/6.03 = ( times_times_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral2
% 5.82/6.03 thf(fact_986_power__add__numeral2,axiom,
% 5.82/6.03 ! [A2: nat,M: num,N: num,B2: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( power_power_nat @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A2 @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.82/6.03 = ( times_times_nat @ ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral2
% 5.82/6.03 thf(fact_987_power__add__numeral2,axiom,
% 5.82/6.03 ! [A2: int,M: num,N: num,B2: int] :
% 5.82/6.03 ( ( times_times_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.82/6.03 = ( times_times_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % power_add_numeral2
% 5.82/6.03 thf(fact_988_del__x__not__mi__newnode__not__nil,axiom,
% 5.82/6.03 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.82/6.03 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( Newnode
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( Newlist
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X2 = 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_not_mi_newnode_not_nil
% 5.82/6.03 thf(fact_989_del__x__mi__lets__in__not__minNull,axiom,
% 5.82/6.03 ! [X2: nat,Mi: 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] :
% 5.82/6.03 ( ( ( X2 = Mi )
% 5.82/6.03 & ( ord_less_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( Xn
% 5.82/6.03 = ( 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 ) ) ) ) ) ) )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( Newnode
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 => ( ( Newlist
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.82/6.03 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_mi_lets_in_not_minNull
% 5.82/6.03 thf(fact_990_del__x__not__mi,axiom,
% 5.82/6.03 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.82/6.03 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( Newnode
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 => ( ( Newlist
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ Mi
% 5.82/6.03 @ ( if_nat @ ( X2 = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ Mi
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ Newlist
% 5.82/6.03 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.82/6.03 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X2 = 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_not_mi
% 5.82/6.03 thf(fact_991_del__x__not__mi__new__node__nil,axiom,
% 5.82/6.03 ! [Mi: nat,X2: 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] :
% 5.82/6.03 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.82/6.03 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.82/6.03 => ( ( Mi != Ma )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.03 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = H2 )
% 5.82/6.03 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = L )
% 5.82/6.03 => ( ( Newnode
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.03 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.82/6.03 => ( ( Sn
% 5.82/6.03 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.82/6.03 => ( ( Newlist
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.82/6.03 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ Mi
% 5.82/6.03 @ ( if_nat @ ( X2 = Ma )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ Mi
% 5.82/6.03 @ ( 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 ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ Deg
% 5.82/6.03 @ Newlist
% 5.82/6.03 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % del_x_not_mi_new_node_nil
% 5.82/6.03 thf(fact_992_z1pdiv2,axiom,
% 5.82/6.03 ! [B2: int] :
% 5.82/6.03 ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.03 = B2 ) ).
% 5.82/6.03
% 5.82/6.03 % z1pdiv2
% 5.82/6.03 thf(fact_993_add__One__commute,axiom,
% 5.82/6.03 ! [N: num] :
% 5.82/6.03 ( ( plus_plus_num @ one @ N )
% 5.82/6.03 = ( plus_plus_num @ N @ one ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_One_commute
% 5.82/6.03 thf(fact_994_add__diff__assoc__enat,axiom,
% 5.82/6.03 ! [Z: extended_enat,Y3: extended_enat,X2: extended_enat] :
% 5.82/6.03 ( ( ord_le2932123472753598470d_enat @ Z @ Y3 )
% 5.82/6.03 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y3 @ Z ) )
% 5.82/6.03 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_diff_assoc_enat
% 5.82/6.03 thf(fact_995_Suc__nat__number__of__add,axiom,
% 5.82/6.03 ! [V: num,N: nat] :
% 5.82/6.03 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.82/6.03 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.82/6.03
% 5.82/6.03 % Suc_nat_number_of_add
% 5.82/6.03 thf(fact_996_set__vebt__def,axiom,
% 5.82/6.03 ( vEBT_set_vebt
% 5.82/6.03 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % set_vebt_def
% 5.82/6.03 thf(fact_997_invar__vebt_Ointros_I2_J,axiom,
% 5.82/6.03 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.82/6.03 ( ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.82/6.03 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.82/6.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( M = N )
% 5.82/6.03 => ( ( Deg
% 5.82/6.03 = ( plus_plus_nat @ N @ M ) )
% 5.82/6.03 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.82/6.03 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % invar_vebt.intros(2)
% 5.82/6.03 thf(fact_998_invar__vebt_Ointros_I3_J,axiom,
% 5.82/6.03 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.82/6.03 ( ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.82/6.03 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.82/6.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.03 => ( ( M
% 5.82/6.03 = ( suc @ N ) )
% 5.82/6.03 => ( ( Deg
% 5.82/6.03 = ( plus_plus_nat @ N @ M ) )
% 5.82/6.03 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.82/6.03 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 5.82/6.03 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % invar_vebt.intros(3)
% 5.82/6.03 thf(fact_999_vebt__delete_Osimps_I7_J,axiom,
% 5.82/6.03 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.03 | ( ord_less_nat @ Ma @ X2 ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 5.82/6.03 & ( ~ ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.03 | ( ord_less_nat @ Ma @ X2 ) )
% 5.82/6.03 => ( ( ( ( X2 = Mi )
% 5.82/6.03 & ( X2 = Ma ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 5.82/6.03 & ( ~ ( ( X2 = Mi )
% 5.82/6.03 & ( X2 = Ma ) )
% 5.82/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.03 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( X2 = Mi ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( ( X2 = Mi )
% 5.82/6.03 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.82/6.03 = Ma ) )
% 5.82/6.03 & ( ( X2 != Mi )
% 5.82/6.03 => ( X2 = Ma ) ) )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 = none_nat )
% 5.82/6.03 @ ( if_nat @ ( X2 = Mi ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.82/6.03 @ ( 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 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ ( suc @ ( suc @ Va ) )
% 5.82/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ ( vEBT_Node
% 5.82/6.03 @ ( some_P7363390416028606310at_nat
% 5.82/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( X2 = Mi ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.82/6.03 @ ( if_nat
% 5.82/6.03 @ ( ( ( X2 = Mi )
% 5.82/6.03 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.82/6.03 = Ma ) )
% 5.82/6.03 & ( ( X2 != Mi )
% 5.82/6.03 => ( X2 = Ma ) ) )
% 5.82/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( 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 @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.03 @ Ma ) ) )
% 5.82/6.03 @ ( suc @ ( suc @ Va ) )
% 5.82/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.03 @ Summary ) )
% 5.82/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % vebt_delete.simps(7)
% 5.82/6.03 thf(fact_1000_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,
% 5.82/6.03 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.03 ( ( ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.03 | ( ord_less_nat @ Ma @ X2 ) )
% 5.82/6.03 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = one_one_nat ) )
% 5.82/6.03 & ( ~ ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.03 | ( ord_less_nat @ Ma @ X2 ) )
% 5.82/6.03 => ( ( ( ( X2 = Mi )
% 5.82/6.03 & ( X2 = Ma ) )
% 5.82/6.03 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = one_one_nat ) )
% 5.82/6.03 & ( ~ ( ( X2 = Mi )
% 5.82/6.03 & ( X2 = Ma ) )
% 5.82/6.03 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.03 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(7)
% 5.82/6.03 thf(fact_1001_sum__squares__bound,axiom,
% 5.82/6.03 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % sum_squares_bound
% 5.82/6.03 thf(fact_1002_sum__squares__bound,axiom,
% 5.82/6.03 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y3 ) @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % sum_squares_bound
% 5.82/6.03 thf(fact_1003_cnt__bound_H,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.03 => ( 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 ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % cnt_bound'
% 5.82/6.03 thf(fact_1004__C7_OIH_C_I2_J,axiom,
% 5.82/6.03 ! [Xa: nat,Xb: nat,Xc: nat,Xd: nat,Xe: vEBT_VEBT,Xf: list_VEBT_VEBT,N: nat,Ti: vEBT_VEBTi] :
% 5.82/6.03 ( ~ ( ( ord_less_nat @ xa @ mi )
% 5.82/6.03 | ( ord_less_nat @ ma @ xa ) )
% 5.82/6.03 => ( ~ ( ( xa = mi )
% 5.82/6.03 & ( xa = ma ) )
% 5.82/6.03 => ( ( ( ( xa = mi )
% 5.82/6.03 => ( Xa
% 5.82/6.03 = ( 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 @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) )
% 5.82/6.03 & ( ( xa != mi )
% 5.82/6.03 => ( Xa = xa ) ) )
% 5.82/6.03 => ( ( ( ( xa = mi )
% 5.82/6.03 => ( Xb = Xa ) )
% 5.82/6.03 & ( ( xa != mi )
% 5.82/6.03 => ( Xb = mi ) ) )
% 5.82/6.03 => ( ( Xc
% 5.82/6.03 = ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.03 => ( ( Xd
% 5.82/6.03 = ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.03 => ( ( ord_less_nat @ Xd @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.82/6.03 => ( ( Xe
% 5.82/6.03 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ Xd ) @ Xc ) )
% 5.82/6.03 => ( ( Xf
% 5.82/6.03 = ( list_u1324408373059187874T_VEBT @ treeList @ Xd @ Xe ) )
% 5.82/6.03 => ( ( vEBT_VEBT_minNull @ Xe )
% 5.82/6.03 => ( ( vEBT_invar_vebt @ summary @ N )
% 5.82/6.03 => ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ summary @ Ti ) @ ( vEBT_V1365221501068881998eletei @ summary @ Ti @ Xd ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ summary @ Xd ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % "7.IH"(2)
% 5.82/6.03 thf(fact_1005_height__node,axiom,
% 5.82/6.03 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.82/6.03 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.82/6.03 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % height_node
% 5.82/6.03 thf(fact_1006_le__add__diff__inverse,axiom,
% 5.82/6.03 ! [B2: real,A2: real] :
% 5.82/6.03 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_real @ B2 @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse
% 5.82/6.03 thf(fact_1007_le__add__diff__inverse,axiom,
% 5.82/6.03 ! [B2: rat,A2: rat] :
% 5.82/6.03 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_rat @ B2 @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse
% 5.82/6.03 thf(fact_1008_le__add__diff__inverse,axiom,
% 5.82/6.03 ! [B2: nat,A2: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse
% 5.82/6.03 thf(fact_1009_le__add__diff__inverse,axiom,
% 5.82/6.03 ! [B2: int,A2: int] :
% 5.82/6.03 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse
% 5.82/6.03 thf(fact_1010_le__add__diff__inverse2,axiom,
% 5.82/6.03 ! [B2: real,A2: real] :
% 5.82/6.03 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_real @ ( minus_minus_real @ A2 @ B2 ) @ B2 )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse2
% 5.82/6.03 thf(fact_1011_le__add__diff__inverse2,axiom,
% 5.82/6.03 ! [B2: rat,A2: rat] :
% 5.82/6.03 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse2
% 5.82/6.03 thf(fact_1012_le__add__diff__inverse2,axiom,
% 5.82/6.03 ! [B2: nat,A2: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse2
% 5.82/6.03 thf(fact_1013_le__add__diff__inverse2,axiom,
% 5.82/6.03 ! [B2: int,A2: int] :
% 5.82/6.03 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.03 => ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % le_add_diff_inverse2
% 5.82/6.03 thf(fact_1014__C7_OIH_C_I1_J,axiom,
% 5.82/6.03 ! [Xa: nat,Xb: nat,Xc: nat,Xd: nat,N: nat,Ti: vEBT_VEBTi] :
% 5.82/6.03 ( ~ ( ( ord_less_nat @ xa @ mi )
% 5.82/6.03 | ( ord_less_nat @ ma @ xa ) )
% 5.82/6.03 => ( ~ ( ( xa = mi )
% 5.82/6.03 & ( xa = ma ) )
% 5.82/6.03 => ( ( ( ( xa = mi )
% 5.82/6.03 => ( Xa
% 5.82/6.03 = ( 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 @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) )
% 5.82/6.03 & ( ( xa != mi )
% 5.82/6.03 => ( Xa = xa ) ) )
% 5.82/6.03 => ( ( ( ( xa = mi )
% 5.82/6.03 => ( Xb = Xa ) )
% 5.82/6.03 & ( ( xa != mi )
% 5.82/6.03 => ( Xb = mi ) ) )
% 5.82/6.03 => ( ( Xc
% 5.82/6.03 = ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.03 => ( ( Xd
% 5.82/6.03 = ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.03 => ( ( ord_less_nat @ Xd @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.82/6.03 => ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ Xd ) @ N )
% 5.82/6.03 => ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ treeList @ Xd ) @ Ti ) @ ( vEBT_V1365221501068881998eletei @ ( nth_VEBT_VEBT @ treeList @ Xd ) @ Ti @ Xc ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ Xd ) @ Xc ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % "7.IH"(1)
% 5.82/6.03 thf(fact_1015_div__exp__eq,axiom,
% 5.82/6.03 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.03 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.03 = ( divide6298287555418463151nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % div_exp_eq
% 5.82/6.03 thf(fact_1016_div__exp__eq,axiom,
% 5.82/6.03 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.03 ( ( divide_divide_nat @ ( divide_divide_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.03 = ( divide_divide_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % div_exp_eq
% 5.82/6.03 thf(fact_1017_div__exp__eq,axiom,
% 5.82/6.03 ! [A2: int,M: nat,N: nat] :
% 5.82/6.03 ( ( divide_divide_int @ ( divide_divide_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.03 = ( divide_divide_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % div_exp_eq
% 5.82/6.03 thf(fact_1018_bits__div__by__1,axiom,
% 5.82/6.03 ! [A2: nat] :
% 5.82/6.03 ( ( divide_divide_nat @ A2 @ one_one_nat )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % bits_div_by_1
% 5.82/6.03 thf(fact_1019_bits__div__by__1,axiom,
% 5.82/6.03 ! [A2: int] :
% 5.82/6.03 ( ( divide_divide_int @ A2 @ one_one_int )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % bits_div_by_1
% 5.82/6.03 thf(fact_1020_div__by__1,axiom,
% 5.82/6.03 ! [A2: complex] :
% 5.82/6.03 ( ( divide1717551699836669952omplex @ A2 @ one_one_complex )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % div_by_1
% 5.82/6.03 thf(fact_1021_div__by__1,axiom,
% 5.82/6.03 ! [A2: real] :
% 5.82/6.03 ( ( divide_divide_real @ A2 @ one_one_real )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % div_by_1
% 5.82/6.03 thf(fact_1022_div__by__1,axiom,
% 5.82/6.03 ! [A2: rat] :
% 5.82/6.03 ( ( divide_divide_rat @ A2 @ one_one_rat )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % div_by_1
% 5.82/6.03 thf(fact_1023_div__by__1,axiom,
% 5.82/6.03 ! [A2: nat] :
% 5.82/6.03 ( ( divide_divide_nat @ A2 @ one_one_nat )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % div_by_1
% 5.82/6.03 thf(fact_1024_div__by__1,axiom,
% 5.82/6.03 ! [A2: int] :
% 5.82/6.03 ( ( divide_divide_int @ A2 @ one_one_int )
% 5.82/6.03 = A2 ) ).
% 5.82/6.03
% 5.82/6.03 % div_by_1
% 5.82/6.03 thf(fact_1025_vebt__inserti_H__rf__abstr,axiom,
% 5.82/6.03 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] : ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X2 ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % vebt_inserti'_rf_abstr
% 5.82/6.03 thf(fact_1026_linorder__neqE__linordered__idom,axiom,
% 5.82/6.03 ! [X2: real,Y3: real] :
% 5.82/6.03 ( ( X2 != Y3 )
% 5.82/6.03 => ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.82/6.03 => ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % linorder_neqE_linordered_idom
% 5.82/6.03 thf(fact_1027_linorder__neqE__linordered__idom,axiom,
% 5.82/6.03 ! [X2: rat,Y3: rat] :
% 5.82/6.03 ( ( X2 != Y3 )
% 5.82/6.03 => ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.03 => ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % linorder_neqE_linordered_idom
% 5.82/6.03 thf(fact_1028_linorder__neqE__linordered__idom,axiom,
% 5.82/6.03 ! [X2: int,Y3: int] :
% 5.82/6.03 ( ( X2 != Y3 )
% 5.82/6.03 => ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.82/6.03 => ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % linorder_neqE_linordered_idom
% 5.82/6.03 thf(fact_1029_combine__common__factor,axiom,
% 5.82/6.03 ! [A2: real,E: real,B2: real,C2: real] :
% 5.82/6.03 ( ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ C2 ) )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A2 @ B2 ) @ E ) @ C2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % combine_common_factor
% 5.82/6.03 thf(fact_1030_combine__common__factor,axiom,
% 5.82/6.03 ! [A2: rat,E: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ C2 ) )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ E ) @ C2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % combine_common_factor
% 5.82/6.03 thf(fact_1031_combine__common__factor,axiom,
% 5.82/6.03 ! [A2: nat,E: nat,B2: nat,C2: nat] :
% 5.82/6.03 ( ( plus_plus_nat @ ( times_times_nat @ A2 @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B2 @ E ) @ C2 ) )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ E ) @ C2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % combine_common_factor
% 5.82/6.03 thf(fact_1032_combine__common__factor,axiom,
% 5.82/6.03 ! [A2: int,E: int,B2: int,C2: int] :
% 5.82/6.03 ( ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ C2 ) )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ E ) @ C2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % combine_common_factor
% 5.82/6.03 thf(fact_1033_distrib__right,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_right
% 5.82/6.03 thf(fact_1034_distrib__right,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_right
% 5.82/6.03 thf(fact_1035_distrib__right,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_right
% 5.82/6.03 thf(fact_1036_distrib__right,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_right
% 5.82/6.03 thf(fact_1037_distrib__left,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ A2 @ B2 ) @ ( times_times_real @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_left
% 5.82/6.03 thf(fact_1038_distrib__left,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_left
% 5.82/6.03 thf(fact_1039_distrib__left,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.03 ( ( times_times_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ A2 @ B2 ) @ ( times_times_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_left
% 5.82/6.03 thf(fact_1040_distrib__left,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % distrib_left
% 5.82/6.03 thf(fact_1041_comm__semiring__class_Odistrib,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % comm_semiring_class.distrib
% 5.82/6.03 thf(fact_1042_comm__semiring__class_Odistrib,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % comm_semiring_class.distrib
% 5.82/6.03 thf(fact_1043_comm__semiring__class_Odistrib,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % comm_semiring_class.distrib
% 5.82/6.03 thf(fact_1044_comm__semiring__class_Odistrib,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % comm_semiring_class.distrib
% 5.82/6.03 thf(fact_1045_ring__class_Oring__distribs_I1_J,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ A2 @ B2 ) @ ( times_times_real @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ring_class.ring_distribs(1)
% 5.82/6.03 thf(fact_1046_ring__class_Oring__distribs_I1_J,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ring_class.ring_distribs(1)
% 5.82/6.03 thf(fact_1047_ring__class_Oring__distribs_I1_J,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ring_class.ring_distribs(1)
% 5.82/6.03 thf(fact_1048_ring__class_Oring__distribs_I2_J,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ring_class.ring_distribs(2)
% 5.82/6.03 thf(fact_1049_ring__class_Oring__distribs_I2_J,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ring_class.ring_distribs(2)
% 5.82/6.03 thf(fact_1050_ring__class_Oring__distribs_I2_J,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % ring_class.ring_distribs(2)
% 5.82/6.03 thf(fact_1051_right__diff__distrib_H,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ A2 @ ( minus_minus_real @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_real @ ( times_times_real @ A2 @ B2 ) @ ( times_times_real @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib'
% 5.82/6.03 thf(fact_1052_right__diff__distrib_H,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ A2 @ ( minus_minus_rat @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib'
% 5.82/6.03 thf(fact_1053_right__diff__distrib_H,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.03 ( ( times_times_nat @ A2 @ ( minus_minus_nat @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_nat @ ( times_times_nat @ A2 @ B2 ) @ ( times_times_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib'
% 5.82/6.03 thf(fact_1054_right__diff__distrib_H,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ A2 @ ( minus_minus_int @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib'
% 5.82/6.03 thf(fact_1055_left__diff__distrib_H,axiom,
% 5.82/6.03 ! [B2: real,C2: real,A2: real] :
% 5.82/6.03 ( ( times_times_real @ ( minus_minus_real @ B2 @ C2 ) @ A2 )
% 5.82/6.03 = ( minus_minus_real @ ( times_times_real @ B2 @ A2 ) @ ( times_times_real @ C2 @ A2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib'
% 5.82/6.03 thf(fact_1056_left__diff__distrib_H,axiom,
% 5.82/6.03 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( minus_minus_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.03 = ( minus_minus_rat @ ( times_times_rat @ B2 @ A2 ) @ ( times_times_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib'
% 5.82/6.03 thf(fact_1057_left__diff__distrib_H,axiom,
% 5.82/6.03 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.03 ( ( times_times_nat @ ( minus_minus_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.03 = ( minus_minus_nat @ ( times_times_nat @ B2 @ A2 ) @ ( times_times_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib'
% 5.82/6.03 thf(fact_1058_left__diff__distrib_H,axiom,
% 5.82/6.03 ! [B2: int,C2: int,A2: int] :
% 5.82/6.03 ( ( times_times_int @ ( minus_minus_int @ B2 @ C2 ) @ A2 )
% 5.82/6.03 = ( minus_minus_int @ ( times_times_int @ B2 @ A2 ) @ ( times_times_int @ C2 @ A2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib'
% 5.82/6.03 thf(fact_1059_right__diff__distrib,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ A2 @ ( minus_minus_real @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_real @ ( times_times_real @ A2 @ B2 ) @ ( times_times_real @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib
% 5.82/6.03 thf(fact_1060_right__diff__distrib,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ A2 @ ( minus_minus_rat @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib
% 5.82/6.03 thf(fact_1061_right__diff__distrib,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ A2 @ ( minus_minus_int @ B2 @ C2 ) )
% 5.82/6.03 = ( minus_minus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % right_diff_distrib
% 5.82/6.03 thf(fact_1062_left__diff__distrib,axiom,
% 5.82/6.03 ! [A2: real,B2: real,C2: real] :
% 5.82/6.03 ( ( times_times_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( minus_minus_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib
% 5.82/6.03 thf(fact_1063_left__diff__distrib,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.03 ( ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( minus_minus_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib
% 5.82/6.03 thf(fact_1064_left__diff__distrib,axiom,
% 5.82/6.03 ! [A2: int,B2: int,C2: int] :
% 5.82/6.03 ( ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.03 = ( minus_minus_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % left_diff_distrib
% 5.82/6.03 thf(fact_1065_lambda__one,axiom,
% 5.82/6.03 ( ( ^ [X3: assn] : X3 )
% 5.82/6.03 = ( times_times_assn @ one_one_assn ) ) ).
% 5.82/6.03
% 5.82/6.03 % lambda_one
% 5.82/6.03 thf(fact_1066_lambda__one,axiom,
% 5.82/6.03 ( ( ^ [X3: real] : X3 )
% 5.82/6.03 = ( times_times_real @ one_one_real ) ) ).
% 5.82/6.03
% 5.82/6.03 % lambda_one
% 5.82/6.03 thf(fact_1067_lambda__one,axiom,
% 5.82/6.03 ( ( ^ [X3: rat] : X3 )
% 5.82/6.03 = ( times_times_rat @ one_one_rat ) ) ).
% 5.82/6.03
% 5.82/6.03 % lambda_one
% 5.82/6.03 thf(fact_1068_lambda__one,axiom,
% 5.82/6.03 ( ( ^ [X3: nat] : X3 )
% 5.82/6.03 = ( times_times_nat @ one_one_nat ) ) ).
% 5.82/6.03
% 5.82/6.03 % lambda_one
% 5.82/6.03 thf(fact_1069_lambda__one,axiom,
% 5.82/6.03 ( ( ^ [X3: int] : X3 )
% 5.82/6.03 = ( times_times_int @ one_one_int ) ) ).
% 5.82/6.03
% 5.82/6.03 % lambda_one
% 5.82/6.03 thf(fact_1070_less__add__one,axiom,
% 5.82/6.03 ! [A2: real] : ( ord_less_real @ A2 @ ( plus_plus_real @ A2 @ one_one_real ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_one
% 5.82/6.03 thf(fact_1071_less__add__one,axiom,
% 5.82/6.03 ! [A2: rat] : ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ one_one_rat ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_one
% 5.82/6.03 thf(fact_1072_less__add__one,axiom,
% 5.82/6.03 ! [A2: nat] : ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_one
% 5.82/6.03 thf(fact_1073_less__add__one,axiom,
% 5.82/6.03 ! [A2: int] : ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ one_one_int ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_add_one
% 5.82/6.03 thf(fact_1074_add__mono1,axiom,
% 5.82/6.03 ! [A2: real,B2: real] :
% 5.82/6.03 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.03 => ( ord_less_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( plus_plus_real @ B2 @ one_one_real ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_mono1
% 5.82/6.03 thf(fact_1075_add__mono1,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat] :
% 5.82/6.03 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.03 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( plus_plus_rat @ B2 @ one_one_rat ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_mono1
% 5.82/6.03 thf(fact_1076_add__mono1,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat] :
% 5.82/6.03 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.03 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ ( plus_plus_nat @ B2 @ one_one_nat ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_mono1
% 5.82/6.03 thf(fact_1077_add__mono1,axiom,
% 5.82/6.03 ! [A2: int,B2: int] :
% 5.82/6.03 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.03 => ( ord_less_int @ ( plus_plus_int @ A2 @ one_one_int ) @ ( plus_plus_int @ B2 @ one_one_int ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_mono1
% 5.82/6.03 thf(fact_1078_less__1__mult,axiom,
% 5.82/6.03 ! [M: real,N: real] :
% 5.82/6.03 ( ( ord_less_real @ one_one_real @ M )
% 5.82/6.03 => ( ( ord_less_real @ one_one_real @ N )
% 5.82/6.03 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_1_mult
% 5.82/6.03 thf(fact_1079_less__1__mult,axiom,
% 5.82/6.03 ! [M: rat,N: rat] :
% 5.82/6.03 ( ( ord_less_rat @ one_one_rat @ M )
% 5.82/6.03 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.82/6.03 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_1_mult
% 5.82/6.03 thf(fact_1080_less__1__mult,axiom,
% 5.82/6.03 ! [M: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_nat @ one_one_nat @ M )
% 5.82/6.03 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.82/6.03 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_1_mult
% 5.82/6.03 thf(fact_1081_less__1__mult,axiom,
% 5.82/6.03 ! [M: int,N: int] :
% 5.82/6.03 ( ( ord_less_int @ one_one_int @ M )
% 5.82/6.03 => ( ( ord_less_int @ one_one_int @ N )
% 5.82/6.03 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % less_1_mult
% 5.82/6.03 thf(fact_1082_add__le__add__imp__diff__le,axiom,
% 5.82/6.03 ! [I: real,K: real,N: real,J: real] :
% 5.82/6.03 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.82/6.03 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.82/6.03 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_add_imp_diff_le
% 5.82/6.03 thf(fact_1083_add__le__add__imp__diff__le,axiom,
% 5.82/6.03 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.82/6.03 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.82/6.03 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.82/6.03 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_add_imp_diff_le
% 5.82/6.03 thf(fact_1084_add__le__add__imp__diff__le,axiom,
% 5.82/6.03 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.82/6.03 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.82/6.03 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_add_imp_diff_le
% 5.82/6.03 thf(fact_1085_add__le__add__imp__diff__le,axiom,
% 5.82/6.03 ! [I: int,K: int,N: int,J: int] :
% 5.82/6.03 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.82/6.03 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.82/6.03 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.82/6.03 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_add_imp_diff_le
% 5.82/6.03 thf(fact_1086_add__le__imp__le__diff,axiom,
% 5.82/6.03 ! [I: real,K: real,N: real] :
% 5.82/6.03 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.82/6.03 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_imp_le_diff
% 5.82/6.03 thf(fact_1087_add__le__imp__le__diff,axiom,
% 5.82/6.03 ! [I: rat,K: rat,N: rat] :
% 5.82/6.03 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.82/6.03 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_imp_le_diff
% 5.82/6.03 thf(fact_1088_add__le__imp__le__diff,axiom,
% 5.82/6.03 ! [I: nat,K: nat,N: nat] :
% 5.82/6.03 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.82/6.03 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_imp_le_diff
% 5.82/6.03 thf(fact_1089_add__le__imp__le__diff,axiom,
% 5.82/6.03 ! [I: int,K: int,N: int] :
% 5.82/6.03 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.82/6.03 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % add_le_imp_le_diff
% 5.82/6.03 thf(fact_1090_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.82/6.03 ! [A2: real,B2: real] :
% 5.82/6.03 ( ~ ( ord_less_real @ A2 @ B2 )
% 5.82/6.03 => ( ( plus_plus_real @ B2 @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % linordered_semidom_class.add_diff_inverse
% 5.82/6.03 thf(fact_1091_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.82/6.03 ! [A2: rat,B2: rat] :
% 5.82/6.03 ( ~ ( ord_less_rat @ A2 @ B2 )
% 5.82/6.03 => ( ( plus_plus_rat @ B2 @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % linordered_semidom_class.add_diff_inverse
% 5.82/6.03 thf(fact_1092_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.82/6.03 ! [A2: nat,B2: nat] :
% 5.82/6.03 ( ~ ( ord_less_nat @ A2 @ B2 )
% 5.82/6.03 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % linordered_semidom_class.add_diff_inverse
% 5.82/6.03 thf(fact_1093_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.82/6.03 ! [A2: int,B2: int] :
% 5.82/6.03 ( ~ ( ord_less_int @ A2 @ B2 )
% 5.82/6.03 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.03 = A2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % linordered_semidom_class.add_diff_inverse
% 5.82/6.03 thf(fact_1094_four__x__squared,axiom,
% 5.82/6.03 ! [X2: real] :
% 5.82/6.03 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.03 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % four_x_squared
% 5.82/6.03 thf(fact_1095_L2__set__mult__ineq__lemma,axiom,
% 5.82/6.03 ! [A2: real,C2: real,B2: real,D2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A2 @ C2 ) ) @ ( times_times_real @ B2 @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % L2_set_mult_ineq_lemma
% 5.82/6.03 thf(fact_1096_eq__add__iff1,axiom,
% 5.82/6.03 ! [A2: real,E: real,C2: real,B2: real,D2: real] :
% 5.82/6.03 ( ( ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ C2 )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D2 ) )
% 5.82/6.03 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A2 @ B2 ) @ E ) @ C2 )
% 5.82/6.03 = D2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % eq_add_iff1
% 5.82/6.03 thf(fact_1097_eq__add__iff1,axiom,
% 5.82/6.03 ! [A2: rat,E: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.03 ( ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C2 )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 5.82/6.03 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ E ) @ C2 )
% 5.82/6.03 = D2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % eq_add_iff1
% 5.82/6.03 thf(fact_1098_eq__add__iff1,axiom,
% 5.82/6.03 ! [A2: int,E: int,C2: int,B2: int,D2: int] :
% 5.82/6.03 ( ( ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C2 )
% 5.82/6.03 = ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 5.82/6.03 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ E ) @ C2 )
% 5.82/6.03 = D2 ) ) ).
% 5.82/6.03
% 5.82/6.03 % eq_add_iff1
% 5.82/6.03 thf(fact_1099_eq__add__iff2,axiom,
% 5.82/6.03 ! [A2: real,E: real,C2: real,B2: real,D2: real] :
% 5.82/6.03 ( ( ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ C2 )
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D2 ) )
% 5.82/6.03 = ( C2
% 5.82/6.03 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.03
% 5.82/6.03 % eq_add_iff2
% 5.82/6.03 thf(fact_1100_eq__add__iff2,axiom,
% 5.82/6.03 ! [A2: rat,E: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.03 ( ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C2 )
% 5.82/6.03 = ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 5.82/6.03 = ( C2
% 5.82/6.04 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % eq_add_iff2
% 5.82/6.04 thf(fact_1101_eq__add__iff2,axiom,
% 5.82/6.04 ! [A2: int,E: int,C2: int,B2: int,D2: int] :
% 5.82/6.04 ( ( ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C2 )
% 5.82/6.04 = ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( C2
% 5.82/6.04 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % eq_add_iff2
% 5.82/6.04 thf(fact_1102_square__diff__square__factored,axiom,
% 5.82/6.04 ! [X2: real,Y3: real] :
% 5.82/6.04 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 5.82/6.04 = ( times_times_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( minus_minus_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % square_diff_square_factored
% 5.82/6.04 thf(fact_1103_square__diff__square__factored,axiom,
% 5.82/6.04 ! [X2: rat,Y3: rat] :
% 5.82/6.04 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 5.82/6.04 = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( minus_minus_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % square_diff_square_factored
% 5.82/6.04 thf(fact_1104_square__diff__square__factored,axiom,
% 5.82/6.04 ! [X2: int,Y3: int] :
% 5.82/6.04 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 5.82/6.04 = ( times_times_int @ ( plus_plus_int @ X2 @ Y3 ) @ ( minus_minus_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % square_diff_square_factored
% 5.82/6.04 thf(fact_1105_vebt__delete_Osimps_I4_J,axiom,
% 5.82/6.04 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.82/6.04 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 5.82/6.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 5.82/6.04
% 5.82/6.04 % vebt_delete.simps(4)
% 5.82/6.04 thf(fact_1106_ordered__ring__class_Ole__add__iff1,axiom,
% 5.82/6.04 ! [A2: real,E: real,C2: real,B2: real,D2: real] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A2 @ B2 ) @ E ) @ C2 ) @ D2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % ordered_ring_class.le_add_iff1
% 5.82/6.04 thf(fact_1107_ordered__ring__class_Ole__add__iff1,axiom,
% 5.82/6.04 ! [A2: rat,E: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ E ) @ C2 ) @ D2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % ordered_ring_class.le_add_iff1
% 5.82/6.04 thf(fact_1108_ordered__ring__class_Ole__add__iff1,axiom,
% 5.82/6.04 ! [A2: int,E: int,C2: int,B2: int,D2: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ E ) @ C2 ) @ D2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % ordered_ring_class.le_add_iff1
% 5.82/6.04 thf(fact_1109_ordered__ring__class_Ole__add__iff2,axiom,
% 5.82/6.04 ! [A2: real,E: real,C2: real,B2: real,D2: real] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_eq_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % ordered_ring_class.le_add_iff2
% 5.82/6.04 thf(fact_1110_ordered__ring__class_Ole__add__iff2,axiom,
% 5.82/6.04 ! [A2: rat,E: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % ordered_ring_class.le_add_iff2
% 5.82/6.04 thf(fact_1111_ordered__ring__class_Ole__add__iff2,axiom,
% 5.82/6.04 ! [A2: int,E: int,C2: int,B2: int,D2: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % ordered_ring_class.le_add_iff2
% 5.82/6.04 thf(fact_1112_less__add__iff2,axiom,
% 5.82/6.04 ! [A2: real,E: real,C2: real,B2: real,D2: real] :
% 5.82/6.04 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_add_iff2
% 5.82/6.04 thf(fact_1113_less__add__iff2,axiom,
% 5.82/6.04 ! [A2: rat,E: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.04 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_add_iff2
% 5.82/6.04 thf(fact_1114_less__add__iff2,axiom,
% 5.82/6.04 ! [A2: int,E: int,C2: int,B2: int,D2: int] :
% 5.82/6.04 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_add_iff2
% 5.82/6.04 thf(fact_1115_less__add__iff1,axiom,
% 5.82/6.04 ! [A2: real,E: real,C2: real,B2: real,D2: real] :
% 5.82/6.04 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A2 @ B2 ) @ E ) @ C2 ) @ D2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_add_iff1
% 5.82/6.04 thf(fact_1116_less__add__iff1,axiom,
% 5.82/6.04 ! [A2: rat,E: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.04 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ E ) @ C2 ) @ D2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_add_iff1
% 5.82/6.04 thf(fact_1117_less__add__iff1,axiom,
% 5.82/6.04 ! [A2: int,E: int,C2: int,B2: int,D2: int] :
% 5.82/6.04 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 5.82/6.04 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ E ) @ C2 ) @ D2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_add_iff1
% 5.82/6.04 thf(fact_1118_square__diff__one__factored,axiom,
% 5.82/6.04 ! [X2: real] :
% 5.82/6.04 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 5.82/6.04 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % square_diff_one_factored
% 5.82/6.04 thf(fact_1119_square__diff__one__factored,axiom,
% 5.82/6.04 ! [X2: rat] :
% 5.82/6.04 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 5.82/6.04 = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % square_diff_one_factored
% 5.82/6.04 thf(fact_1120_square__diff__one__factored,axiom,
% 5.82/6.04 ! [X2: int] :
% 5.82/6.04 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 5.82/6.04 = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % square_diff_one_factored
% 5.82/6.04 thf(fact_1121_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,
% 5.82/6.04 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.82/6.04 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 5.82/6.04 = one_one_nat ) ).
% 5.82/6.04
% 5.82/6.04 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(4)
% 5.82/6.04 thf(fact_1122__092_060open_062_092_060And_062x22_Ax21_O_Ati_A_061_ALeafi_Ax21_Ax22_A_092_060Longrightarrow_062_A_060vebt__assn__raw_A_INode_A_ISome_A_Imi_M_Ama_J_J_A_ISuc_A_ISuc_Ava_J_J_AtreeList_Asummary_J_Ati_062_Avebt__deletei_H_A_INode_A_ISome_A_Imi_M_Ama_J_J_A_ISuc_A_ISuc_Ava_J_J_AtreeList_Asummary_J_Ati_Ax_A_060vebt__assn__raw_A_Ivebt__delete_A_INode_A_ISome_A_Imi_M_Ama_J_J_A_ISuc_A_ISuc_Ava_J_J_AtreeList_Asummary_J_Ax_J_062_092_060close_062,axiom,
% 5.82/6.04 ! [X21: $o,X222: $o] :
% 5.82/6.04 ( ( tia
% 5.82/6.04 = ( vEBT_Leafi @ X21 @ X222 ) )
% 5.82/6.04 => ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ treeList @ summary ) @ tia ) @ ( vEBT_V1365221501068881998eletei @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ treeList @ summary ) @ tia @ xa ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ treeList @ summary ) @ xa ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % \<open>\<And>x22 x21. ti = Leafi x21 x22 \<Longrightarrow> <vebt_assn_raw (Node (Some (mi, ma)) (Suc (Suc va)) treeList summary) ti> vebt_deletei' (Node (Some (mi, ma)) (Suc (Suc va)) treeList summary) ti x <vebt_assn_raw (vebt_delete (Node (Some (mi, ma)) (Suc (Suc va)) treeList summary) x)>\<close>
% 5.82/6.04 thf(fact_1123_real__average__minus__first,axiom,
% 5.82/6.04 ! [A2: real,B2: real] :
% 5.82/6.04 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A2 @ B2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A2 )
% 5.82/6.04 = ( divide_divide_real @ ( minus_minus_real @ B2 @ A2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_average_minus_first
% 5.82/6.04 thf(fact_1124_real__average__minus__second,axiom,
% 5.82/6.04 ! [B2: real,A2: real] :
% 5.82/6.04 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B2 @ A2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A2 )
% 5.82/6.04 = ( divide_divide_real @ ( minus_minus_real @ B2 @ A2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_average_minus_second
% 5.82/6.04 thf(fact_1125_count__buildup,axiom,
% 5.82/6.04 ! [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 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % count_buildup
% 5.82/6.04 thf(fact_1126_zdiv__numeral__Bit0,axiom,
% 5.82/6.04 ! [V: num,W: num] :
% 5.82/6.04 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.82/6.04 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % zdiv_numeral_Bit0
% 5.82/6.04 thf(fact_1127_cnt__bound,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % cnt_bound
% 5.82/6.04 thf(fact_1128_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 5.82/6.04 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.04 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.04 = ( if_nat
% 5.82/6.04 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.04 & ~ ( ( X2 = Mi )
% 5.82/6.04 | ( X2 = Ma ) ) )
% 5.82/6.04 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.04 @ one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 5.82/6.04 thf(fact_1129_two__realpow__ge__one,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % two_realpow_ge_one
% 5.82/6.04 thf(fact_1130_field__less__half__sum,axiom,
% 5.82/6.04 ! [X2: real,Y3: real] :
% 5.82/6.04 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.04 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % field_less_half_sum
% 5.82/6.04 thf(fact_1131_field__less__half__sum,axiom,
% 5.82/6.04 ! [X2: rat,Y3: rat] :
% 5.82/6.04 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.04 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % field_less_half_sum
% 5.82/6.04 thf(fact_1132_succ__empty,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.82/6.04 = none_nat )
% 5.82/6.04 = ( ( collect_nat
% 5.82/6.04 @ ^ [Y: nat] :
% 5.82/6.04 ( ( vEBT_vebt_member @ T @ Y )
% 5.82/6.04 & ( ord_less_nat @ X2 @ Y ) ) )
% 5.82/6.04 = bot_bot_set_nat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % succ_empty
% 5.82/6.04 thf(fact_1133_buildup__gives__empty,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.82/6.04 = bot_bot_set_nat ) ).
% 5.82/6.04
% 5.82/6.04 % buildup_gives_empty
% 5.82/6.04 thf(fact_1134_semiring__norm_I90_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ( bit1 @ M )
% 5.82/6.04 = ( bit1 @ N ) )
% 5.82/6.04 = ( M = N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(90)
% 5.82/6.04 thf(fact_1135_mint__corr__help__empty,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( ( vEBT_vebt_mint @ T )
% 5.82/6.04 = none_nat )
% 5.82/6.04 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.82/6.04 = bot_bot_set_nat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mint_corr_help_empty
% 5.82/6.04 thf(fact_1136_maxt__corr__help__empty,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( ( vEBT_vebt_maxt @ T )
% 5.82/6.04 = none_nat )
% 5.82/6.04 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.82/6.04 = bot_bot_set_nat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % maxt_corr_help_empty
% 5.82/6.04 thf(fact_1137_pred__empty,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.82/6.04 = none_nat )
% 5.82/6.04 = ( ( collect_nat
% 5.82/6.04 @ ^ [Y: nat] :
% 5.82/6.04 ( ( vEBT_vebt_member @ T @ Y )
% 5.82/6.04 & ( ord_less_nat @ Y @ X2 ) ) )
% 5.82/6.04 = bot_bot_set_nat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % pred_empty
% 5.82/6.04 thf(fact_1138_semiring__norm_I89_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( bit1 @ M )
% 5.82/6.04 != ( bit0 @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(89)
% 5.82/6.04 thf(fact_1139_semiring__norm_I88_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( bit0 @ M )
% 5.82/6.04 != ( bit1 @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(88)
% 5.82/6.04 thf(fact_1140_semiring__norm_I86_J,axiom,
% 5.82/6.04 ! [M: num] :
% 5.82/6.04 ( ( bit1 @ M )
% 5.82/6.04 != one ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(86)
% 5.82/6.04 thf(fact_1141_semiring__norm_I84_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( one
% 5.82/6.04 != ( bit1 @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(84)
% 5.82/6.04 thf(fact_1142_semiring__norm_I80_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( ord_less_num @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(80)
% 5.82/6.04 thf(fact_1143_semiring__norm_I73_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(73)
% 5.82/6.04 thf(fact_1144_semiring__norm_I7_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(7)
% 5.82/6.04 thf(fact_1145_semiring__norm_I9_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.82/6.04 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(9)
% 5.82/6.04 thf(fact_1146_semiring__norm_I14_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(14)
% 5.82/6.04 thf(fact_1147_semiring__norm_I15_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.82/6.04 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(15)
% 5.82/6.04 thf(fact_1148_semiring__norm_I72_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(72)
% 5.82/6.04 thf(fact_1149_semiring__norm_I81_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.82/6.04 = ( ord_less_num @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(81)
% 5.82/6.04 thf(fact_1150_semiring__norm_I70_J,axiom,
% 5.82/6.04 ! [M: num] :
% 5.82/6.04 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(70)
% 5.82/6.04 thf(fact_1151_semiring__norm_I77_J,axiom,
% 5.82/6.04 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(77)
% 5.82/6.04 thf(fact_1152_zdiv__numeral__Bit1,axiom,
% 5.82/6.04 ! [V: num,W: num] :
% 5.82/6.04 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.82/6.04 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % zdiv_numeral_Bit1
% 5.82/6.04 thf(fact_1153_semiring__norm_I10_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(10)
% 5.82/6.04 thf(fact_1154_semiring__norm_I8_J,axiom,
% 5.82/6.04 ! [M: num] :
% 5.82/6.04 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.82/6.04 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(8)
% 5.82/6.04 thf(fact_1155_semiring__norm_I5_J,axiom,
% 5.82/6.04 ! [M: num] :
% 5.82/6.04 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.82/6.04 = ( bit1 @ M ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(5)
% 5.82/6.04 thf(fact_1156_semiring__norm_I4_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.82/6.04 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(4)
% 5.82/6.04 thf(fact_1157_semiring__norm_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.82/6.04 = ( bit1 @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(3)
% 5.82/6.04 thf(fact_1158_semiring__norm_I16_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(16)
% 5.82/6.04 thf(fact_1159_semiring__norm_I79_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.04 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(79)
% 5.82/6.04 thf(fact_1160_semiring__norm_I74_J,axiom,
% 5.82/6.04 ! [M: num,N: num] :
% 5.82/6.04 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.82/6.04 = ( ord_less_num @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_norm(74)
% 5.82/6.04 thf(fact_1161_div__Suc__eq__div__add3,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.82/6.04 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % div_Suc_eq_div_add3
% 5.82/6.04 thf(fact_1162_Suc__div__eq__add3__div__numeral,axiom,
% 5.82/6.04 ! [M: nat,V: num] :
% 5.82/6.04 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.04 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Suc_div_eq_add3_div_numeral
% 5.82/6.04 thf(fact_1163_set__notEmptyE,axiom,
% 5.82/6.04 ! [S: set_VEBT_VEBT] :
% 5.82/6.04 ( ( S != bot_bo8194388402131092736T_VEBT )
% 5.82/6.04 => ~ ! [X4: vEBT_VEBT] :
% 5.82/6.04 ~ ( member_VEBT_VEBT @ X4 @ S ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_notEmptyE
% 5.82/6.04 thf(fact_1164_set__notEmptyE,axiom,
% 5.82/6.04 ! [S: set_real] :
% 5.82/6.04 ( ( S != bot_bot_set_real )
% 5.82/6.04 => ~ ! [X4: real] :
% 5.82/6.04 ~ ( member_real @ X4 @ S ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_notEmptyE
% 5.82/6.04 thf(fact_1165_set__notEmptyE,axiom,
% 5.82/6.04 ! [S: set_nat] :
% 5.82/6.04 ( ( S != bot_bot_set_nat )
% 5.82/6.04 => ~ ! [X4: nat] :
% 5.82/6.04 ~ ( member_nat @ X4 @ S ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_notEmptyE
% 5.82/6.04 thf(fact_1166_set__notEmptyE,axiom,
% 5.82/6.04 ! [S: set_int] :
% 5.82/6.04 ( ( S != bot_bot_set_int )
% 5.82/6.04 => ~ ! [X4: int] :
% 5.82/6.04 ~ ( member_int @ X4 @ S ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_notEmptyE
% 5.82/6.04 thf(fact_1167_memb__imp__not__empty,axiom,
% 5.82/6.04 ! [X2: vEBT_VEBT,S: set_VEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ X2 @ S )
% 5.82/6.04 => ( S != bot_bo8194388402131092736T_VEBT ) ) ).
% 5.82/6.04
% 5.82/6.04 % memb_imp_not_empty
% 5.82/6.04 thf(fact_1168_memb__imp__not__empty,axiom,
% 5.82/6.04 ! [X2: real,S: set_real] :
% 5.82/6.04 ( ( member_real @ X2 @ S )
% 5.82/6.04 => ( S != bot_bot_set_real ) ) ).
% 5.82/6.04
% 5.82/6.04 % memb_imp_not_empty
% 5.82/6.04 thf(fact_1169_memb__imp__not__empty,axiom,
% 5.82/6.04 ! [X2: nat,S: set_nat] :
% 5.82/6.04 ( ( member_nat @ X2 @ S )
% 5.82/6.04 => ( S != bot_bot_set_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % memb_imp_not_empty
% 5.82/6.04 thf(fact_1170_memb__imp__not__empty,axiom,
% 5.82/6.04 ! [X2: int,S: set_int] :
% 5.82/6.04 ( ( member_int @ X2 @ S )
% 5.82/6.04 => ( S != bot_bot_set_int ) ) ).
% 5.82/6.04
% 5.82/6.04 % memb_imp_not_empty
% 5.82/6.04 thf(fact_1171_subset__minus__empty,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.04 => ( ( minus_minus_set_nat @ A @ B )
% 5.82/6.04 = bot_bot_set_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_minus_empty
% 5.82/6.04 thf(fact_1172_subset__minus__empty,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( minus_minus_set_int @ A @ B )
% 5.82/6.04 = bot_bot_set_int ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_minus_empty
% 5.82/6.04 thf(fact_1173_num_Oexhaust,axiom,
% 5.82/6.04 ! [Y3: num] :
% 5.82/6.04 ( ( Y3 != one )
% 5.82/6.04 => ( ! [X23: num] :
% 5.82/6.04 ( Y3
% 5.82/6.04 != ( bit0 @ X23 ) )
% 5.82/6.04 => ~ ! [X32: num] :
% 5.82/6.04 ( Y3
% 5.82/6.04 != ( bit1 @ X32 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % num.exhaust
% 5.82/6.04 thf(fact_1174_xor__num_Ocases,axiom,
% 5.82/6.04 ! [X2: product_prod_num_num] :
% 5.82/6.04 ( ( X2
% 5.82/6.04 != ( product_Pair_num_num @ one @ one ) )
% 5.82/6.04 => ( ! [N3: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.82/6.04 => ( ! [N3: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.82/6.04 => ( ! [M5: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 5.82/6.04 => ( ! [M5: num,N3: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.82/6.04 => ( ! [M5: num,N3: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) )
% 5.82/6.04 => ( ! [M5: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 5.82/6.04 => ( ! [M5: num,N3: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.82/6.04 => ~ ! [M5: num,N3: num] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % xor_num.cases
% 5.82/6.04 thf(fact_1175_numeral__Bit1,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1
% 5.82/6.04 thf(fact_1176_numeral__Bit1,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1
% 5.82/6.04 thf(fact_1177_numeral__Bit1,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1
% 5.82/6.04 thf(fact_1178_numeral__Bit1,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1
% 5.82/6.04 thf(fact_1179_numeral__Bit1,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1
% 5.82/6.04 thf(fact_1180_eval__nat__numeral_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.82/6.04 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % eval_nat_numeral(3)
% 5.82/6.04 thf(fact_1181_less__eq__real__def,axiom,
% 5.82/6.04 ( ord_less_eq_real
% 5.82/6.04 = ( ^ [X3: real,Y: real] :
% 5.82/6.04 ( ( ord_less_real @ X3 @ Y )
% 5.82/6.04 | ( X3 = Y ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_eq_real_def
% 5.82/6.04 thf(fact_1182_complete__real,axiom,
% 5.82/6.04 ! [S: set_real] :
% 5.82/6.04 ( ? [X8: real] : ( member_real @ X8 @ S )
% 5.82/6.04 => ( ? [Z5: real] :
% 5.82/6.04 ! [X4: real] :
% 5.82/6.04 ( ( member_real @ X4 @ S )
% 5.82/6.04 => ( ord_less_eq_real @ X4 @ Z5 ) )
% 5.82/6.04 => ? [Y4: real] :
% 5.82/6.04 ( ! [X8: real] :
% 5.82/6.04 ( ( member_real @ X8 @ S )
% 5.82/6.04 => ( ord_less_eq_real @ X8 @ Y4 ) )
% 5.82/6.04 & ! [Z5: real] :
% 5.82/6.04 ( ! [X4: real] :
% 5.82/6.04 ( ( member_real @ X4 @ S )
% 5.82/6.04 => ( ord_less_eq_real @ X4 @ Z5 ) )
% 5.82/6.04 => ( ord_less_eq_real @ Y4 @ Z5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % complete_real
% 5.82/6.04 thf(fact_1183_numeral__code_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_code(3)
% 5.82/6.04 thf(fact_1184_numeral__code_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_code(3)
% 5.82/6.04 thf(fact_1185_numeral__code_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_code(3)
% 5.82/6.04 thf(fact_1186_numeral__code_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_code(3)
% 5.82/6.04 thf(fact_1187_numeral__code_I3_J,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.82/6.04 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_code(3)
% 5.82/6.04 thf(fact_1188_power__numeral__odd,axiom,
% 5.82/6.04 ! [Z: complex,W: num] :
% 5.82/6.04 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.82/6.04 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % power_numeral_odd
% 5.82/6.04 thf(fact_1189_power__numeral__odd,axiom,
% 5.82/6.04 ! [Z: code_integer,W: num] :
% 5.82/6.04 ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.82/6.04 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ Z @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % power_numeral_odd
% 5.82/6.04 thf(fact_1190_power__numeral__odd,axiom,
% 5.82/6.04 ! [Z: real,W: num] :
% 5.82/6.04 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.82/6.04 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % power_numeral_odd
% 5.82/6.04 thf(fact_1191_power__numeral__odd,axiom,
% 5.82/6.04 ! [Z: rat,W: num] :
% 5.82/6.04 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.82/6.04 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % power_numeral_odd
% 5.82/6.04 thf(fact_1192_power__numeral__odd,axiom,
% 5.82/6.04 ! [Z: nat,W: num] :
% 5.82/6.04 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.82/6.04 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % power_numeral_odd
% 5.82/6.04 thf(fact_1193_power__numeral__odd,axiom,
% 5.82/6.04 ! [Z: int,W: num] :
% 5.82/6.04 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.82/6.04 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % power_numeral_odd
% 5.82/6.04 thf(fact_1194_numeral__Bit1__div__2,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.04 = ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1_div_2
% 5.82/6.04 thf(fact_1195_numeral__Bit1__div__2,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.04 = ( numeral_numeral_int @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_Bit1_div_2
% 5.82/6.04 thf(fact_1196_power3__eq__cube,axiom,
% 5.82/6.04 ! [A2: complex] :
% 5.82/6.04 ( ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.04 = ( times_times_complex @ ( times_times_complex @ A2 @ A2 ) @ A2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % power3_eq_cube
% 5.82/6.04 thf(fact_1197_power3__eq__cube,axiom,
% 5.82/6.04 ! [A2: code_integer] :
% 5.82/6.04 ( ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.04 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A2 @ A2 ) @ A2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % power3_eq_cube
% 5.82/6.04 thf(fact_1198_power3__eq__cube,axiom,
% 5.82/6.04 ! [A2: real] :
% 5.82/6.04 ( ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.04 = ( times_times_real @ ( times_times_real @ A2 @ A2 ) @ A2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % power3_eq_cube
% 5.82/6.04 thf(fact_1199_power3__eq__cube,axiom,
% 5.82/6.04 ! [A2: rat] :
% 5.82/6.04 ( ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.04 = ( times_times_rat @ ( times_times_rat @ A2 @ A2 ) @ A2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % power3_eq_cube
% 5.82/6.04 thf(fact_1200_power3__eq__cube,axiom,
% 5.82/6.04 ! [A2: nat] :
% 5.82/6.04 ( ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.04 = ( times_times_nat @ ( times_times_nat @ A2 @ A2 ) @ A2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % power3_eq_cube
% 5.82/6.04 thf(fact_1201_power3__eq__cube,axiom,
% 5.82/6.04 ! [A2: int] :
% 5.82/6.04 ( ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.04 = ( times_times_int @ ( times_times_int @ A2 @ A2 ) @ A2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % power3_eq_cube
% 5.82/6.04 thf(fact_1202_Suc3__eq__add__3,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.82/6.04 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % Suc3_eq_add_3
% 5.82/6.04 thf(fact_1203_mult__commute__abs,axiom,
% 5.82/6.04 ! [C2: real] :
% 5.82/6.04 ( ( ^ [X3: real] : ( times_times_real @ X3 @ C2 ) )
% 5.82/6.04 = ( times_times_real @ C2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_commute_abs
% 5.82/6.04 thf(fact_1204_mult__commute__abs,axiom,
% 5.82/6.04 ! [C2: rat] :
% 5.82/6.04 ( ( ^ [X3: rat] : ( times_times_rat @ X3 @ C2 ) )
% 5.82/6.04 = ( times_times_rat @ C2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_commute_abs
% 5.82/6.04 thf(fact_1205_mult__commute__abs,axiom,
% 5.82/6.04 ! [C2: nat] :
% 5.82/6.04 ( ( ^ [X3: nat] : ( times_times_nat @ X3 @ C2 ) )
% 5.82/6.04 = ( times_times_nat @ C2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_commute_abs
% 5.82/6.04 thf(fact_1206_mult__commute__abs,axiom,
% 5.82/6.04 ! [C2: int] :
% 5.82/6.04 ( ( ^ [X3: int] : ( times_times_int @ X3 @ C2 ) )
% 5.82/6.04 = ( times_times_int @ C2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_commute_abs
% 5.82/6.04 thf(fact_1207_Suc__div__eq__add3__div,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.82/6.04 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % Suc_div_eq_add3_div
% 5.82/6.04 thf(fact_1208_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 5.82/6.04 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.04 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.04 = one_one_nat ) ).
% 5.82/6.04
% 5.82/6.04 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 5.82/6.04 thf(fact_1209_insersimp_H,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,Y3: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y3 ) @ one_one_nat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % insersimp'
% 5.82/6.04 thf(fact_1210_insertsimp_H,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( vEBT_VEBT_minNull @ T )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % insertsimp'
% 5.82/6.04 thf(fact_1211_add__diff__add,axiom,
% 5.82/6.04 ! [A2: real,C2: real,B2: real,D2: real] :
% 5.82/6.04 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ D2 ) )
% 5.82/6.04 = ( plus_plus_real @ ( minus_minus_real @ A2 @ B2 ) @ ( minus_minus_real @ C2 @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % add_diff_add
% 5.82/6.04 thf(fact_1212_add__diff__add,axiom,
% 5.82/6.04 ! [A2: rat,C2: rat,B2: rat,D2: rat] :
% 5.82/6.04 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ D2 ) )
% 5.82/6.04 = ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ ( minus_minus_rat @ C2 @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % add_diff_add
% 5.82/6.04 thf(fact_1213_add__diff__add,axiom,
% 5.82/6.04 ! [A2: int,C2: int,B2: int,D2: int] :
% 5.82/6.04 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ D2 ) )
% 5.82/6.04 = ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ ( minus_minus_int @ C2 @ D2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % add_diff_add
% 5.82/6.04 thf(fact_1214_real__arch__pow,axiom,
% 5.82/6.04 ! [X2: real,Y3: real] :
% 5.82/6.04 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.04 => ? [N3: nat] : ( ord_less_real @ Y3 @ ( power_power_real @ X2 @ N3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_arch_pow
% 5.82/6.04 thf(fact_1215_insert_H__bound__height,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % insert'_bound_height
% 5.82/6.04 thf(fact_1216_small__powers__of__2,axiom,
% 5.82/6.04 ! [X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ X2 )
% 5.82/6.04 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ X2 @ one_one_nat ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % small_powers_of_2
% 5.82/6.04 thf(fact_1217_mult__diff__mult,axiom,
% 5.82/6.04 ! [X2: real,Y3: real,A2: real,B2: real] :
% 5.82/6.04 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y3 ) @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.04 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y3 @ B2 ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A2 ) @ B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_diff_mult
% 5.82/6.04 thf(fact_1218_mult__diff__mult,axiom,
% 5.82/6.04 ! [X2: rat,Y3: rat,A2: rat,B2: rat] :
% 5.82/6.04 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ Y3 ) @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.04 = ( plus_plus_rat @ ( times_times_rat @ X2 @ ( minus_minus_rat @ Y3 @ B2 ) ) @ ( times_times_rat @ ( minus_minus_rat @ X2 @ A2 ) @ B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_diff_mult
% 5.82/6.04 thf(fact_1219_mult__diff__mult,axiom,
% 5.82/6.04 ! [X2: int,Y3: int,A2: int,B2: int] :
% 5.82/6.04 ( ( minus_minus_int @ ( times_times_int @ X2 @ Y3 ) @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.04 = ( plus_plus_int @ ( times_times_int @ X2 @ ( minus_minus_int @ Y3 @ B2 ) ) @ ( times_times_int @ ( minus_minus_int @ X2 @ A2 ) @ B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_diff_mult
% 5.82/6.04 thf(fact_1220_discrete,axiom,
% 5.82/6.04 ( ord_less_nat
% 5.82/6.04 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % discrete
% 5.82/6.04 thf(fact_1221_discrete,axiom,
% 5.82/6.04 ( ord_less_int
% 5.82/6.04 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % discrete
% 5.82/6.04 thf(fact_1222_field__sum__of__halves,axiom,
% 5.82/6.04 ! [X2: real] :
% 5.82/6.04 ( ( plus_plus_real @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.04 = X2 ) ).
% 5.82/6.04
% 5.82/6.04 % field_sum_of_halves
% 5.82/6.04 thf(fact_1223_field__sum__of__halves,axiom,
% 5.82/6.04 ! [X2: rat] :
% 5.82/6.04 ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.82/6.04 = X2 ) ).
% 5.82/6.04
% 5.82/6.04 % field_sum_of_halves
% 5.82/6.04 thf(fact_1224_space__bound,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( U
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % space_bound
% 5.82/6.04 thf(fact_1225_space_H__bound,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( U
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_VEBT_space2 @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % space'_bound
% 5.82/6.04 thf(fact_1226_delete__bound__height,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % delete_bound_height
% 5.82/6.04 thf(fact_1227_minNull__delete__time__bound,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X2 ) )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minNull_delete_time_bound
% 5.82/6.04 thf(fact_1228_tdeletemimi,axiom,
% 5.82/6.04 ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % tdeletemimi
% 5.82/6.04 thf(fact_1229_vebt__buildup__bound,axiom,
% 5.82/6.04 ! [U: nat,N: nat] :
% 5.82/6.04 ( ( U
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % vebt_buildup_bound
% 5.82/6.04 thf(fact_1230_T__vebt__buildupi__univ,axiom,
% 5.82/6.04 ! [U: nat,N: nat] :
% 5.82/6.04 ( ( U
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_V441764108873111860ildupi @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % T_vebt_buildupi_univ
% 5.82/6.04 thf(fact_1231_divmod__step__eq,axiom,
% 5.82/6.04 ! [L: num,R2: nat,Q3: nat] :
% 5.82/6.04 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.82/6.04 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.82/6.04 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.82/6.04 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.82/6.04 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.82/6.04 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % divmod_step_eq
% 5.82/6.04 thf(fact_1232_divmod__step__eq,axiom,
% 5.82/6.04 ! [L: num,R2: int,Q3: int] :
% 5.82/6.04 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.82/6.04 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.04 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.82/6.04 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.82/6.04 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.04 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % divmod_step_eq
% 5.82/6.04 thf(fact_1233_divmod__step__eq,axiom,
% 5.82/6.04 ! [L: num,R2: code_integer,Q3: code_integer] :
% 5.82/6.04 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.82/6.04 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.82/6.04 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.82/6.04 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.82/6.04 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.82/6.04 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % divmod_step_eq
% 5.82/6.04 thf(fact_1234_TBOUND__vebt__inserti,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X2 ) @ ( if_nat @ ( vEBT_VEBT_minNull @ T ) @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_vebt_inserti
% 5.82/6.04 thf(fact_1235_builupi_Hcorr,axiom,
% 5.82/6.04 ! [N: nat] : ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % builupi'corr
% 5.82/6.04 thf(fact_1236_space__space_H,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT] : ( ord_less_nat @ ( vEBT_VEBT_space @ T ) @ ( vEBT_VEBT_space2 @ T ) ) ).
% 5.82/6.04
% 5.82/6.04 % space_space'
% 5.82/6.04 thf(fact_1237_TBOUND__vebt__buildupi,axiom,
% 5.82/6.04 ! [N: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_vebt_buildupi
% 5.82/6.04 thf(fact_1238_TBOUND__minNull,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.04 ( ( vEBT_VEBT_minNull @ T )
% 5.82/6.04 => ( time_T5737551269749752165_VEBTi @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X2 ) @ one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_minNull
% 5.82/6.04 thf(fact_1239_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,
% 5.82/6.04 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.82/6.04 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 5.82/6.04 = one_one_nat ) ).
% 5.82/6.04
% 5.82/6.04 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(4)
% 5.82/6.04 thf(fact_1240_TBOUND__replicate,axiom,
% 5.82/6.04 ! [X2: heap_T8145700208782473153_VEBTi,C2: nat,N: nat] :
% 5.82/6.04 ( ( time_T5737551269749752165_VEBTi @ X2 @ C2 )
% 5.82/6.04 => ( time_T8149879359713347829_VEBTi @ ( vEBT_V1859673955506687831_VEBTi @ N @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ C2 ) @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_replicate
% 5.82/6.04 thf(fact_1241_TBOUND__replicate,axiom,
% 5.82/6.04 ! [X2: heap_Time_Heap_o,C2: nat,N: nat] :
% 5.82/6.04 ( ( time_TBOUND_o @ X2 @ C2 )
% 5.82/6.04 => ( time_TBOUND_list_o @ ( vEBT_V2326993469660664182atei_o @ N @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ C2 ) @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_replicate
% 5.82/6.04 thf(fact_1242_TBOUND__replicate,axiom,
% 5.82/6.04 ! [X2: heap_T2636463487746394924on_nat,C2: nat,N: nat] :
% 5.82/6.04 ( ( time_T8353473612707095248on_nat @ X2 @ C2 )
% 5.82/6.04 => ( time_T3808005469503390304on_nat @ ( vEBT_V792416675989592002on_nat @ N @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ C2 ) @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_replicate
% 5.82/6.04 thf(fact_1243_TBOUND__replicate,axiom,
% 5.82/6.04 ! [X2: heap_Time_Heap_nat,C2: nat,N: nat] :
% 5.82/6.04 ( ( time_TBOUND_nat @ X2 @ C2 )
% 5.82/6.04 => ( time_TBOUND_list_nat @ ( vEBT_V7726092123322077554ei_nat @ N @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ C2 ) @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_replicate
% 5.82/6.04 thf(fact_1244_htt__vebt__buildupi_H__univ,axiom,
% 5.82/6.04 ! [U: nat,N: nat] :
% 5.82/6.04 ( ( U
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % htt_vebt_buildupi'_univ
% 5.82/6.04 thf(fact_1245_Tb__T__vebt__buildupi_H_H,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_eq_nat @ ( vEBT_V441764108873111860ildupi @ N ) @ ( minus_minus_nat @ ( vEBT_VEBT_Tb2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Tb_T_vebt_buildupi''
% 5.82/6.04 thf(fact_1246_T__vebt__buildupi,axiom,
% 5.82/6.04 ! [N: nat,H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ H2 ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % T_vebt_buildupi
% 5.82/6.04 thf(fact_1247_builupicorr,axiom,
% 5.82/6.04 ! [N: nat] : ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % builupicorr
% 5.82/6.04 thf(fact_1248_htt__vebt__buildupi_H,axiom,
% 5.82/6.04 ! [N: nat] : ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % htt_vebt_buildupi'
% 5.82/6.04 thf(fact_1249_space__2__pow__bound,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( 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 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % space_2_pow_bound
% 5.82/6.04 thf(fact_1250_zle__add1__eq__le,axiom,
% 5.82/6.04 ! [W: int,Z: int] :
% 5.82/6.04 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.82/6.04 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.82/6.04
% 5.82/6.04 % zle_add1_eq_le
% 5.82/6.04 thf(fact_1251_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 5.82/6.04 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.04 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.04 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 5.82/6.04 thf(fact_1252_Diff__eq__empty__iff,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( ( minus_minus_set_nat @ A @ B )
% 5.82/6.04 = bot_bot_set_nat )
% 5.82/6.04 = ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_eq_empty_iff
% 5.82/6.04 thf(fact_1253_Diff__eq__empty__iff,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ( minus_minus_set_int @ A @ B )
% 5.82/6.04 = bot_bot_set_int )
% 5.82/6.04 = ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_eq_empty_iff
% 5.82/6.04 thf(fact_1254_subsetI,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat] :
% 5.82/6.04 ( ! [X4: nat] :
% 5.82/6.04 ( ( member_nat @ X4 @ A )
% 5.82/6.04 => ( member_nat @ X4 @ B ) )
% 5.82/6.04 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetI
% 5.82/6.04 thf(fact_1255_subsetI,axiom,
% 5.82/6.04 ! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ! [X4: vEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.04 => ( member_VEBT_VEBT @ X4 @ B ) )
% 5.82/6.04 => ( ord_le4337996190870823476T_VEBT @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetI
% 5.82/6.04 thf(fact_1256_subsetI,axiom,
% 5.82/6.04 ! [A: set_real,B: set_real] :
% 5.82/6.04 ( ! [X4: real] :
% 5.82/6.04 ( ( member_real @ X4 @ A )
% 5.82/6.04 => ( member_real @ X4 @ B ) )
% 5.82/6.04 => ( ord_less_eq_set_real @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetI
% 5.82/6.04 thf(fact_1257_subsetI,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ! [X4: int] :
% 5.82/6.04 ( ( member_int @ X4 @ A )
% 5.82/6.04 => ( member_int @ X4 @ B ) )
% 5.82/6.04 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetI
% 5.82/6.04 thf(fact_1258_psubsetI,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( A != B )
% 5.82/6.04 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubsetI
% 5.82/6.04 thf(fact_1259_subset__antisym,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( ord_less_eq_set_int @ B @ A )
% 5.82/6.04 => ( A = B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_antisym
% 5.82/6.04 thf(fact_1260_of__nat__eq__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ( semiri5074537144036343181t_real @ M )
% 5.82/6.04 = ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 = ( M = N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_iff
% 5.82/6.04 thf(fact_1261_of__nat__eq__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ( semiri1314217659103216013at_int @ M )
% 5.82/6.04 = ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.04 = ( M = N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_iff
% 5.82/6.04 thf(fact_1262_of__nat__eq__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.82/6.04 = ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.04 = ( M = N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_iff
% 5.82/6.04 thf(fact_1263_DiffI,axiom,
% 5.82/6.04 ! [C2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ C2 @ A )
% 5.82/6.04 => ( ~ ( member_VEBT_VEBT @ C2 @ B )
% 5.82/6.04 => ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A @ B ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffI
% 5.82/6.04 thf(fact_1264_DiffI,axiom,
% 5.82/6.04 ! [C2: real,A: set_real,B: set_real] :
% 5.82/6.04 ( ( member_real @ C2 @ A )
% 5.82/6.04 => ( ~ ( member_real @ C2 @ B )
% 5.82/6.04 => ( member_real @ C2 @ ( minus_minus_set_real @ A @ B ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffI
% 5.82/6.04 thf(fact_1265_DiffI,axiom,
% 5.82/6.04 ! [C2: int,A: set_int,B: set_int] :
% 5.82/6.04 ( ( member_int @ C2 @ A )
% 5.82/6.04 => ( ~ ( member_int @ C2 @ B )
% 5.82/6.04 => ( member_int @ C2 @ ( minus_minus_set_int @ A @ B ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffI
% 5.82/6.04 thf(fact_1266_DiffI,axiom,
% 5.82/6.04 ! [C2: nat,A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( member_nat @ C2 @ A )
% 5.82/6.04 => ( ~ ( member_nat @ C2 @ B )
% 5.82/6.04 => ( member_nat @ C2 @ ( minus_minus_set_nat @ A @ B ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffI
% 5.82/6.04 thf(fact_1267_Diff__iff,axiom,
% 5.82/6.04 ! [C2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A @ B ) )
% 5.82/6.04 = ( ( member_VEBT_VEBT @ C2 @ A )
% 5.82/6.04 & ~ ( member_VEBT_VEBT @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_iff
% 5.82/6.04 thf(fact_1268_Diff__iff,axiom,
% 5.82/6.04 ! [C2: real,A: set_real,B: set_real] :
% 5.82/6.04 ( ( member_real @ C2 @ ( minus_minus_set_real @ A @ B ) )
% 5.82/6.04 = ( ( member_real @ C2 @ A )
% 5.82/6.04 & ~ ( member_real @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_iff
% 5.82/6.04 thf(fact_1269_Diff__iff,axiom,
% 5.82/6.04 ! [C2: int,A: set_int,B: set_int] :
% 5.82/6.04 ( ( member_int @ C2 @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.04 = ( ( member_int @ C2 @ A )
% 5.82/6.04 & ~ ( member_int @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_iff
% 5.82/6.04 thf(fact_1270_Diff__iff,axiom,
% 5.82/6.04 ! [C2: nat,A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.04 = ( ( member_nat @ C2 @ A )
% 5.82/6.04 & ~ ( member_nat @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_iff
% 5.82/6.04 thf(fact_1271_Diff__idemp,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B ) @ B )
% 5.82/6.04 = ( minus_minus_set_nat @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_idemp
% 5.82/6.04 thf(fact_1272_time__replicate,axiom,
% 5.82/6.04 ! [X2: heap_T8145700208782473153_VEBTi,C2: nat,N: nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.04 ( ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ X2 @ H3 ) @ C2 )
% 5.82/6.04 => ( ord_less_eq_nat @ ( time_t3534373299052942712_VEBTi @ ( vEBT_V1859673955506687831_VEBTi @ N @ X2 ) @ H2 ) @ ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ C2 ) @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % time_replicate
% 5.82/6.04 thf(fact_1273_two__realpow__ge__two,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % two_realpow_ge_two
% 5.82/6.04 thf(fact_1274_htt__vebt__buildupi,axiom,
% 5.82/6.04 ! [N: nat] : ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % htt_vebt_buildupi
% 5.82/6.04 thf(fact_1275_subset__empty,axiom,
% 5.82/6.04 ! [A: set_nat] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.82/6.04 = ( A = bot_bot_set_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_empty
% 5.82/6.04 thf(fact_1276_subset__empty,axiom,
% 5.82/6.04 ! [A: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.82/6.04 = ( A = bot_bot_set_int ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_empty
% 5.82/6.04 thf(fact_1277_empty__subsetI,axiom,
% 5.82/6.04 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.82/6.04
% 5.82/6.04 % empty_subsetI
% 5.82/6.04 thf(fact_1278_empty__subsetI,axiom,
% 5.82/6.04 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.82/6.04
% 5.82/6.04 % empty_subsetI
% 5.82/6.04 thf(fact_1279_Diff__empty,axiom,
% 5.82/6.04 ! [A: set_int] :
% 5.82/6.04 ( ( minus_minus_set_int @ A @ bot_bot_set_int )
% 5.82/6.04 = A ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_empty
% 5.82/6.04 thf(fact_1280_Diff__empty,axiom,
% 5.82/6.04 ! [A: set_nat] :
% 5.82/6.04 ( ( minus_minus_set_nat @ A @ bot_bot_set_nat )
% 5.82/6.04 = A ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_empty
% 5.82/6.04 thf(fact_1281_empty__Diff,axiom,
% 5.82/6.04 ! [A: set_int] :
% 5.82/6.04 ( ( minus_minus_set_int @ bot_bot_set_int @ A )
% 5.82/6.04 = bot_bot_set_int ) ).
% 5.82/6.04
% 5.82/6.04 % empty_Diff
% 5.82/6.04 thf(fact_1282_empty__Diff,axiom,
% 5.82/6.04 ! [A: set_nat] :
% 5.82/6.04 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A )
% 5.82/6.04 = bot_bot_set_nat ) ).
% 5.82/6.04
% 5.82/6.04 % empty_Diff
% 5.82/6.04 thf(fact_1283_Diff__cancel,axiom,
% 5.82/6.04 ! [A: set_int] :
% 5.82/6.04 ( ( minus_minus_set_int @ A @ A )
% 5.82/6.04 = bot_bot_set_int ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_cancel
% 5.82/6.04 thf(fact_1284_Diff__cancel,axiom,
% 5.82/6.04 ! [A: set_nat] :
% 5.82/6.04 ( ( minus_minus_set_nat @ A @ A )
% 5.82/6.04 = bot_bot_set_nat ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_cancel
% 5.82/6.04 thf(fact_1285_count__buildup_H,axiom,
% 5.82/6.04 ! [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 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % count_buildup'
% 5.82/6.04 thf(fact_1286_space__cnt,axiom,
% 5.82/6.04 ! [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 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % space_cnt
% 5.82/6.04 thf(fact_1287_T__vebt__buildupi__cnt_H,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V441764108873111860ildupi @ N ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % T_vebt_buildupi_cnt'
% 5.82/6.04 thf(fact_1288_t__buildup__cnt,axiom,
% 5.82/6.04 ! [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 ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % t_buildup_cnt
% 5.82/6.04 thf(fact_1289_of__nat__numeral,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.82/6.04 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_numeral
% 5.82/6.04 thf(fact_1290_of__nat__numeral,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.82/6.04 = ( numeral_numeral_rat @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_numeral
% 5.82/6.04 thf(fact_1291_of__nat__numeral,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.82/6.04 = ( numeral_numeral_real @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_numeral
% 5.82/6.04 thf(fact_1292_of__nat__numeral,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.82/6.04 = ( numeral_numeral_int @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_numeral
% 5.82/6.04 thf(fact_1293_of__nat__numeral,axiom,
% 5.82/6.04 ! [N: num] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.82/6.04 = ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_numeral
% 5.82/6.04 thf(fact_1294_of__nat__less__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.82/6.04 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_iff
% 5.82/6.04 thf(fact_1295_of__nat__less__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_iff
% 5.82/6.04 thf(fact_1296_of__nat__less__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.04 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_iff
% 5.82/6.04 thf(fact_1297_of__nat__less__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.04 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_iff
% 5.82/6.04 thf(fact_1298_of__nat__le__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_iff
% 5.82/6.04 thf(fact_1299_of__nat__le__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_iff
% 5.82/6.04 thf(fact_1300_of__nat__le__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_iff
% 5.82/6.04 thf(fact_1301_of__nat__le__iff,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_iff
% 5.82/6.04 thf(fact_1302_of__nat__add,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.04 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_add
% 5.82/6.04 thf(fact_1303_of__nat__add,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.04 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_add
% 5.82/6.04 thf(fact_1304_of__nat__add,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.04 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_add
% 5.82/6.04 thf(fact_1305_of__nat__add,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.04 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_add
% 5.82/6.04 thf(fact_1306_of__nat__1,axiom,
% 5.82/6.04 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.82/6.04 = one_one_rat ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1
% 5.82/6.04 thf(fact_1307_of__nat__1,axiom,
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.82/6.04 = one_one_real ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1
% 5.82/6.04 thf(fact_1308_of__nat__1,axiom,
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.82/6.04 = one_one_int ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1
% 5.82/6.04 thf(fact_1309_of__nat__1,axiom,
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.82/6.04 = one_one_nat ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1
% 5.82/6.04 thf(fact_1310_of__nat__1__eq__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( one_one_rat
% 5.82/6.04 = ( semiri681578069525770553at_rat @ N ) )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1_eq_iff
% 5.82/6.04 thf(fact_1311_of__nat__1__eq__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( one_one_real
% 5.82/6.04 = ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1_eq_iff
% 5.82/6.04 thf(fact_1312_of__nat__1__eq__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( one_one_int
% 5.82/6.04 = ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1_eq_iff
% 5.82/6.04 thf(fact_1313_of__nat__1__eq__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( one_one_nat
% 5.82/6.04 = ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_1_eq_iff
% 5.82/6.04 thf(fact_1314_of__nat__eq__1__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ( semiri681578069525770553at_rat @ N )
% 5.82/6.04 = one_one_rat )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_1_iff
% 5.82/6.04 thf(fact_1315_of__nat__eq__1__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ( semiri5074537144036343181t_real @ N )
% 5.82/6.04 = one_one_real )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_1_iff
% 5.82/6.04 thf(fact_1316_of__nat__eq__1__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ( semiri1314217659103216013at_int @ N )
% 5.82/6.04 = one_one_int )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_1_iff
% 5.82/6.04 thf(fact_1317_of__nat__eq__1__iff,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.82/6.04 = one_one_nat )
% 5.82/6.04 = ( N = one_one_nat ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_1_iff
% 5.82/6.04 thf(fact_1318_of__nat__mult,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.82/6.04 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mult
% 5.82/6.04 thf(fact_1319_of__nat__mult,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.82/6.04 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mult
% 5.82/6.04 thf(fact_1320_of__nat__mult,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.82/6.04 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mult
% 5.82/6.04 thf(fact_1321_of__nat__mult,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.82/6.04 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mult
% 5.82/6.04 thf(fact_1322_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ( semiri8010041392384452111omplex @ X2 )
% 5.82/6.04 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B2 ) @ W ) )
% 5.82/6.04 = ( X2
% 5.82/6.04 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1323_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ( semiri4939895301339042750nteger @ X2 )
% 5.82/6.04 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B2 ) @ W ) )
% 5.82/6.04 = ( X2
% 5.82/6.04 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1324_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ( semiri5074537144036343181t_real @ X2 )
% 5.82/6.04 = ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) )
% 5.82/6.04 = ( X2
% 5.82/6.04 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1325_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ( semiri1314217659103216013at_int @ X2 )
% 5.82/6.04 = ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) )
% 5.82/6.04 = ( X2
% 5.82/6.04 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1326_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ( semiri1316708129612266289at_nat @ X2 )
% 5.82/6.04 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) )
% 5.82/6.04 = ( X2
% 5.82/6.04 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1327_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B2 ) @ W )
% 5.82/6.04 = ( semiri8010041392384452111omplex @ X2 ) )
% 5.82/6.04 = ( ( power_power_nat @ B2 @ W )
% 5.82/6.04 = X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1328_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B2 ) @ W )
% 5.82/6.04 = ( semiri4939895301339042750nteger @ X2 ) )
% 5.82/6.04 = ( ( power_power_nat @ B2 @ W )
% 5.82/6.04 = X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1329_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W )
% 5.82/6.04 = ( semiri5074537144036343181t_real @ X2 ) )
% 5.82/6.04 = ( ( power_power_nat @ B2 @ W )
% 5.82/6.04 = X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1330_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W )
% 5.82/6.04 = ( semiri1314217659103216013at_int @ X2 ) )
% 5.82/6.04 = ( ( power_power_nat @ B2 @ W )
% 5.82/6.04 = X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1331_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W )
% 5.82/6.04 = ( semiri1316708129612266289at_nat @ X2 ) )
% 5.82/6.04 = ( ( power_power_nat @ B2 @ W )
% 5.82/6.04 = X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_eq_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1332_semiring__1__class_Oof__nat__power,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.82/6.04 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_1_class.of_nat_power
% 5.82/6.04 thf(fact_1333_semiring__1__class_Oof__nat__power,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N ) )
% 5.82/6.04 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_1_class.of_nat_power
% 5.82/6.04 thf(fact_1334_semiring__1__class_Oof__nat__power,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.82/6.04 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_1_class.of_nat_power
% 5.82/6.04 thf(fact_1335_semiring__1__class_Oof__nat__power,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.82/6.04 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_1_class.of_nat_power
% 5.82/6.04 thf(fact_1336_semiring__1__class_Oof__nat__power,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.82/6.04 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % semiring_1_class.of_nat_power
% 5.82/6.04 thf(fact_1337_zle__diff1__eq,axiom,
% 5.82/6.04 ! [W: int,Z: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.82/6.04 = ( ord_less_int @ W @ Z ) ) ).
% 5.82/6.04
% 5.82/6.04 % zle_diff1_eq
% 5.82/6.04 thf(fact_1338_htt__vebt__buildupi__univ,axiom,
% 5.82/6.04 ! [U: nat,N: nat] :
% 5.82/6.04 ( ( U
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % htt_vebt_buildupi_univ
% 5.82/6.04 thf(fact_1339_of__nat__Suc,axiom,
% 5.82/6.04 ! [M: nat] :
% 5.82/6.04 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.82/6.04 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_Suc
% 5.82/6.04 thf(fact_1340_of__nat__Suc,axiom,
% 5.82/6.04 ! [M: nat] :
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.82/6.04 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_Suc
% 5.82/6.04 thf(fact_1341_of__nat__Suc,axiom,
% 5.82/6.04 ! [M: nat] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.82/6.04 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_Suc
% 5.82/6.04 thf(fact_1342_of__nat__Suc,axiom,
% 5.82/6.04 ! [M: nat] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.82/6.04 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_Suc
% 5.82/6.04 thf(fact_1343_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: num,N: nat,Y3: nat] :
% 5.82/6.04 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 5.82/6.04 = ( semiri4939895301339042750nteger @ Y3 ) )
% 5.82/6.04 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = Y3 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1344_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: num,N: nat,Y3: nat] :
% 5.82/6.04 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.82/6.04 = ( semiri8010041392384452111omplex @ Y3 ) )
% 5.82/6.04 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = Y3 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1345_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: num,N: nat,Y3: nat] :
% 5.82/6.04 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.82/6.04 = ( semiri681578069525770553at_rat @ Y3 ) )
% 5.82/6.04 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = Y3 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1346_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: num,N: nat,Y3: nat] :
% 5.82/6.04 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.82/6.04 = ( semiri5074537144036343181t_real @ Y3 ) )
% 5.82/6.04 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = Y3 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1347_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: num,N: nat,Y3: nat] :
% 5.82/6.04 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.04 = ( semiri1314217659103216013at_int @ Y3 ) )
% 5.82/6.04 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = Y3 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1348_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: num,N: nat,Y3: nat] :
% 5.82/6.04 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = ( semiri1316708129612266289at_nat @ Y3 ) )
% 5.82/6.04 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.04 = Y3 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_eq_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1349_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [Y3: nat,X2: num,N: nat] :
% 5.82/6.04 ( ( ( semiri4939895301339042750nteger @ Y3 )
% 5.82/6.04 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 5.82/6.04 = ( Y3
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_eq_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1350_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [Y3: nat,X2: num,N: nat] :
% 5.82/6.04 ( ( ( semiri8010041392384452111omplex @ Y3 )
% 5.82/6.04 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.82/6.04 = ( Y3
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_eq_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1351_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [Y3: nat,X2: num,N: nat] :
% 5.82/6.04 ( ( ( semiri681578069525770553at_rat @ Y3 )
% 5.82/6.04 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.82/6.04 = ( Y3
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_eq_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1352_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [Y3: nat,X2: num,N: nat] :
% 5.82/6.04 ( ( ( semiri5074537144036343181t_real @ Y3 )
% 5.82/6.04 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.82/6.04 = ( Y3
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_eq_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1353_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [Y3: nat,X2: num,N: nat] :
% 5.82/6.04 ( ( ( semiri1314217659103216013at_int @ Y3 )
% 5.82/6.04 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.82/6.04 = ( Y3
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_eq_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1354_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [Y3: nat,X2: num,N: nat] :
% 5.82/6.04 ( ( ( semiri1316708129612266289at_nat @ Y3 )
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.82/6.04 = ( Y3
% 5.82/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_eq_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1355_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B2 ) @ W ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1356_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1357_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1358_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1359_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1360_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1361_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1362_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1363_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1364_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1365_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1366_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1367_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1368_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1369_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,B2: nat,W: nat] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1370_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B2 ) @ W ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1371_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1372_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1373_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1374_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.82/6.04 ! [B2: nat,W: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_of_nat_power_cancel_iff
% 5.82/6.04 thf(fact_1375_numeral__less__real__of__nat__iff,axiom,
% 5.82/6.04 ! [W: num,N: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_less_real_of_nat_iff
% 5.82/6.04 thf(fact_1376_real__of__nat__less__numeral__iff,axiom,
% 5.82/6.04 ! [N: nat,W: num] :
% 5.82/6.04 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.82/6.04 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_less_numeral_iff
% 5.82/6.04 thf(fact_1377_numeral__le__real__of__nat__iff,axiom,
% 5.82/6.04 ! [N: num,M: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_le_real_of_nat_iff
% 5.82/6.04 thf(fact_1378_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1379_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1380_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1381_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1382_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.82/6.04 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_less_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1383_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1384_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1385_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1386_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1387_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1388_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1389_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1390_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1391_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1392_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.82/6.04 ! [X2: nat,I: num,N: nat] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.82/6.04 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_le_numeral_power_cancel_iff
% 5.82/6.04 thf(fact_1393_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1394_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1395_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1396_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1397_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.82/6.04 ! [I: num,N: nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.82/6.04 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.82/6.04
% 5.82/6.04 % numeral_power_le_of_nat_cancel_iff
% 5.82/6.04 thf(fact_1398_TBOUND__vebt__memberi,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] : ( time_TBOUND_o @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_vebt_memberi
% 5.82/6.04 thf(fact_1399_TBOUND__vebt__predi,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] : ( time_T8353473612707095248on_nat @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_vebt_predi
% 5.82/6.04 thf(fact_1400_TBOUND__vebt__succi,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] : ( time_T8353473612707095248on_nat @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_vebt_succi
% 5.82/6.04 thf(fact_1401_htt__vebt__inserti,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] : ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X2 ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X2 ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % htt_vebt_inserti
% 5.82/6.04 thf(fact_1402_mult__of__nat__commute,axiom,
% 5.82/6.04 ! [X2: nat,Y3: rat] :
% 5.82/6.04 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y3 )
% 5.82/6.04 = ( times_times_rat @ Y3 @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_of_nat_commute
% 5.82/6.04 thf(fact_1403_mult__of__nat__commute,axiom,
% 5.82/6.04 ! [X2: nat,Y3: real] :
% 5.82/6.04 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y3 )
% 5.82/6.04 = ( times_times_real @ Y3 @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_of_nat_commute
% 5.82/6.04 thf(fact_1404_mult__of__nat__commute,axiom,
% 5.82/6.04 ! [X2: nat,Y3: int] :
% 5.82/6.04 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y3 )
% 5.82/6.04 = ( times_times_int @ Y3 @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_of_nat_commute
% 5.82/6.04 thf(fact_1405_mult__of__nat__commute,axiom,
% 5.82/6.04 ! [X2: nat,Y3: nat] :
% 5.82/6.04 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y3 )
% 5.82/6.04 = ( times_times_nat @ Y3 @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_of_nat_commute
% 5.82/6.04 thf(fact_1406_less__imp__of__nat__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ M @ N )
% 5.82/6.04 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_imp_of_nat_less
% 5.82/6.04 thf(fact_1407_less__imp__of__nat__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ M @ N )
% 5.82/6.04 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_imp_of_nat_less
% 5.82/6.04 thf(fact_1408_less__imp__of__nat__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ M @ N )
% 5.82/6.04 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_imp_of_nat_less
% 5.82/6.04 thf(fact_1409_less__imp__of__nat__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ M @ N )
% 5.82/6.04 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_imp_of_nat_less
% 5.82/6.04 thf(fact_1410_of__nat__less__imp__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.82/6.04 => ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_imp_less
% 5.82/6.04 thf(fact_1411_of__nat__less__imp__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.04 => ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_imp_less
% 5.82/6.04 thf(fact_1412_of__nat__less__imp__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.04 => ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_imp_less
% 5.82/6.04 thf(fact_1413_of__nat__less__imp__less,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.04 => ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_imp_less
% 5.82/6.04 thf(fact_1414_div__mult2__eq_H,axiom,
% 5.82/6.04 ! [A2: int,M: nat,N: nat] :
% 5.82/6.04 ( ( divide_divide_int @ A2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.04 = ( divide_divide_int @ ( divide_divide_int @ A2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % div_mult2_eq'
% 5.82/6.04 thf(fact_1415_div__mult2__eq_H,axiom,
% 5.82/6.04 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.04 ( ( divide_divide_nat @ A2 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.82/6.04 = ( divide_divide_nat @ ( divide_divide_nat @ A2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % div_mult2_eq'
% 5.82/6.04 thf(fact_1416_of__nat__mono,axiom,
% 5.82/6.04 ! [I: nat,J: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.04 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mono
% 5.82/6.04 thf(fact_1417_of__nat__mono,axiom,
% 5.82/6.04 ! [I: nat,J: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.04 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mono
% 5.82/6.04 thf(fact_1418_of__nat__mono,axiom,
% 5.82/6.04 ! [I: nat,J: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.04 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mono
% 5.82/6.04 thf(fact_1419_of__nat__mono,axiom,
% 5.82/6.04 ! [I: nat,J: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.04 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_mono
% 5.82/6.04 thf(fact_1420_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.04 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.82/6.04 thf(fact_1421_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.82/6.04 ! [M: nat,N: nat] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.04 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.82/6.04 thf(fact_1422_of__nat__max,axiom,
% 5.82/6.04 ! [X2: nat,Y3: nat] :
% 5.82/6.04 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.82/6.04 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X2 ) @ ( semiri4216267220026989637d_enat @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_max
% 5.82/6.04 thf(fact_1423_of__nat__max,axiom,
% 5.82/6.04 ! [X2: nat,Y3: nat] :
% 5.82/6.04 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.82/6.04 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_max
% 5.82/6.04 thf(fact_1424_of__nat__max,axiom,
% 5.82/6.04 ! [X2: nat,Y3: nat] :
% 5.82/6.04 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.82/6.04 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_max
% 5.82/6.04 thf(fact_1425_of__nat__max,axiom,
% 5.82/6.04 ! [X2: nat,Y3: nat] :
% 5.82/6.04 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.82/6.04 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( semiri1316708129612266289at_nat @ Y3 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_max
% 5.82/6.04 thf(fact_1426_of__nat__diff,axiom,
% 5.82/6.04 ! [N: nat,M: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.04 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.04 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_diff
% 5.82/6.04 thf(fact_1427_of__nat__diff,axiom,
% 5.82/6.04 ! [N: nat,M: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.04 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.04 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_diff
% 5.82/6.04 thf(fact_1428_of__nat__diff,axiom,
% 5.82/6.04 ! [N: nat,M: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.04 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.04 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_diff
% 5.82/6.04 thf(fact_1429_of__nat__diff,axiom,
% 5.82/6.04 ! [N: nat,M: nat] :
% 5.82/6.04 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.04 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.04 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_diff
% 5.82/6.04 thf(fact_1430_real__of__nat__div4,axiom,
% 5.82/6.04 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_div4
% 5.82/6.04 thf(fact_1431_in__mono,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat,X2: nat] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.04 => ( ( member_nat @ X2 @ A )
% 5.82/6.04 => ( member_nat @ X2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % in_mono
% 5.82/6.04 thf(fact_1432_in__mono,axiom,
% 5.82/6.04 ! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.04 ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.04 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.04 => ( member_VEBT_VEBT @ X2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % in_mono
% 5.82/6.04 thf(fact_1433_in__mono,axiom,
% 5.82/6.04 ! [A: set_real,B: set_real,X2: real] :
% 5.82/6.04 ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.04 => ( ( member_real @ X2 @ A )
% 5.82/6.04 => ( member_real @ X2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % in_mono
% 5.82/6.04 thf(fact_1434_in__mono,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int,X2: int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( member_int @ X2 @ A )
% 5.82/6.04 => ( member_int @ X2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % in_mono
% 5.82/6.04 thf(fact_1435_subsetD,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat,C2: nat] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.04 => ( ( member_nat @ C2 @ A )
% 5.82/6.04 => ( member_nat @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetD
% 5.82/6.04 thf(fact_1436_subsetD,axiom,
% 5.82/6.04 ! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 5.82/6.04 ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.04 => ( ( member_VEBT_VEBT @ C2 @ A )
% 5.82/6.04 => ( member_VEBT_VEBT @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetD
% 5.82/6.04 thf(fact_1437_subsetD,axiom,
% 5.82/6.04 ! [A: set_real,B: set_real,C2: real] :
% 5.82/6.04 ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.04 => ( ( member_real @ C2 @ A )
% 5.82/6.04 => ( member_real @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetD
% 5.82/6.04 thf(fact_1438_subsetD,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int,C2: int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( member_int @ C2 @ A )
% 5.82/6.04 => ( member_int @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subsetD
% 5.82/6.04 thf(fact_1439_psubsetE,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_set_int @ A @ B )
% 5.82/6.04 => ~ ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ord_less_eq_set_int @ B @ A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubsetE
% 5.82/6.04 thf(fact_1440_equalityE,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( A = B )
% 5.82/6.04 => ~ ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ~ ( ord_less_eq_set_int @ B @ A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % equalityE
% 5.82/6.04 thf(fact_1441_subset__eq,axiom,
% 5.82/6.04 ( ord_less_eq_set_nat
% 5.82/6.04 = ( ^ [A6: set_nat,B5: set_nat] :
% 5.82/6.04 ! [X3: nat] :
% 5.82/6.04 ( ( member_nat @ X3 @ A6 )
% 5.82/6.04 => ( member_nat @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_eq
% 5.82/6.04 thf(fact_1442_subset__eq,axiom,
% 5.82/6.04 ( ord_le4337996190870823476T_VEBT
% 5.82/6.04 = ( ^ [A6: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.82/6.04 ! [X3: vEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ X3 @ A6 )
% 5.82/6.04 => ( member_VEBT_VEBT @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_eq
% 5.82/6.04 thf(fact_1443_subset__eq,axiom,
% 5.82/6.04 ( ord_less_eq_set_real
% 5.82/6.04 = ( ^ [A6: set_real,B5: set_real] :
% 5.82/6.04 ! [X3: real] :
% 5.82/6.04 ( ( member_real @ X3 @ A6 )
% 5.82/6.04 => ( member_real @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_eq
% 5.82/6.04 thf(fact_1444_subset__eq,axiom,
% 5.82/6.04 ( ord_less_eq_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ! [X3: int] :
% 5.82/6.04 ( ( member_int @ X3 @ A6 )
% 5.82/6.04 => ( member_int @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_eq
% 5.82/6.04 thf(fact_1445_equalityD1,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( A = B )
% 5.82/6.04 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % equalityD1
% 5.82/6.04 thf(fact_1446_Set_OequalityD2,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( A = B )
% 5.82/6.04 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.82/6.04
% 5.82/6.04 % Set.equalityD2
% 5.82/6.04 thf(fact_1447_psubset__eq,axiom,
% 5.82/6.04 ( ord_less_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A6 @ B5 )
% 5.82/6.04 & ( A6 != B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_eq
% 5.82/6.04 thf(fact_1448_subset__iff,axiom,
% 5.82/6.04 ( ord_less_eq_set_nat
% 5.82/6.04 = ( ^ [A6: set_nat,B5: set_nat] :
% 5.82/6.04 ! [T2: nat] :
% 5.82/6.04 ( ( member_nat @ T2 @ A6 )
% 5.82/6.04 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_iff
% 5.82/6.04 thf(fact_1449_subset__iff,axiom,
% 5.82/6.04 ( ord_le4337996190870823476T_VEBT
% 5.82/6.04 = ( ^ [A6: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.82/6.04 ! [T2: vEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ T2 @ A6 )
% 5.82/6.04 => ( member_VEBT_VEBT @ T2 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_iff
% 5.82/6.04 thf(fact_1450_subset__iff,axiom,
% 5.82/6.04 ( ord_less_eq_set_real
% 5.82/6.04 = ( ^ [A6: set_real,B5: set_real] :
% 5.82/6.04 ! [T2: real] :
% 5.82/6.04 ( ( member_real @ T2 @ A6 )
% 5.82/6.04 => ( member_real @ T2 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_iff
% 5.82/6.04 thf(fact_1451_subset__iff,axiom,
% 5.82/6.04 ( ord_less_eq_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ! [T2: int] :
% 5.82/6.04 ( ( member_int @ T2 @ A6 )
% 5.82/6.04 => ( member_int @ T2 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_iff
% 5.82/6.04 thf(fact_1452_subset__refl,axiom,
% 5.82/6.04 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.82/6.04
% 5.82/6.04 % subset_refl
% 5.82/6.04 thf(fact_1453_Collect__mono,axiom,
% 5.82/6.04 ! [P: nat > $o,Q: nat > $o] :
% 5.82/6.04 ( ! [X4: nat] :
% 5.82/6.04 ( ( P @ X4 )
% 5.82/6.04 => ( Q @ X4 ) )
% 5.82/6.04 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono
% 5.82/6.04 thf(fact_1454_Collect__mono,axiom,
% 5.82/6.04 ! [P: complex > $o,Q: complex > $o] :
% 5.82/6.04 ( ! [X4: complex] :
% 5.82/6.04 ( ( P @ X4 )
% 5.82/6.04 => ( Q @ X4 ) )
% 5.82/6.04 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono
% 5.82/6.04 thf(fact_1455_Collect__mono,axiom,
% 5.82/6.04 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.82/6.04 ( ! [X4: product_prod_int_int] :
% 5.82/6.04 ( ( P @ X4 )
% 5.82/6.04 => ( Q @ X4 ) )
% 5.82/6.04 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono
% 5.82/6.04 thf(fact_1456_Collect__mono,axiom,
% 5.82/6.04 ! [P: int > $o,Q: int > $o] :
% 5.82/6.04 ( ! [X4: int] :
% 5.82/6.04 ( ( P @ X4 )
% 5.82/6.04 => ( Q @ X4 ) )
% 5.82/6.04 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono
% 5.82/6.04 thf(fact_1457_subset__trans,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int,C: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( ord_less_eq_set_int @ B @ C )
% 5.82/6.04 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_trans
% 5.82/6.04 thf(fact_1458_set__eq__subset,axiom,
% 5.82/6.04 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A6 @ B5 )
% 5.82/6.04 & ( ord_less_eq_set_int @ B5 @ A6 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_eq_subset
% 5.82/6.04 thf(fact_1459_Collect__mono__iff,axiom,
% 5.82/6.04 ! [P: nat > $o,Q: nat > $o] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.82/6.04 = ( ! [X3: nat] :
% 5.82/6.04 ( ( P @ X3 )
% 5.82/6.04 => ( Q @ X3 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono_iff
% 5.82/6.04 thf(fact_1460_Collect__mono__iff,axiom,
% 5.82/6.04 ! [P: complex > $o,Q: complex > $o] :
% 5.82/6.04 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.82/6.04 = ( ! [X3: complex] :
% 5.82/6.04 ( ( P @ X3 )
% 5.82/6.04 => ( Q @ X3 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono_iff
% 5.82/6.04 thf(fact_1461_Collect__mono__iff,axiom,
% 5.82/6.04 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.82/6.04 ( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
% 5.82/6.04 = ( ! [X3: product_prod_int_int] :
% 5.82/6.04 ( ( P @ X3 )
% 5.82/6.04 => ( Q @ X3 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono_iff
% 5.82/6.04 thf(fact_1462_Collect__mono__iff,axiom,
% 5.82/6.04 ! [P: int > $o,Q: int > $o] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.82/6.04 = ( ! [X3: int] :
% 5.82/6.04 ( ( P @ X3 )
% 5.82/6.04 => ( Q @ X3 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_mono_iff
% 5.82/6.04 thf(fact_1463_psubset__imp__subset,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_set_int @ A @ B )
% 5.82/6.04 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_imp_subset
% 5.82/6.04 thf(fact_1464_psubset__subset__trans,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int,C: set_int] :
% 5.82/6.04 ( ( ord_less_set_int @ A @ B )
% 5.82/6.04 => ( ( ord_less_eq_set_int @ B @ C )
% 5.82/6.04 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_subset_trans
% 5.82/6.04 thf(fact_1465_subset__not__subset__eq,axiom,
% 5.82/6.04 ( ord_less_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A6 @ B5 )
% 5.82/6.04 & ~ ( ord_less_eq_set_int @ B5 @ A6 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_not_subset_eq
% 5.82/6.04 thf(fact_1466_subset__psubset__trans,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int,C: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( ord_less_set_int @ B @ C )
% 5.82/6.04 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_psubset_trans
% 5.82/6.04 thf(fact_1467_subset__iff__psubset__eq,axiom,
% 5.82/6.04 ( ord_less_eq_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( ( ord_less_set_int @ A6 @ B5 )
% 5.82/6.04 | ( A6 = B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % subset_iff_psubset_eq
% 5.82/6.04 thf(fact_1468_int__less__induct,axiom,
% 5.82/6.04 ! [I: int,K: int,P: int > $o] :
% 5.82/6.04 ( ( ord_less_int @ I @ K )
% 5.82/6.04 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.82/6.04 => ( ! [I2: int] :
% 5.82/6.04 ( ( ord_less_int @ I2 @ K )
% 5.82/6.04 => ( ( P @ I2 )
% 5.82/6.04 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.82/6.04 => ( P @ I ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_less_induct
% 5.82/6.04 thf(fact_1469_psubset__imp__ex__mem,axiom,
% 5.82/6.04 ! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ( ord_le3480810397992357184T_VEBT @ A @ B )
% 5.82/6.04 => ? [B3: vEBT_VEBT] : ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B @ A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_imp_ex_mem
% 5.82/6.04 thf(fact_1470_psubset__imp__ex__mem,axiom,
% 5.82/6.04 ! [A: set_real,B: set_real] :
% 5.82/6.04 ( ( ord_less_set_real @ A @ B )
% 5.82/6.04 => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B @ A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_imp_ex_mem
% 5.82/6.04 thf(fact_1471_psubset__imp__ex__mem,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_set_int @ A @ B )
% 5.82/6.04 => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B @ A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_imp_ex_mem
% 5.82/6.04 thf(fact_1472_psubset__imp__ex__mem,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( ord_less_set_nat @ A @ B )
% 5.82/6.04 => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B @ A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % psubset_imp_ex_mem
% 5.82/6.04 thf(fact_1473_DiffE,axiom,
% 5.82/6.04 ! [C2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A @ B ) )
% 5.82/6.04 => ~ ( ( member_VEBT_VEBT @ C2 @ A )
% 5.82/6.04 => ( member_VEBT_VEBT @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffE
% 5.82/6.04 thf(fact_1474_DiffE,axiom,
% 5.82/6.04 ! [C2: real,A: set_real,B: set_real] :
% 5.82/6.04 ( ( member_real @ C2 @ ( minus_minus_set_real @ A @ B ) )
% 5.82/6.04 => ~ ( ( member_real @ C2 @ A )
% 5.82/6.04 => ( member_real @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffE
% 5.82/6.04 thf(fact_1475_DiffE,axiom,
% 5.82/6.04 ! [C2: int,A: set_int,B: set_int] :
% 5.82/6.04 ( ( member_int @ C2 @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.04 => ~ ( ( member_int @ C2 @ A )
% 5.82/6.04 => ( member_int @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffE
% 5.82/6.04 thf(fact_1476_DiffE,axiom,
% 5.82/6.04 ! [C2: nat,A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.04 => ~ ( ( member_nat @ C2 @ A )
% 5.82/6.04 => ( member_nat @ C2 @ B ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffE
% 5.82/6.04 thf(fact_1477_DiffD1,axiom,
% 5.82/6.04 ! [C2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A @ B ) )
% 5.82/6.04 => ( member_VEBT_VEBT @ C2 @ A ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD1
% 5.82/6.04 thf(fact_1478_DiffD1,axiom,
% 5.82/6.04 ! [C2: real,A: set_real,B: set_real] :
% 5.82/6.04 ( ( member_real @ C2 @ ( minus_minus_set_real @ A @ B ) )
% 5.82/6.04 => ( member_real @ C2 @ A ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD1
% 5.82/6.04 thf(fact_1479_DiffD1,axiom,
% 5.82/6.04 ! [C2: int,A: set_int,B: set_int] :
% 5.82/6.04 ( ( member_int @ C2 @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.04 => ( member_int @ C2 @ A ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD1
% 5.82/6.04 thf(fact_1480_DiffD1,axiom,
% 5.82/6.04 ! [C2: nat,A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.04 => ( member_nat @ C2 @ A ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD1
% 5.82/6.04 thf(fact_1481_DiffD2,axiom,
% 5.82/6.04 ! [C2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A @ B ) )
% 5.82/6.04 => ~ ( member_VEBT_VEBT @ C2 @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD2
% 5.82/6.04 thf(fact_1482_DiffD2,axiom,
% 5.82/6.04 ! [C2: real,A: set_real,B: set_real] :
% 5.82/6.04 ( ( member_real @ C2 @ ( minus_minus_set_real @ A @ B ) )
% 5.82/6.04 => ~ ( member_real @ C2 @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD2
% 5.82/6.04 thf(fact_1483_DiffD2,axiom,
% 5.82/6.04 ! [C2: int,A: set_int,B: set_int] :
% 5.82/6.04 ( ( member_int @ C2 @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.04 => ~ ( member_int @ C2 @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD2
% 5.82/6.04 thf(fact_1484_DiffD2,axiom,
% 5.82/6.04 ! [C2: nat,A: set_nat,B: set_nat] :
% 5.82/6.04 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.04 => ~ ( member_nat @ C2 @ B ) ) ).
% 5.82/6.04
% 5.82/6.04 % DiffD2
% 5.82/6.04 thf(fact_1485_int__distrib_I3_J,axiom,
% 5.82/6.04 ! [Z1: int,Z22: int,W: int] :
% 5.82/6.04 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.82/6.04 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_distrib(3)
% 5.82/6.04 thf(fact_1486_int__distrib_I4_J,axiom,
% 5.82/6.04 ! [W: int,Z1: int,Z22: int] :
% 5.82/6.04 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.82/6.04 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_distrib(4)
% 5.82/6.04 thf(fact_1487_nat__less__real__le,axiom,
% 5.82/6.04 ( ord_less_nat
% 5.82/6.04 = ( ^ [N4: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N4 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % nat_less_real_le
% 5.82/6.04 thf(fact_1488_nat__le__real__less,axiom,
% 5.82/6.04 ( ord_less_eq_nat
% 5.82/6.04 = ( ^ [N4: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % nat_le_real_less
% 5.82/6.04 thf(fact_1489_Set_Oempty__def,axiom,
% 5.82/6.04 ( bot_bot_set_complex
% 5.82/6.04 = ( collect_complex
% 5.82/6.04 @ ^ [X3: complex] : $false ) ) ).
% 5.82/6.04
% 5.82/6.04 % Set.empty_def
% 5.82/6.04 thf(fact_1490_Set_Oempty__def,axiom,
% 5.82/6.04 ( bot_bo1796632182523588997nt_int
% 5.82/6.04 = ( collec213857154873943460nt_int
% 5.82/6.04 @ ^ [X3: product_prod_int_int] : $false ) ) ).
% 5.82/6.04
% 5.82/6.04 % Set.empty_def
% 5.82/6.04 thf(fact_1491_Set_Oempty__def,axiom,
% 5.82/6.04 ( bot_bot_set_nat
% 5.82/6.04 = ( collect_nat
% 5.82/6.04 @ ^ [X3: nat] : $false ) ) ).
% 5.82/6.04
% 5.82/6.04 % Set.empty_def
% 5.82/6.04 thf(fact_1492_Set_Oempty__def,axiom,
% 5.82/6.04 ( bot_bot_set_int
% 5.82/6.04 = ( collect_int
% 5.82/6.04 @ ^ [X3: int] : $false ) ) ).
% 5.82/6.04
% 5.82/6.04 % Set.empty_def
% 5.82/6.04 thf(fact_1493_Collect__subset,axiom,
% 5.82/6.04 ! [A: set_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.04 ( ord_le4337996190870823476T_VEBT
% 5.82/6.04 @ ( collect_VEBT_VEBT
% 5.82/6.04 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.04 & ( P @ X3 ) ) )
% 5.82/6.04 @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_subset
% 5.82/6.04 thf(fact_1494_Collect__subset,axiom,
% 5.82/6.04 ! [A: set_real,P: real > $o] :
% 5.82/6.04 ( ord_less_eq_set_real
% 5.82/6.04 @ ( collect_real
% 5.82/6.04 @ ^ [X3: real] :
% 5.82/6.04 ( ( member_real @ X3 @ A )
% 5.82/6.04 & ( P @ X3 ) ) )
% 5.82/6.04 @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_subset
% 5.82/6.04 thf(fact_1495_Collect__subset,axiom,
% 5.82/6.04 ! [A: set_nat,P: nat > $o] :
% 5.82/6.04 ( ord_less_eq_set_nat
% 5.82/6.04 @ ( collect_nat
% 5.82/6.04 @ ^ [X3: nat] :
% 5.82/6.04 ( ( member_nat @ X3 @ A )
% 5.82/6.04 & ( P @ X3 ) ) )
% 5.82/6.04 @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_subset
% 5.82/6.04 thf(fact_1496_Collect__subset,axiom,
% 5.82/6.04 ! [A: set_complex,P: complex > $o] :
% 5.82/6.04 ( ord_le211207098394363844omplex
% 5.82/6.04 @ ( collect_complex
% 5.82/6.04 @ ^ [X3: complex] :
% 5.82/6.04 ( ( member_complex @ X3 @ A )
% 5.82/6.04 & ( P @ X3 ) ) )
% 5.82/6.04 @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_subset
% 5.82/6.04 thf(fact_1497_Collect__subset,axiom,
% 5.82/6.04 ! [A: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.82/6.04 ( ord_le2843351958646193337nt_int
% 5.82/6.04 @ ( collec213857154873943460nt_int
% 5.82/6.04 @ ^ [X3: product_prod_int_int] :
% 5.82/6.04 ( ( member5262025264175285858nt_int @ X3 @ A )
% 5.82/6.04 & ( P @ X3 ) ) )
% 5.82/6.04 @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_subset
% 5.82/6.04 thf(fact_1498_Collect__subset,axiom,
% 5.82/6.04 ! [A: set_int,P: int > $o] :
% 5.82/6.04 ( ord_less_eq_set_int
% 5.82/6.04 @ ( collect_int
% 5.82/6.04 @ ^ [X3: int] :
% 5.82/6.04 ( ( member_int @ X3 @ A )
% 5.82/6.04 & ( P @ X3 ) ) )
% 5.82/6.04 @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Collect_subset
% 5.82/6.04 thf(fact_1499_less__eq__set__def,axiom,
% 5.82/6.04 ( ord_less_eq_set_nat
% 5.82/6.04 = ( ^ [A6: set_nat,B5: set_nat] :
% 5.82/6.04 ( ord_less_eq_nat_o
% 5.82/6.04 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: nat] : ( member_nat @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_eq_set_def
% 5.82/6.04 thf(fact_1500_less__eq__set__def,axiom,
% 5.82/6.04 ( ord_le4337996190870823476T_VEBT
% 5.82/6.04 = ( ^ [A6: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.82/6.04 ( ord_le418104280809901481VEBT_o
% 5.82/6.04 @ ^ [X3: vEBT_VEBT] : ( member_VEBT_VEBT @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: vEBT_VEBT] : ( member_VEBT_VEBT @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_eq_set_def
% 5.82/6.04 thf(fact_1501_less__eq__set__def,axiom,
% 5.82/6.04 ( ord_less_eq_set_real
% 5.82/6.04 = ( ^ [A6: set_real,B5: set_real] :
% 5.82/6.04 ( ord_less_eq_real_o
% 5.82/6.04 @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: real] : ( member_real @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_eq_set_def
% 5.82/6.04 thf(fact_1502_less__eq__set__def,axiom,
% 5.82/6.04 ( ord_less_eq_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( ord_less_eq_int_o
% 5.82/6.04 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: int] : ( member_int @ X3 @ B5 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % less_eq_set_def
% 5.82/6.04 thf(fact_1503_of__nat__less__two__power,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_two_power
% 5.82/6.04 thf(fact_1504_of__nat__less__two__power,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_two_power
% 5.82/6.04 thf(fact_1505_of__nat__less__two__power,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_two_power
% 5.82/6.04 thf(fact_1506_of__nat__less__two__power,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % of_nat_less_two_power
% 5.82/6.04 thf(fact_1507_set__diff__eq,axiom,
% 5.82/6.04 ( minus_5127226145743854075T_VEBT
% 5.82/6.04 = ( ^ [A6: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.82/6.04 ( collect_VEBT_VEBT
% 5.82/6.04 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.04 ( ( member_VEBT_VEBT @ X3 @ A6 )
% 5.82/6.04 & ~ ( member_VEBT_VEBT @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_diff_eq
% 5.82/6.04 thf(fact_1508_set__diff__eq,axiom,
% 5.82/6.04 ( minus_minus_set_real
% 5.82/6.04 = ( ^ [A6: set_real,B5: set_real] :
% 5.82/6.04 ( collect_real
% 5.82/6.04 @ ^ [X3: real] :
% 5.82/6.04 ( ( member_real @ X3 @ A6 )
% 5.82/6.04 & ~ ( member_real @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_diff_eq
% 5.82/6.04 thf(fact_1509_set__diff__eq,axiom,
% 5.82/6.04 ( minus_minus_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( collect_int
% 5.82/6.04 @ ^ [X3: int] :
% 5.82/6.04 ( ( member_int @ X3 @ A6 )
% 5.82/6.04 & ~ ( member_int @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_diff_eq
% 5.82/6.04 thf(fact_1510_set__diff__eq,axiom,
% 5.82/6.04 ( minus_811609699411566653omplex
% 5.82/6.04 = ( ^ [A6: set_complex,B5: set_complex] :
% 5.82/6.04 ( collect_complex
% 5.82/6.04 @ ^ [X3: complex] :
% 5.82/6.04 ( ( member_complex @ X3 @ A6 )
% 5.82/6.04 & ~ ( member_complex @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_diff_eq
% 5.82/6.04 thf(fact_1511_set__diff__eq,axiom,
% 5.82/6.04 ( minus_1052850069191792384nt_int
% 5.82/6.04 = ( ^ [A6: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
% 5.82/6.04 ( collec213857154873943460nt_int
% 5.82/6.04 @ ^ [X3: product_prod_int_int] :
% 5.82/6.04 ( ( member5262025264175285858nt_int @ X3 @ A6 )
% 5.82/6.04 & ~ ( member5262025264175285858nt_int @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_diff_eq
% 5.82/6.04 thf(fact_1512_set__diff__eq,axiom,
% 5.82/6.04 ( minus_minus_set_nat
% 5.82/6.04 = ( ^ [A6: set_nat,B5: set_nat] :
% 5.82/6.04 ( collect_nat
% 5.82/6.04 @ ^ [X3: nat] :
% 5.82/6.04 ( ( member_nat @ X3 @ A6 )
% 5.82/6.04 & ~ ( member_nat @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % set_diff_eq
% 5.82/6.04 thf(fact_1513_minus__set__def,axiom,
% 5.82/6.04 ( minus_5127226145743854075T_VEBT
% 5.82/6.04 = ( ^ [A6: set_VEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.82/6.04 ( collect_VEBT_VEBT
% 5.82/6.04 @ ( minus_2794559001203777698VEBT_o
% 5.82/6.04 @ ^ [X3: vEBT_VEBT] : ( member_VEBT_VEBT @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: vEBT_VEBT] : ( member_VEBT_VEBT @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minus_set_def
% 5.82/6.04 thf(fact_1514_minus__set__def,axiom,
% 5.82/6.04 ( minus_minus_set_real
% 5.82/6.04 = ( ^ [A6: set_real,B5: set_real] :
% 5.82/6.04 ( collect_real
% 5.82/6.04 @ ( minus_minus_real_o
% 5.82/6.04 @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: real] : ( member_real @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minus_set_def
% 5.82/6.04 thf(fact_1515_minus__set__def,axiom,
% 5.82/6.04 ( minus_minus_set_int
% 5.82/6.04 = ( ^ [A6: set_int,B5: set_int] :
% 5.82/6.04 ( collect_int
% 5.82/6.04 @ ( minus_minus_int_o
% 5.82/6.04 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: int] : ( member_int @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minus_set_def
% 5.82/6.04 thf(fact_1516_minus__set__def,axiom,
% 5.82/6.04 ( minus_811609699411566653omplex
% 5.82/6.04 = ( ^ [A6: set_complex,B5: set_complex] :
% 5.82/6.04 ( collect_complex
% 5.82/6.04 @ ( minus_8727706125548526216plex_o
% 5.82/6.04 @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: complex] : ( member_complex @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minus_set_def
% 5.82/6.04 thf(fact_1517_minus__set__def,axiom,
% 5.82/6.04 ( minus_1052850069191792384nt_int
% 5.82/6.04 = ( ^ [A6: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
% 5.82/6.04 ( collec213857154873943460nt_int
% 5.82/6.04 @ ( minus_711738161318947805_int_o
% 5.82/6.04 @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minus_set_def
% 5.82/6.04 thf(fact_1518_minus__set__def,axiom,
% 5.82/6.04 ( minus_minus_set_nat
% 5.82/6.04 = ( ^ [A6: set_nat,B5: set_nat] :
% 5.82/6.04 ( collect_nat
% 5.82/6.04 @ ( minus_minus_nat_o
% 5.82/6.04 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 5.82/6.04 @ ^ [X3: nat] : ( member_nat @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % minus_set_def
% 5.82/6.04 thf(fact_1519_real__of__nat__div3,axiom,
% 5.82/6.04 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.82/6.04
% 5.82/6.04 % real_of_nat_div3
% 5.82/6.04 thf(fact_1520_double__diff,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.04 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.82/6.04 => ( ( minus_minus_set_nat @ B @ ( minus_minus_set_nat @ C @ A ) )
% 5.82/6.04 = A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % double_diff
% 5.82/6.04 thf(fact_1521_double__diff,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int,C: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.04 => ( ( ord_less_eq_set_int @ B @ C )
% 5.82/6.04 => ( ( minus_minus_set_int @ B @ ( minus_minus_set_int @ C @ A ) )
% 5.82/6.04 = A ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % double_diff
% 5.82/6.04 thf(fact_1522_Diff__subset,axiom,
% 5.82/6.04 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B ) @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_subset
% 5.82/6.04 thf(fact_1523_Diff__subset,axiom,
% 5.82/6.04 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ B ) @ A ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_subset
% 5.82/6.04 thf(fact_1524_Diff__mono,axiom,
% 5.82/6.04 ! [A: set_nat,C: set_nat,D: set_nat,B: set_nat] :
% 5.82/6.04 ( ( ord_less_eq_set_nat @ A @ C )
% 5.82/6.04 => ( ( ord_less_eq_set_nat @ D @ B )
% 5.82/6.04 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( minus_minus_set_nat @ C @ D ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_mono
% 5.82/6.04 thf(fact_1525_Diff__mono,axiom,
% 5.82/6.04 ! [A: set_int,C: set_int,D: set_int,B: set_int] :
% 5.82/6.04 ( ( ord_less_eq_set_int @ A @ C )
% 5.82/6.04 => ( ( ord_less_eq_set_int @ D @ B )
% 5.82/6.04 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ B ) @ ( minus_minus_set_int @ C @ D ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Diff_mono
% 5.82/6.04 thf(fact_1526_int__le__induct,axiom,
% 5.82/6.04 ! [I: int,K: int,P: int > $o] :
% 5.82/6.04 ( ( ord_less_eq_int @ I @ K )
% 5.82/6.04 => ( ( P @ K )
% 5.82/6.04 => ( ! [I2: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ I2 @ K )
% 5.82/6.04 => ( ( P @ I2 )
% 5.82/6.04 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.82/6.04 => ( P @ I ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_le_induct
% 5.82/6.04 thf(fact_1527_zless__add1__eq,axiom,
% 5.82/6.04 ! [W: int,Z: int] :
% 5.82/6.04 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.82/6.04 = ( ( ord_less_int @ W @ Z )
% 5.82/6.04 | ( W = Z ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % zless_add1_eq
% 5.82/6.04 thf(fact_1528_int__gr__induct,axiom,
% 5.82/6.04 ! [K: int,I: int,P: int > $o] :
% 5.82/6.04 ( ( ord_less_int @ K @ I )
% 5.82/6.04 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.82/6.04 => ( ! [I2: int] :
% 5.82/6.04 ( ( ord_less_int @ K @ I2 )
% 5.82/6.04 => ( ( P @ I2 )
% 5.82/6.04 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.82/6.04 => ( P @ I ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_gr_induct
% 5.82/6.04 thf(fact_1529_int__distrib_I1_J,axiom,
% 5.82/6.04 ! [Z1: int,Z22: int,W: int] :
% 5.82/6.04 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.82/6.04 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_distrib(1)
% 5.82/6.04 thf(fact_1530_int__distrib_I2_J,axiom,
% 5.82/6.04 ! [W: int,Z1: int,Z22: int] :
% 5.82/6.04 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.82/6.04 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_distrib(2)
% 5.82/6.04 thf(fact_1531_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 5.82/6.04 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.82/6.04 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 )
% 5.82/6.04 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 5.82/6.04 thf(fact_1532_add1__zle__eq,axiom,
% 5.82/6.04 ! [W: int,Z: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.82/6.04 = ( ord_less_int @ W @ Z ) ) ).
% 5.82/6.04
% 5.82/6.04 % add1_zle_eq
% 5.82/6.04 thf(fact_1533_int__ge__induct,axiom,
% 5.82/6.04 ! [K: int,I: int,P: int > $o] :
% 5.82/6.04 ( ( ord_less_eq_int @ K @ I )
% 5.82/6.04 => ( ( P @ K )
% 5.82/6.04 => ( ! [I2: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ K @ I2 )
% 5.82/6.04 => ( ( P @ I2 )
% 5.82/6.04 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.82/6.04 => ( P @ I ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_ge_induct
% 5.82/6.04 thf(fact_1534_zless__imp__add1__zle,axiom,
% 5.82/6.04 ! [W: int,Z: int] :
% 5.82/6.04 ( ( ord_less_int @ W @ Z )
% 5.82/6.04 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.82/6.04
% 5.82/6.04 % zless_imp_add1_zle
% 5.82/6.04 thf(fact_1535_int__induct,axiom,
% 5.82/6.04 ! [P: int > $o,K: int,I: int] :
% 5.82/6.04 ( ( P @ K )
% 5.82/6.04 => ( ! [I2: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ K @ I2 )
% 5.82/6.04 => ( ( P @ I2 )
% 5.82/6.04 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.82/6.04 => ( ! [I2: int] :
% 5.82/6.04 ( ( ord_less_eq_int @ I2 @ K )
% 5.82/6.04 => ( ( P @ I2 )
% 5.82/6.04 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.82/6.04 => ( P @ I ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % int_induct
% 5.82/6.04 thf(fact_1536_member__bound__height,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % member_bound_height
% 5.82/6.04 thf(fact_1537_Tb_H__cnt,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_eq_nat @ ( vEBT_VEBT_Tb2 @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_cnt2 @ ( vEBT_vebt_buildup @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % Tb'_cnt
% 5.82/6.04 thf(fact_1538_cnt__cnt__eq,axiom,
% 5.82/6.04 ( vEBT_VEBT_cnt
% 5.82/6.04 = ( ^ [T2: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( vEBT_VEBT_cnt2 @ T2 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % cnt_cnt_eq
% 5.82/6.04 thf(fact_1539_t__build__cnt,axiom,
% 5.82/6.04 ! [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 ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % t_build_cnt
% 5.82/6.04 thf(fact_1540_TBOUND__buildupi,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.04 => ( time_T5737551269749752165_VEBTi @ ( vEBT_vebt_buildupi @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % TBOUND_buildupi
% 5.82/6.04 thf(fact_1541_delete__bound__size__univ,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( U
% 5.82/6.04 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_d_e_l_e_t_e @ T @ X2 ) ) @ ( 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 ) ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % delete_bound_size_univ
% 5.82/6.04 thf(fact_1542_buildup__build__time,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % buildup_build_time
% 5.82/6.04 thf(fact_1543_height__double__log__univ__size,axiom,
% 5.82/6.04 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 5.82/6.04 ( ( U
% 5.82/6.04 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 5.82/6.04 => ( ( vEBT_invar_vebt @ T @ Deg )
% 5.82/6.04 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % height_double_log_univ_size
% 5.82/6.04 thf(fact_1544_delete__bound__size__univ_H,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ( U
% 5.82/6.04 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.04 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V1232361888498592333_e_t_e @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % delete_bound_size_univ'
% 5.82/6.04 thf(fact_1545_vebt__minti_Ocases,axiom,
% 5.82/6.04 ! [X2: vEBT_VEBTi] :
% 5.82/6.04 ( ! [A3: $o,B3: $o] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.04 => ( ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.04 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 5.82/6.04 ( X2
% 5.82/6.04 != ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % vebt_minti.cases
% 5.82/6.04 thf(fact_1546_valid__0__not,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT] :
% 5.82/6.04 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.82/6.04
% 5.82/6.04 % valid_0_not
% 5.82/6.04 thf(fact_1547_valid__tree__deg__neq__0,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT] :
% 5.82/6.04 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.82/6.04
% 5.82/6.04 % valid_tree_deg_neq_0
% 5.82/6.04 thf(fact_1548_deg__not__0,axiom,
% 5.82/6.04 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.04 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.04 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % deg_not_0
% 5.82/6.04 thf(fact_1549_T__vebt__buildupi__gq__0,axiom,
% 5.82/6.04 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % T_vebt_buildupi_gq_0
% 5.82/6.04 thf(fact_1550_buildup__gives__valid,axiom,
% 5.82/6.04 ! [N: nat] :
% 5.82/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.04 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.82/6.04
% 5.82/6.04 % buildup_gives_valid
% 5.82/6.04 thf(fact_1551_VEBTi_Oinject_I1_J,axiom,
% 5.82/6.04 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,Y11: option4927543243414619207at_nat,Y12: nat,Y13: array_VEBT_VEBTi,Y14: vEBT_VEBTi] :
% 5.82/6.04 ( ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 5.82/6.04 = ( vEBT_Nodei @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.82/6.04 = ( ( X11 = Y11 )
% 5.82/6.04 & ( X12 = Y12 )
% 5.82/6.04 & ( X13 = Y13 )
% 5.82/6.04 & ( X14 = Y14 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % VEBTi.inject(1)
% 5.82/6.04 thf(fact_1552_double__eq__0__iff,axiom,
% 5.82/6.04 ! [A2: real] :
% 5.82/6.04 ( ( ( plus_plus_real @ A2 @ A2 )
% 5.82/6.04 = zero_zero_real )
% 5.82/6.04 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.04
% 5.82/6.04 % double_eq_0_iff
% 5.82/6.04 thf(fact_1553_double__eq__0__iff,axiom,
% 5.82/6.04 ! [A2: rat] :
% 5.82/6.04 ( ( ( plus_plus_rat @ A2 @ A2 )
% 5.82/6.04 = zero_zero_rat )
% 5.82/6.04 = ( A2 = zero_zero_rat ) ) ).
% 5.82/6.04
% 5.82/6.04 % double_eq_0_iff
% 5.82/6.04 thf(fact_1554_double__eq__0__iff,axiom,
% 5.82/6.04 ! [A2: int] :
% 5.82/6.04 ( ( ( plus_plus_int @ A2 @ A2 )
% 5.82/6.04 = zero_zero_int )
% 5.82/6.04 = ( A2 = zero_zero_int ) ) ).
% 5.82/6.04
% 5.82/6.04 % double_eq_0_iff
% 5.82/6.04 thf(fact_1555_mult__cancel__right,axiom,
% 5.82/6.04 ! [A2: complex,C2: complex,B2: complex] :
% 5.82/6.04 ( ( ( times_times_complex @ A2 @ C2 )
% 5.82/6.04 = ( times_times_complex @ B2 @ C2 ) )
% 5.82/6.04 = ( ( C2 = zero_zero_complex )
% 5.82/6.04 | ( A2 = B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_cancel_right
% 5.82/6.04 thf(fact_1556_mult__cancel__right,axiom,
% 5.82/6.04 ! [A2: real,C2: real,B2: real] :
% 5.82/6.04 ( ( ( times_times_real @ A2 @ C2 )
% 5.82/6.04 = ( times_times_real @ B2 @ C2 ) )
% 5.82/6.04 = ( ( C2 = zero_zero_real )
% 5.82/6.04 | ( A2 = B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_cancel_right
% 5.82/6.04 thf(fact_1557_mult__cancel__right,axiom,
% 5.82/6.04 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.04 ( ( ( times_times_rat @ A2 @ C2 )
% 5.82/6.04 = ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.04 = ( ( C2 = zero_zero_rat )
% 5.82/6.04 | ( A2 = B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_cancel_right
% 5.82/6.04 thf(fact_1558_mult__cancel__right,axiom,
% 5.82/6.04 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.04 ( ( ( times_times_nat @ A2 @ C2 )
% 5.82/6.04 = ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.04 = ( ( C2 = zero_zero_nat )
% 5.82/6.04 | ( A2 = B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_cancel_right
% 5.82/6.04 thf(fact_1559_mult__cancel__right,axiom,
% 5.82/6.04 ! [A2: int,C2: int,B2: int] :
% 5.82/6.04 ( ( ( times_times_int @ A2 @ C2 )
% 5.82/6.04 = ( times_times_int @ B2 @ C2 ) )
% 5.82/6.04 = ( ( C2 = zero_zero_int )
% 5.82/6.04 | ( A2 = B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_cancel_right
% 5.82/6.04 thf(fact_1560_mult__cancel__left,axiom,
% 5.82/6.04 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.04 ( ( ( times_times_complex @ C2 @ A2 )
% 5.82/6.04 = ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.04 = ( ( C2 = zero_zero_complex )
% 5.82/6.04 | ( A2 = B2 ) ) ) ).
% 5.82/6.04
% 5.82/6.04 % mult_cancel_left
% 5.82/6.05 thf(fact_1561_mult__cancel__left,axiom,
% 5.82/6.05 ! [C2: real,A2: real,B2: real] :
% 5.82/6.05 ( ( ( times_times_real @ C2 @ A2 )
% 5.82/6.05 = ( times_times_real @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_real )
% 5.82/6.05 | ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left
% 5.82/6.05 thf(fact_1562_mult__cancel__left,axiom,
% 5.82/6.05 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.05 ( ( ( times_times_rat @ C2 @ A2 )
% 5.82/6.05 = ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_rat )
% 5.82/6.05 | ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left
% 5.82/6.05 thf(fact_1563_mult__cancel__left,axiom,
% 5.82/6.05 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ C2 @ A2 )
% 5.82/6.05 = ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_nat )
% 5.82/6.05 | ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left
% 5.82/6.05 thf(fact_1564_mult__cancel__left,axiom,
% 5.82/6.05 ! [C2: int,A2: int,B2: int] :
% 5.82/6.05 ( ( ( times_times_int @ C2 @ A2 )
% 5.82/6.05 = ( times_times_int @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_int )
% 5.82/6.05 | ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left
% 5.82/6.05 thf(fact_1565_mult__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: complex,B2: complex] :
% 5.82/6.05 ( ( ( times_times_complex @ A2 @ B2 )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 = ( ( A2 = zero_zero_complex )
% 5.82/6.05 | ( B2 = zero_zero_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_eq_0_iff
% 5.82/6.05 thf(fact_1566_mult__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ( times_times_real @ A2 @ B2 )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 = ( ( A2 = zero_zero_real )
% 5.82/6.05 | ( B2 = zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_eq_0_iff
% 5.82/6.05 thf(fact_1567_mult__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ( times_times_rat @ A2 @ B2 )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 = ( ( A2 = zero_zero_rat )
% 5.82/6.05 | ( B2 = zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_eq_0_iff
% 5.82/6.05 thf(fact_1568_mult__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ A2 @ B2 )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( ( A2 = zero_zero_nat )
% 5.82/6.05 | ( B2 = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_eq_0_iff
% 5.82/6.05 thf(fact_1569_mult__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ( times_times_int @ A2 @ B2 )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 = ( ( A2 = zero_zero_int )
% 5.82/6.05 | ( B2 = zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_eq_0_iff
% 5.82/6.05 thf(fact_1570_mult__zero__right,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( times_times_complex @ A2 @ zero_zero_complex )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_right
% 5.82/6.05 thf(fact_1571_mult__zero__right,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( times_times_real @ A2 @ zero_zero_real )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_right
% 5.82/6.05 thf(fact_1572_mult__zero__right,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( times_times_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_right
% 5.82/6.05 thf(fact_1573_mult__zero__right,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( times_times_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_right
% 5.82/6.05 thf(fact_1574_mult__zero__right,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( times_times_int @ A2 @ zero_zero_int )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_right
% 5.82/6.05 thf(fact_1575_mult__zero__left,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( times_times_complex @ zero_zero_complex @ A2 )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_left
% 5.82/6.05 thf(fact_1576_mult__zero__left,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( times_times_real @ zero_zero_real @ A2 )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_left
% 5.82/6.05 thf(fact_1577_mult__zero__left,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( times_times_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_left
% 5.82/6.05 thf(fact_1578_mult__zero__left,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( times_times_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_left
% 5.82/6.05 thf(fact_1579_mult__zero__left,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( times_times_int @ zero_zero_int @ A2 )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % mult_zero_left
% 5.82/6.05 thf(fact_1580_bits__div__by__0,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( divide_divide_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % bits_div_by_0
% 5.82/6.05 thf(fact_1581_bits__div__by__0,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( divide_divide_int @ A2 @ zero_zero_int )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % bits_div_by_0
% 5.82/6.05 thf(fact_1582_bits__div__0,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( divide_divide_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % bits_div_0
% 5.82/6.05 thf(fact_1583_bits__div__0,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( divide_divide_int @ zero_zero_int @ A2 )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % bits_div_0
% 5.82/6.05 thf(fact_1584_div__by__0,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( divide1717551699836669952omplex @ A2 @ zero_zero_complex )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % div_by_0
% 5.82/6.05 thf(fact_1585_div__by__0,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( divide_divide_real @ A2 @ zero_zero_real )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % div_by_0
% 5.82/6.05 thf(fact_1586_div__by__0,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( divide_divide_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % div_by_0
% 5.82/6.05 thf(fact_1587_div__by__0,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( divide_divide_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % div_by_0
% 5.82/6.05 thf(fact_1588_div__by__0,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( divide_divide_int @ A2 @ zero_zero_int )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % div_by_0
% 5.82/6.05 thf(fact_1589_div__0,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A2 )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % div_0
% 5.82/6.05 thf(fact_1590_div__0,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( divide_divide_real @ zero_zero_real @ A2 )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % div_0
% 5.82/6.05 thf(fact_1591_div__0,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( divide_divide_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % div_0
% 5.82/6.05 thf(fact_1592_div__0,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( divide_divide_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % div_0
% 5.82/6.05 thf(fact_1593_div__0,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( divide_divide_int @ zero_zero_int @ A2 )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % div_0
% 5.82/6.05 thf(fact_1594_less__nat__zero__code,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % less_nat_zero_code
% 5.82/6.05 thf(fact_1595_neq0__conv,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( N != zero_zero_nat )
% 5.82/6.05 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % neq0_conv
% 5.82/6.05 thf(fact_1596_bot__nat__0_Onot__eq__extremum,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_nat )
% 5.82/6.05 = ( ord_less_nat @ zero_zero_nat @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % bot_nat_0.not_eq_extremum
% 5.82/6.05 thf(fact_1597_Nat_Oadd__0__right,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.82/6.05 = M ) ).
% 5.82/6.05
% 5.82/6.05 % Nat.add_0_right
% 5.82/6.05 thf(fact_1598_add__is__0,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( plus_plus_nat @ M @ N )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( ( M = zero_zero_nat )
% 5.82/6.05 & ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % add_is_0
% 5.82/6.05 thf(fact_1599_bot__nat__0_Oextremum,axiom,
% 5.82/6.05 ! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ) ).
% 5.82/6.05
% 5.82/6.05 % bot_nat_0.extremum
% 5.82/6.05 thf(fact_1600_le0,axiom,
% 5.82/6.05 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.82/6.05
% 5.82/6.05 % le0
% 5.82/6.05 thf(fact_1601_int__eq__iff__numeral,axiom,
% 5.82/6.05 ! [M: nat,V: num] :
% 5.82/6.05 ( ( ( semiri1314217659103216013at_int @ M )
% 5.82/6.05 = ( numeral_numeral_int @ V ) )
% 5.82/6.05 = ( M
% 5.82/6.05 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % int_eq_iff_numeral
% 5.82/6.05 thf(fact_1602_diff__self__eq__0,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( minus_minus_nat @ M @ M )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % diff_self_eq_0
% 5.82/6.05 thf(fact_1603_diff__0__eq__0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % diff_0_eq_0
% 5.82/6.05 thf(fact_1604_mult__cancel2,axiom,
% 5.82/6.05 ! [M: nat,K: nat,N: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ M @ K )
% 5.82/6.05 = ( times_times_nat @ N @ K ) )
% 5.82/6.05 = ( ( M = N )
% 5.82/6.05 | ( K = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel2
% 5.82/6.05 thf(fact_1605_mult__cancel1,axiom,
% 5.82/6.05 ! [K: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ K @ M )
% 5.82/6.05 = ( times_times_nat @ K @ N ) )
% 5.82/6.05 = ( ( M = N )
% 5.82/6.05 | ( K = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel1
% 5.82/6.05 thf(fact_1606_mult__0__right,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % mult_0_right
% 5.82/6.05 thf(fact_1607_mult__is__0,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ M @ N )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( ( M = zero_zero_nat )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_is_0
% 5.82/6.05 thf(fact_1608_max__0R,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.82/6.05 = N ) ).
% 5.82/6.05
% 5.82/6.05 % max_0R
% 5.82/6.05 thf(fact_1609_max__0L,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.82/6.05 = N ) ).
% 5.82/6.05
% 5.82/6.05 % max_0L
% 5.82/6.05 thf(fact_1610_max__nat_Oright__neutral,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( ord_max_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % max_nat.right_neutral
% 5.82/6.05 thf(fact_1611_max__nat_Oneutr__eq__iff,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( zero_zero_nat
% 5.82/6.05 = ( ord_max_nat @ A2 @ B2 ) )
% 5.82/6.05 = ( ( A2 = zero_zero_nat )
% 5.82/6.05 & ( B2 = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_nat.neutr_eq_iff
% 5.82/6.05 thf(fact_1612_max__nat_Oleft__neutral,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( ord_max_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % max_nat.left_neutral
% 5.82/6.05 thf(fact_1613_max__nat_Oeq__neutr__iff,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( ord_max_nat @ A2 @ B2 )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( ( A2 = zero_zero_nat )
% 5.82/6.05 & ( B2 = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_nat.eq_neutr_iff
% 5.82/6.05 thf(fact_1614_zero__comp__diff__simps_I1_J,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.05 = ( ord_less_eq_real @ B2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_comp_diff_simps(1)
% 5.82/6.05 thf(fact_1615_zero__comp__diff__simps_I1_J,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.05 = ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_comp_diff_simps(1)
% 5.82/6.05 thf(fact_1616_zero__comp__diff__simps_I1_J,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.05 = ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_comp_diff_simps(1)
% 5.82/6.05 thf(fact_1617_zero__comp__diff__simps_I2_J,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.05 = ( ord_less_real @ B2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_comp_diff_simps(2)
% 5.82/6.05 thf(fact_1618_zero__comp__diff__simps_I2_J,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.05 = ( ord_less_rat @ B2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_comp_diff_simps(2)
% 5.82/6.05 thf(fact_1619_zero__comp__diff__simps_I2_J,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.05 = ( ord_less_int @ B2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_comp_diff_simps(2)
% 5.82/6.05 thf(fact_1620_sum__squares__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: real,Y3: real] :
% 5.82/6.05 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 = ( ( X2 = zero_zero_real )
% 5.82/6.05 & ( Y3 = zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_squares_eq_zero_iff
% 5.82/6.05 thf(fact_1621_sum__squares__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: rat,Y3: rat] :
% 5.82/6.05 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 = ( ( X2 = zero_zero_rat )
% 5.82/6.05 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_squares_eq_zero_iff
% 5.82/6.05 thf(fact_1622_sum__squares__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: int,Y3: int] :
% 5.82/6.05 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 = ( ( X2 = zero_zero_int )
% 5.82/6.05 & ( Y3 = zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_squares_eq_zero_iff
% 5.82/6.05 thf(fact_1623_mult__cancel__left1,axiom,
% 5.82/6.05 ! [C2: complex,B2: complex] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_complex )
% 5.82/6.05 | ( B2 = one_one_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left1
% 5.82/6.05 thf(fact_1624_mult__cancel__left1,axiom,
% 5.82/6.05 ! [C2: real,B2: real] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_real @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_real )
% 5.82/6.05 | ( B2 = one_one_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left1
% 5.82/6.05 thf(fact_1625_mult__cancel__left1,axiom,
% 5.82/6.05 ! [C2: rat,B2: rat] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_rat )
% 5.82/6.05 | ( B2 = one_one_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left1
% 5.82/6.05 thf(fact_1626_mult__cancel__left1,axiom,
% 5.82/6.05 ! [C2: int,B2: int] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_int @ C2 @ B2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_int )
% 5.82/6.05 | ( B2 = one_one_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left1
% 5.82/6.05 thf(fact_1627_mult__cancel__left2,axiom,
% 5.82/6.05 ! [C2: complex,A2: complex] :
% 5.82/6.05 ( ( ( times_times_complex @ C2 @ A2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_complex )
% 5.82/6.05 | ( A2 = one_one_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left2
% 5.82/6.05 thf(fact_1628_mult__cancel__left2,axiom,
% 5.82/6.05 ! [C2: real,A2: real] :
% 5.82/6.05 ( ( ( times_times_real @ C2 @ A2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_real )
% 5.82/6.05 | ( A2 = one_one_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left2
% 5.82/6.05 thf(fact_1629_mult__cancel__left2,axiom,
% 5.82/6.05 ! [C2: rat,A2: rat] :
% 5.82/6.05 ( ( ( times_times_rat @ C2 @ A2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_rat )
% 5.82/6.05 | ( A2 = one_one_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left2
% 5.82/6.05 thf(fact_1630_mult__cancel__left2,axiom,
% 5.82/6.05 ! [C2: int,A2: int] :
% 5.82/6.05 ( ( ( times_times_int @ C2 @ A2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_int )
% 5.82/6.05 | ( A2 = one_one_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_left2
% 5.82/6.05 thf(fact_1631_mult__cancel__right1,axiom,
% 5.82/6.05 ! [C2: complex,B2: complex] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_complex @ B2 @ C2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_complex )
% 5.82/6.05 | ( B2 = one_one_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right1
% 5.82/6.05 thf(fact_1632_mult__cancel__right1,axiom,
% 5.82/6.05 ! [C2: real,B2: real] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_real @ B2 @ C2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_real )
% 5.82/6.05 | ( B2 = one_one_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right1
% 5.82/6.05 thf(fact_1633_mult__cancel__right1,axiom,
% 5.82/6.05 ! [C2: rat,B2: rat] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_rat )
% 5.82/6.05 | ( B2 = one_one_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right1
% 5.82/6.05 thf(fact_1634_mult__cancel__right1,axiom,
% 5.82/6.05 ! [C2: int,B2: int] :
% 5.82/6.05 ( ( C2
% 5.82/6.05 = ( times_times_int @ B2 @ C2 ) )
% 5.82/6.05 = ( ( C2 = zero_zero_int )
% 5.82/6.05 | ( B2 = one_one_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right1
% 5.82/6.05 thf(fact_1635_mult__cancel__right2,axiom,
% 5.82/6.05 ! [A2: complex,C2: complex] :
% 5.82/6.05 ( ( ( times_times_complex @ A2 @ C2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_complex )
% 5.82/6.05 | ( A2 = one_one_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right2
% 5.82/6.05 thf(fact_1636_mult__cancel__right2,axiom,
% 5.82/6.05 ! [A2: real,C2: real] :
% 5.82/6.05 ( ( ( times_times_real @ A2 @ C2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_real )
% 5.82/6.05 | ( A2 = one_one_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right2
% 5.82/6.05 thf(fact_1637_mult__cancel__right2,axiom,
% 5.82/6.05 ! [A2: rat,C2: rat] :
% 5.82/6.05 ( ( ( times_times_rat @ A2 @ C2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_rat )
% 5.82/6.05 | ( A2 = one_one_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right2
% 5.82/6.05 thf(fact_1638_mult__cancel__right2,axiom,
% 5.82/6.05 ! [A2: int,C2: int] :
% 5.82/6.05 ( ( ( times_times_int @ A2 @ C2 )
% 5.82/6.05 = C2 )
% 5.82/6.05 = ( ( C2 = zero_zero_int )
% 5.82/6.05 | ( A2 = one_one_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_cancel_right2
% 5.82/6.05 thf(fact_1639_diff__numeral__special_I9_J,axiom,
% 5.82/6.05 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % diff_numeral_special(9)
% 5.82/6.05 thf(fact_1640_diff__numeral__special_I9_J,axiom,
% 5.82/6.05 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % diff_numeral_special(9)
% 5.82/6.05 thf(fact_1641_diff__numeral__special_I9_J,axiom,
% 5.82/6.05 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % diff_numeral_special(9)
% 5.82/6.05 thf(fact_1642_diff__numeral__special_I9_J,axiom,
% 5.82/6.05 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % diff_numeral_special(9)
% 5.82/6.05 thf(fact_1643_div__self,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( A2 != zero_zero_complex )
% 5.82/6.05 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.82/6.05 = one_one_complex ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_self
% 5.82/6.05 thf(fact_1644_div__self,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( A2 != zero_zero_real )
% 5.82/6.05 => ( ( divide_divide_real @ A2 @ A2 )
% 5.82/6.05 = one_one_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_self
% 5.82/6.05 thf(fact_1645_div__self,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( A2 != zero_zero_rat )
% 5.82/6.05 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.82/6.05 = one_one_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_self
% 5.82/6.05 thf(fact_1646_div__self,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ A2 @ A2 )
% 5.82/6.05 = one_one_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_self
% 5.82/6.05 thf(fact_1647_div__self,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( A2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ A2 @ A2 )
% 5.82/6.05 = one_one_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_self
% 5.82/6.05 thf(fact_1648_nonzero__mult__div__cancel__right,axiom,
% 5.82/6.05 ! [B2: complex,A2: complex] :
% 5.82/6.05 ( ( B2 != zero_zero_complex )
% 5.82/6.05 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ B2 ) @ B2 )
% 5.82/6.05 = A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_right
% 5.82/6.05 thf(fact_1649_nonzero__mult__div__cancel__right,axiom,
% 5.82/6.05 ! [B2: real,A2: real] :
% 5.82/6.05 ( ( B2 != zero_zero_real )
% 5.82/6.05 => ( ( divide_divide_real @ ( times_times_real @ A2 @ B2 ) @ B2 )
% 5.82/6.05 = A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_right
% 5.82/6.05 thf(fact_1650_nonzero__mult__div__cancel__right,axiom,
% 5.82/6.05 ! [B2: rat,A2: rat] :
% 5.82/6.05 ( ( B2 != zero_zero_rat )
% 5.82/6.05 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.05 = A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_right
% 5.82/6.05 thf(fact_1651_nonzero__mult__div__cancel__right,axiom,
% 5.82/6.05 ! [B2: nat,A2: nat] :
% 5.82/6.05 ( ( B2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.05 = A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_right
% 5.82/6.05 thf(fact_1652_nonzero__mult__div__cancel__right,axiom,
% 5.82/6.05 ! [B2: int,A2: int] :
% 5.82/6.05 ( ( B2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( times_times_int @ A2 @ B2 ) @ B2 )
% 5.82/6.05 = A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_right
% 5.82/6.05 thf(fact_1653_nonzero__mult__div__cancel__left,axiom,
% 5.82/6.05 ! [A2: complex,B2: complex] :
% 5.82/6.05 ( ( A2 != zero_zero_complex )
% 5.82/6.05 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ B2 ) @ A2 )
% 5.82/6.05 = B2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_left
% 5.82/6.05 thf(fact_1654_nonzero__mult__div__cancel__left,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( A2 != zero_zero_real )
% 5.82/6.05 => ( ( divide_divide_real @ ( times_times_real @ A2 @ B2 ) @ A2 )
% 5.82/6.05 = B2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_left
% 5.82/6.05 thf(fact_1655_nonzero__mult__div__cancel__left,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( A2 != zero_zero_rat )
% 5.82/6.05 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ B2 ) @ A2 )
% 5.82/6.05 = B2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_left
% 5.82/6.05 thf(fact_1656_nonzero__mult__div__cancel__left,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ A2 @ B2 ) @ A2 )
% 5.82/6.05 = B2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_left
% 5.82/6.05 thf(fact_1657_nonzero__mult__div__cancel__left,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( A2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( times_times_int @ A2 @ B2 ) @ A2 )
% 5.82/6.05 = B2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nonzero_mult_div_cancel_left
% 5.82/6.05 thf(fact_1658_div__mult__mult1__if,axiom,
% 5.82/6.05 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( C2 = zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.05 = zero_zero_nat ) )
% 5.82/6.05 & ( ( C2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.05 = ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_mult1_if
% 5.82/6.05 thf(fact_1659_div__mult__mult1__if,axiom,
% 5.82/6.05 ! [C2: int,A2: int,B2: int] :
% 5.82/6.05 ( ( ( C2 = zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.05 = zero_zero_int ) )
% 5.82/6.05 & ( ( C2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.05 = ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_mult1_if
% 5.82/6.05 thf(fact_1660_div__mult__mult2,axiom,
% 5.82/6.05 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( C2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.05 = ( divide_divide_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_mult2
% 5.82/6.05 thf(fact_1661_div__mult__mult2,axiom,
% 5.82/6.05 ! [C2: int,A2: int,B2: int] :
% 5.82/6.05 ( ( C2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.05 = ( divide_divide_int @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_mult2
% 5.82/6.05 thf(fact_1662_div__mult__mult1,axiom,
% 5.82/6.05 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( C2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.05 = ( divide_divide_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_mult1
% 5.82/6.05 thf(fact_1663_div__mult__mult1,axiom,
% 5.82/6.05 ! [C2: int,A2: int,B2: int] :
% 5.82/6.05 ( ( C2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.05 = ( divide_divide_int @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_mult1
% 5.82/6.05 thf(fact_1664_power__0__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_Suc
% 5.82/6.05 thf(fact_1665_power__0__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_Suc
% 5.82/6.05 thf(fact_1666_power__0__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_Suc
% 5.82/6.05 thf(fact_1667_power__0__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_Suc
% 5.82/6.05 thf(fact_1668_power__0__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_Suc
% 5.82/6.05 thf(fact_1669_power__0__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( suc @ N ) )
% 5.82/6.05 = zero_z3403309356797280102nteger ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_Suc
% 5.82/6.05 thf(fact_1670_power__zero__numeral,axiom,
% 5.82/6.05 ! [K: num] :
% 5.82/6.05 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % power_zero_numeral
% 5.82/6.05 thf(fact_1671_power__zero__numeral,axiom,
% 5.82/6.05 ! [K: num] :
% 5.82/6.05 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % power_zero_numeral
% 5.82/6.05 thf(fact_1672_power__zero__numeral,axiom,
% 5.82/6.05 ! [K: num] :
% 5.82/6.05 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % power_zero_numeral
% 5.82/6.05 thf(fact_1673_power__zero__numeral,axiom,
% 5.82/6.05 ! [K: num] :
% 5.82/6.05 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % power_zero_numeral
% 5.82/6.05 thf(fact_1674_power__zero__numeral,axiom,
% 5.82/6.05 ! [K: num] :
% 5.82/6.05 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % power_zero_numeral
% 5.82/6.05 thf(fact_1675_power__zero__numeral,axiom,
% 5.82/6.05 ! [K: num] :
% 5.82/6.05 ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( numeral_numeral_nat @ K ) )
% 5.82/6.05 = zero_z3403309356797280102nteger ) ).
% 5.82/6.05
% 5.82/6.05 % power_zero_numeral
% 5.82/6.05 thf(fact_1676_of__nat__eq__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ( semiri8010041392384452111omplex @ M )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_eq_0_iff
% 5.82/6.05 thf(fact_1677_of__nat__eq__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ( semiri681578069525770553at_rat @ M )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_eq_0_iff
% 5.82/6.05 thf(fact_1678_of__nat__eq__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ( semiri5074537144036343181t_real @ M )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_eq_0_iff
% 5.82/6.05 thf(fact_1679_of__nat__eq__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ( semiri1314217659103216013at_int @ M )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_eq_0_iff
% 5.82/6.05 thf(fact_1680_of__nat__eq__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_eq_0_iff
% 5.82/6.05 thf(fact_1681_of__nat__0__eq__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( zero_zero_complex
% 5.82/6.05 = ( semiri8010041392384452111omplex @ N ) )
% 5.82/6.05 = ( zero_zero_nat = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_eq_iff
% 5.82/6.05 thf(fact_1682_of__nat__0__eq__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( zero_zero_rat
% 5.82/6.05 = ( semiri681578069525770553at_rat @ N ) )
% 5.82/6.05 = ( zero_zero_nat = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_eq_iff
% 5.82/6.05 thf(fact_1683_of__nat__0__eq__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( zero_zero_real
% 5.82/6.05 = ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.05 = ( zero_zero_nat = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_eq_iff
% 5.82/6.05 thf(fact_1684_of__nat__0__eq__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( zero_zero_int
% 5.82/6.05 = ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.05 = ( zero_zero_nat = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_eq_iff
% 5.82/6.05 thf(fact_1685_of__nat__0__eq__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( zero_zero_nat
% 5.82/6.05 = ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.05 = ( zero_zero_nat = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_eq_iff
% 5.82/6.05 thf(fact_1686_semiring__1__class_Oof__nat__0,axiom,
% 5.82/6.05 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.82/6.05 = zero_zero_complex ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_class.of_nat_0
% 5.82/6.05 thf(fact_1687_semiring__1__class_Oof__nat__0,axiom,
% 5.82/6.05 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.82/6.05 = zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_class.of_nat_0
% 5.82/6.05 thf(fact_1688_semiring__1__class_Oof__nat__0,axiom,
% 5.82/6.05 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.82/6.05 = zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_class.of_nat_0
% 5.82/6.05 thf(fact_1689_semiring__1__class_Oof__nat__0,axiom,
% 5.82/6.05 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_class.of_nat_0
% 5.82/6.05 thf(fact_1690_semiring__1__class_Oof__nat__0,axiom,
% 5.82/6.05 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_class.of_nat_0
% 5.82/6.05 thf(fact_1691_power__Suc0__right,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( power_power_nat @ A2 @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % power_Suc0_right
% 5.82/6.05 thf(fact_1692_power__Suc0__right,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( power_power_real @ A2 @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % power_Suc0_right
% 5.82/6.05 thf(fact_1693_power__Suc0__right,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( power_power_int @ A2 @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % power_Suc0_right
% 5.82/6.05 thf(fact_1694_power__Suc0__right,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( power_power_complex @ A2 @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % power_Suc0_right
% 5.82/6.05 thf(fact_1695_power__Suc0__right,axiom,
% 5.82/6.05 ! [A2: code_integer] :
% 5.82/6.05 ( ( power_8256067586552552935nteger @ A2 @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = A2 ) ).
% 5.82/6.05
% 5.82/6.05 % power_Suc0_right
% 5.82/6.05 thf(fact_1696_zero__less__Suc,axiom,
% 5.82/6.05 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_Suc
% 5.82/6.05 thf(fact_1697_less__Suc0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = ( N = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % less_Suc0
% 5.82/6.05 thf(fact_1698_div__by__Suc__0,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = M ) ).
% 5.82/6.05
% 5.82/6.05 % div_by_Suc_0
% 5.82/6.05 thf(fact_1699_add__gr__0,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.05 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % add_gr_0
% 5.82/6.05 thf(fact_1700_less__one,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ N @ one_one_nat )
% 5.82/6.05 = ( N = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % less_one
% 5.82/6.05 thf(fact_1701_mult__eq__1__iff,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ M @ N )
% 5.82/6.05 = ( suc @ zero_zero_nat ) )
% 5.82/6.05 = ( ( M
% 5.82/6.05 = ( suc @ zero_zero_nat ) )
% 5.82/6.05 & ( N
% 5.82/6.05 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_eq_1_iff
% 5.82/6.05 thf(fact_1702_one__eq__mult__iff,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( suc @ zero_zero_nat )
% 5.82/6.05 = ( times_times_nat @ M @ N ) )
% 5.82/6.05 = ( ( M
% 5.82/6.05 = ( suc @ zero_zero_nat ) )
% 5.82/6.05 & ( N
% 5.82/6.05 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % one_eq_mult_iff
% 5.82/6.05 thf(fact_1703_div__less,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ M @ N )
% 5.82/6.05 => ( ( divide_divide_nat @ M @ N )
% 5.82/6.05 = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_less
% 5.82/6.05 thf(fact_1704_zero__less__diff,axiom,
% 5.82/6.05 ! [N: nat,M: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.05 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_diff
% 5.82/6.05 thf(fact_1705_power__Suc__0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.05 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_Suc_0
% 5.82/6.05 thf(fact_1706_nat__power__eq__Suc__0__iff,axiom,
% 5.82/6.05 ! [X2: nat,M: nat] :
% 5.82/6.05 ( ( ( power_power_nat @ X2 @ M )
% 5.82/6.05 = ( suc @ zero_zero_nat ) )
% 5.82/6.05 = ( ( M = zero_zero_nat )
% 5.82/6.05 | ( X2
% 5.82/6.05 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_power_eq_Suc_0_iff
% 5.82/6.05 thf(fact_1707_max__0__1_I4_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ zero_z5237406670263579293d_enat )
% 5.82/6.05 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(4)
% 5.82/6.05 thf(fact_1708_max__0__1_I4_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ zero_zero_real )
% 5.82/6.05 = ( numeral_numeral_real @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(4)
% 5.82/6.05 thf(fact_1709_max__0__1_I4_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ zero_zero_rat )
% 5.82/6.05 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(4)
% 5.82/6.05 thf(fact_1710_max__0__1_I4_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ zero_zero_nat )
% 5.82/6.05 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(4)
% 5.82/6.05 thf(fact_1711_max__0__1_I4_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ zero_zero_int )
% 5.82/6.05 = ( numeral_numeral_int @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(4)
% 5.82/6.05 thf(fact_1712_max__0__1_I3_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.82/6.05 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(3)
% 5.82/6.05 thf(fact_1713_max__0__1_I3_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X2 ) )
% 5.82/6.05 = ( numeral_numeral_real @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(3)
% 5.82/6.05 thf(fact_1714_max__0__1_I3_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.82/6.05 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(3)
% 5.82/6.05 thf(fact_1715_max__0__1_I3_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.82/6.05 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(3)
% 5.82/6.05 thf(fact_1716_max__0__1_I3_J,axiom,
% 5.82/6.05 ! [X2: num] :
% 5.82/6.05 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X2 ) )
% 5.82/6.05 = ( numeral_numeral_int @ X2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(3)
% 5.82/6.05 thf(fact_1717_nat__mult__less__cancel__disj,axiom,
% 5.82/6.05 ! [K: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.05 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_mult_less_cancel_disj
% 5.82/6.05 thf(fact_1718_mult__less__cancel2,axiom,
% 5.82/6.05 ! [M: nat,K: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.05 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_less_cancel2
% 5.82/6.05 thf(fact_1719_nat__0__less__mult__iff,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_0_less_mult_iff
% 5.82/6.05 thf(fact_1720_max__0__1_I1_J,axiom,
% 5.82/6.05 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.82/6.05 = one_one_real ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(1)
% 5.82/6.05 thf(fact_1721_max__0__1_I1_J,axiom,
% 5.82/6.05 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.82/6.05 = one_one_rat ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(1)
% 5.82/6.05 thf(fact_1722_max__0__1_I1_J,axiom,
% 5.82/6.05 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.82/6.05 = one_one_nat ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(1)
% 5.82/6.05 thf(fact_1723_max__0__1_I1_J,axiom,
% 5.82/6.05 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.82/6.05 = one_on7984719198319812577d_enat ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(1)
% 5.82/6.05 thf(fact_1724_max__0__1_I1_J,axiom,
% 5.82/6.05 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.82/6.05 = one_one_int ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(1)
% 5.82/6.05 thf(fact_1725_max__0__1_I2_J,axiom,
% 5.82/6.05 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.82/6.05 = one_one_real ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(2)
% 5.82/6.05 thf(fact_1726_max__0__1_I2_J,axiom,
% 5.82/6.05 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.82/6.05 = one_one_rat ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(2)
% 5.82/6.05 thf(fact_1727_max__0__1_I2_J,axiom,
% 5.82/6.05 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.82/6.05 = one_one_nat ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(2)
% 5.82/6.05 thf(fact_1728_max__0__1_I2_J,axiom,
% 5.82/6.05 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.82/6.05 = one_on7984719198319812577d_enat ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(2)
% 5.82/6.05 thf(fact_1729_max__0__1_I2_J,axiom,
% 5.82/6.05 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.82/6.05 = one_one_int ) ).
% 5.82/6.05
% 5.82/6.05 % max_0_1(2)
% 5.82/6.05 thf(fact_1730_nat__zero__less__power__iff,axiom,
% 5.82/6.05 ! [X2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_zero_less_power_iff
% 5.82/6.05 thf(fact_1731_diff__is__0__eq,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( minus_minus_nat @ M @ N )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % diff_is_0_eq
% 5.82/6.05 thf(fact_1732_diff__is__0__eq_H,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.05 => ( ( minus_minus_nat @ M @ N )
% 5.82/6.05 = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % diff_is_0_eq'
% 5.82/6.05 thf(fact_1733_nat__mult__div__cancel__disj,axiom,
% 5.82/6.05 ! [K: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ( K = zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.05 = zero_zero_nat ) )
% 5.82/6.05 & ( ( K != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.05 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_mult_div_cancel_disj
% 5.82/6.05 thf(fact_1734_eq__divide__eq__numeral1_I1_J,axiom,
% 5.82/6.05 ! [A2: complex,B2: complex,W: num] :
% 5.82/6.05 ( ( A2
% 5.82/6.05 = ( divide1717551699836669952omplex @ B2 @ ( numera6690914467698888265omplex @ W ) ) )
% 5.82/6.05 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.82/6.05 != zero_zero_complex )
% 5.82/6.05 => ( ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ W ) )
% 5.82/6.05 = B2 ) )
% 5.82/6.05 & ( ( ( numera6690914467698888265omplex @ W )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % eq_divide_eq_numeral1(1)
% 5.82/6.05 thf(fact_1735_eq__divide__eq__numeral1_I1_J,axiom,
% 5.82/6.05 ! [A2: real,B2: real,W: num] :
% 5.82/6.05 ( ( A2
% 5.82/6.05 = ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) )
% 5.82/6.05 = ( ( ( ( numeral_numeral_real @ W )
% 5.82/6.05 != zero_zero_real )
% 5.82/6.05 => ( ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) )
% 5.82/6.05 = B2 ) )
% 5.82/6.05 & ( ( ( numeral_numeral_real @ W )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % eq_divide_eq_numeral1(1)
% 5.82/6.05 thf(fact_1736_eq__divide__eq__numeral1_I1_J,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,W: num] :
% 5.82/6.05 ( ( A2
% 5.82/6.05 = ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) )
% 5.82/6.05 = ( ( ( ( numeral_numeral_rat @ W )
% 5.82/6.05 != zero_zero_rat )
% 5.82/6.05 => ( ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W ) )
% 5.82/6.05 = B2 ) )
% 5.82/6.05 & ( ( ( numeral_numeral_rat @ W )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % eq_divide_eq_numeral1(1)
% 5.82/6.05 thf(fact_1737_divide__eq__eq__numeral1_I1_J,axiom,
% 5.82/6.05 ! [B2: complex,W: num,A2: complex] :
% 5.82/6.05 ( ( ( divide1717551699836669952omplex @ B2 @ ( numera6690914467698888265omplex @ W ) )
% 5.82/6.05 = A2 )
% 5.82/6.05 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.82/6.05 != zero_zero_complex )
% 5.82/6.05 => ( B2
% 5.82/6.05 = ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.82/6.05 & ( ( ( numera6690914467698888265omplex @ W )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divide_eq_eq_numeral1(1)
% 5.82/6.05 thf(fact_1738_divide__eq__eq__numeral1_I1_J,axiom,
% 5.82/6.05 ! [B2: real,W: num,A2: real] :
% 5.82/6.05 ( ( ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) )
% 5.82/6.05 = A2 )
% 5.82/6.05 = ( ( ( ( numeral_numeral_real @ W )
% 5.82/6.05 != zero_zero_real )
% 5.82/6.05 => ( B2
% 5.82/6.05 = ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) ) ) )
% 5.82/6.05 & ( ( ( numeral_numeral_real @ W )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divide_eq_eq_numeral1(1)
% 5.82/6.05 thf(fact_1739_divide__eq__eq__numeral1_I1_J,axiom,
% 5.82/6.05 ! [B2: rat,W: num,A2: rat] :
% 5.82/6.05 ( ( ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) )
% 5.82/6.05 = A2 )
% 5.82/6.05 = ( ( ( ( numeral_numeral_rat @ W )
% 5.82/6.05 != zero_zero_rat )
% 5.82/6.05 => ( B2
% 5.82/6.05 = ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W ) ) ) )
% 5.82/6.05 & ( ( ( numeral_numeral_rat @ W )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divide_eq_eq_numeral1(1)
% 5.82/6.05 thf(fact_1740_div__mult__self4,axiom,
% 5.82/6.05 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.05 ( ( B2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ C2 ) @ A2 ) @ B2 )
% 5.82/6.05 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self4
% 5.82/6.05 thf(fact_1741_div__mult__self4,axiom,
% 5.82/6.05 ! [B2: int,C2: int,A2: int] :
% 5.82/6.05 ( ( B2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B2 @ C2 ) @ A2 ) @ B2 )
% 5.82/6.05 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self4
% 5.82/6.05 thf(fact_1742_div__mult__self3,axiom,
% 5.82/6.05 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.05 ( ( B2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B2 ) @ A2 ) @ B2 )
% 5.82/6.05 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self3
% 5.82/6.05 thf(fact_1743_div__mult__self3,axiom,
% 5.82/6.05 ! [B2: int,C2: int,A2: int] :
% 5.82/6.05 ( ( B2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B2 ) @ A2 ) @ B2 )
% 5.82/6.05 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self3
% 5.82/6.05 thf(fact_1744_div__mult__self2,axiom,
% 5.82/6.05 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.05 ( ( B2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) ) @ B2 )
% 5.82/6.05 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self2
% 5.82/6.05 thf(fact_1745_div__mult__self2,axiom,
% 5.82/6.05 ! [B2: int,A2: int,C2: int] :
% 5.82/6.05 ( ( B2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ ( times_times_int @ B2 @ C2 ) ) @ B2 )
% 5.82/6.05 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self2
% 5.82/6.05 thf(fact_1746_div__mult__self1,axiom,
% 5.82/6.05 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.05 ( ( B2 != zero_zero_nat )
% 5.82/6.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ ( times_times_nat @ C2 @ B2 ) ) @ B2 )
% 5.82/6.05 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self1
% 5.82/6.05 thf(fact_1747_div__mult__self1,axiom,
% 5.82/6.05 ! [B2: int,A2: int,C2: int] :
% 5.82/6.05 ( ( B2 != zero_zero_int )
% 5.82/6.05 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ ( times_times_int @ C2 @ B2 ) ) @ B2 )
% 5.82/6.05 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self1
% 5.82/6.05 thf(fact_1748_of__nat__le__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_le_0_iff
% 5.82/6.05 thf(fact_1749_of__nat__le__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_le_0_iff
% 5.82/6.05 thf(fact_1750_of__nat__le__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_le_0_iff
% 5.82/6.05 thf(fact_1751_of__nat__le__0__iff,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.82/6.05 = ( M = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_le_0_iff
% 5.82/6.05 thf(fact_1752_power__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: rat,N: nat] :
% 5.82/6.05 ( ( ( power_power_rat @ A2 @ N )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 = ( ( A2 = zero_zero_rat )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_0_iff
% 5.82/6.05 thf(fact_1753_power__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: nat,N: nat] :
% 5.82/6.05 ( ( ( power_power_nat @ A2 @ N )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( ( A2 = zero_zero_nat )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_0_iff
% 5.82/6.05 thf(fact_1754_power__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: real,N: nat] :
% 5.82/6.05 ( ( ( power_power_real @ A2 @ N )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 = ( ( A2 = zero_zero_real )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_0_iff
% 5.82/6.05 thf(fact_1755_power__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: int,N: nat] :
% 5.82/6.05 ( ( ( power_power_int @ A2 @ N )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 = ( ( A2 = zero_zero_int )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_0_iff
% 5.82/6.05 thf(fact_1756_power__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: complex,N: nat] :
% 5.82/6.05 ( ( ( power_power_complex @ A2 @ N )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 = ( ( A2 = zero_zero_complex )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_0_iff
% 5.82/6.05 thf(fact_1757_power__eq__0__iff,axiom,
% 5.82/6.05 ! [A2: code_integer,N: nat] :
% 5.82/6.05 ( ( ( power_8256067586552552935nteger @ A2 @ N )
% 5.82/6.05 = zero_z3403309356797280102nteger )
% 5.82/6.05 = ( ( A2 = zero_z3403309356797280102nteger )
% 5.82/6.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_0_iff
% 5.82/6.05 thf(fact_1758_Suc__pred,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.82/6.05 = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % Suc_pred
% 5.82/6.05 thf(fact_1759_one__le__mult__iff,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.82/6.05 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.82/6.05 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % one_le_mult_iff
% 5.82/6.05 thf(fact_1760_div__eq__dividend__iff,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.05 => ( ( ( divide_divide_nat @ M @ N )
% 5.82/6.05 = M )
% 5.82/6.05 = ( N = one_one_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_eq_dividend_iff
% 5.82/6.05 thf(fact_1761_nat__mult__le__cancel__disj,axiom,
% 5.82/6.05 ! [K: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.05 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_mult_le_cancel_disj
% 5.82/6.05 thf(fact_1762_mult__le__cancel2,axiom,
% 5.82/6.05 ! [M: nat,K: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.05 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_le_cancel2
% 5.82/6.05 thf(fact_1763_div__mult__self1__is__m,axiom,
% 5.82/6.05 ! [N: nat,M: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.82/6.05 = M ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self1_is_m
% 5.82/6.05 thf(fact_1764_div__mult__self__is__m,axiom,
% 5.82/6.05 ! [N: nat,M: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.82/6.05 = M ) ) ).
% 5.82/6.05
% 5.82/6.05 % div_mult_self_is_m
% 5.82/6.05 thf(fact_1765_zero__eq__power2,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 = ( A2 = zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_eq_power2
% 5.82/6.05 thf(fact_1766_zero__eq__power2,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 = ( A2 = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_eq_power2
% 5.82/6.05 thf(fact_1767_zero__eq__power2,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_eq_power2
% 5.82/6.05 thf(fact_1768_zero__eq__power2,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 = ( A2 = zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_eq_power2
% 5.82/6.05 thf(fact_1769_zero__eq__power2,axiom,
% 5.82/6.05 ! [A2: complex] :
% 5.82/6.05 ( ( ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 = ( A2 = zero_zero_complex ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_eq_power2
% 5.82/6.05 thf(fact_1770_zero__eq__power2,axiom,
% 5.82/6.05 ! [A2: code_integer] :
% 5.82/6.05 ( ( ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_z3403309356797280102nteger )
% 5.82/6.05 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_eq_power2
% 5.82/6.05 thf(fact_1771_power__strict__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: code_integer,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.05 => ( ( ord_le6747313008572928689nteger @ B2 @ one_one_Code_integer )
% 5.82/6.05 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B2 @ M ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_decreasing_iff
% 5.82/6.05 thf(fact_1772_power__strict__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: real,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ( ord_less_real @ B2 @ one_one_real )
% 5.82/6.05 => ( ( ord_less_real @ ( power_power_real @ B2 @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_decreasing_iff
% 5.82/6.05 thf(fact_1773_power__strict__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: rat,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ( ord_less_rat @ B2 @ one_one_rat )
% 5.82/6.05 => ( ( ord_less_rat @ ( power_power_rat @ B2 @ M ) @ ( power_power_rat @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_decreasing_iff
% 5.82/6.05 thf(fact_1774_power__strict__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 5.82/6.05 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ M ) @ ( power_power_nat @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_decreasing_iff
% 5.82/6.05 thf(fact_1775_power__strict__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: int,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ( ord_less_int @ B2 @ one_one_int )
% 5.82/6.05 => ( ( ord_less_int @ ( power_power_int @ B2 @ M ) @ ( power_power_int @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_decreasing_iff
% 5.82/6.05 thf(fact_1776_power__mono__iff,axiom,
% 5.82/6.05 ! [A2: real,B2: real,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_real @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_mono_iff
% 5.82/6.05 thf(fact_1777_power__mono__iff,axiom,
% 5.82/6.05 ! [A2: code_integer,B2: code_integer,N: nat] :
% 5.82/6.05 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 5.82/6.05 = ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_mono_iff
% 5.82/6.05 thf(fact_1778_power__mono__iff,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_rat @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_mono_iff
% 5.82/6.05 thf(fact_1779_power__mono__iff,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_mono_iff
% 5.82/6.05 thf(fact_1780_power__mono__iff,axiom,
% 5.82/6.05 ! [A2: int,B2: int,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_int @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_mono_iff
% 5.82/6.05 thf(fact_1781_of__nat__0__less__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.82/6.05 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_less_iff
% 5.82/6.05 thf(fact_1782_of__nat__0__less__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.05 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_less_iff
% 5.82/6.05 thf(fact_1783_of__nat__0__less__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.05 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_less_iff
% 5.82/6.05 thf(fact_1784_of__nat__0__less__iff,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.05 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_0_less_iff
% 5.82/6.05 thf(fact_1785_Suc__diff__1,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.82/6.05 = N ) ) ).
% 5.82/6.05
% 5.82/6.05 % Suc_diff_1
% 5.82/6.05 thf(fact_1786_bits__1__div__2,axiom,
% 5.82/6.05 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % bits_1_div_2
% 5.82/6.05 thf(fact_1787_bits__1__div__2,axiom,
% 5.82/6.05 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % bits_1_div_2
% 5.82/6.05 thf(fact_1788_one__div__two__eq__zero,axiom,
% 5.82/6.05 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % one_div_two_eq_zero
% 5.82/6.05 thf(fact_1789_one__div__two__eq__zero,axiom,
% 5.82/6.05 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.05 = zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % one_div_two_eq_zero
% 5.82/6.05 thf(fact_1790_power2__eq__iff__nonneg,axiom,
% 5.82/6.05 ! [X2: real,Y3: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.05 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_eq_iff_nonneg
% 5.82/6.05 thf(fact_1791_power2__eq__iff__nonneg,axiom,
% 5.82/6.05 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.05 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 5.82/6.05 => ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_eq_iff_nonneg
% 5.82/6.05 thf(fact_1792_power2__eq__iff__nonneg,axiom,
% 5.82/6.05 ! [X2: rat,Y3: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.05 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_eq_iff_nonneg
% 5.82/6.05 thf(fact_1793_power2__eq__iff__nonneg,axiom,
% 5.82/6.05 ! [X2: nat,Y3: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.82/6.05 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_eq_iff_nonneg
% 5.82/6.05 thf(fact_1794_power2__eq__iff__nonneg,axiom,
% 5.82/6.05 ! [X2: int,Y3: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.05 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.05 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_eq_iff_nonneg
% 5.82/6.05 thf(fact_1795_power2__less__eq__zero__iff,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.82/6.05 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_less_eq_zero_iff
% 5.82/6.05 thf(fact_1796_power2__less__eq__zero__iff,axiom,
% 5.82/6.05 ! [A2: code_integer] :
% 5.82/6.05 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger )
% 5.82/6.05 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_less_eq_zero_iff
% 5.82/6.05 thf(fact_1797_power2__less__eq__zero__iff,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.82/6.05 = ( A2 = zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_less_eq_zero_iff
% 5.82/6.05 thf(fact_1798_power2__less__eq__zero__iff,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.82/6.05 = ( A2 = zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % power2_less_eq_zero_iff
% 5.82/6.05 thf(fact_1799_zero__less__power2,axiom,
% 5.82/6.05 ! [A2: code_integer] :
% 5.82/6.05 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( A2 != zero_z3403309356797280102nteger ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_power2
% 5.82/6.05 thf(fact_1800_zero__less__power2,axiom,
% 5.82/6.05 ! [A2: real] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( A2 != zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_power2
% 5.82/6.05 thf(fact_1801_zero__less__power2,axiom,
% 5.82/6.05 ! [A2: rat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( A2 != zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_power2
% 5.82/6.05 thf(fact_1802_zero__less__power2,axiom,
% 5.82/6.05 ! [A2: int] :
% 5.82/6.05 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = ( A2 != zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_power2
% 5.82/6.05 thf(fact_1803_sum__power2__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: rat,Y3: rat] :
% 5.82/6.05 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 = ( ( X2 = zero_zero_rat )
% 5.82/6.05 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_power2_eq_zero_iff
% 5.82/6.05 thf(fact_1804_sum__power2__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: real,Y3: real] :
% 5.82/6.05 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 = ( ( X2 = zero_zero_real )
% 5.82/6.05 & ( Y3 = zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_power2_eq_zero_iff
% 5.82/6.05 thf(fact_1805_sum__power2__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: int,Y3: int] :
% 5.82/6.05 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 = ( ( X2 = zero_zero_int )
% 5.82/6.05 & ( Y3 = zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_power2_eq_zero_iff
% 5.82/6.05 thf(fact_1806_sum__power2__eq__zero__iff,axiom,
% 5.82/6.05 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.05 ( ( ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.05 = zero_z3403309356797280102nteger )
% 5.82/6.05 = ( ( X2 = zero_z3403309356797280102nteger )
% 5.82/6.05 & ( Y3 = zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % sum_power2_eq_zero_iff
% 5.82/6.05 thf(fact_1807_power__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: code_integer,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.05 => ( ( ord_le6747313008572928689nteger @ B2 @ one_one_Code_integer )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B2 @ M ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_decreasing_iff
% 5.82/6.05 thf(fact_1808_power__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: real,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ( ord_less_real @ B2 @ one_one_real )
% 5.82/6.05 => ( ( ord_less_eq_real @ ( power_power_real @ B2 @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_decreasing_iff
% 5.82/6.05 thf(fact_1809_power__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: rat,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ( ord_less_rat @ B2 @ one_one_rat )
% 5.82/6.05 => ( ( ord_less_eq_rat @ ( power_power_rat @ B2 @ M ) @ ( power_power_rat @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_decreasing_iff
% 5.82/6.05 thf(fact_1810_power__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 5.82/6.05 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ M ) @ ( power_power_nat @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_decreasing_iff
% 5.82/6.05 thf(fact_1811_power__decreasing__iff,axiom,
% 5.82/6.05 ! [B2: int,M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ( ord_less_int @ B2 @ one_one_int )
% 5.82/6.05 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ M ) @ ( power_power_int @ B2 @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_decreasing_iff
% 5.82/6.05 thf(fact_1812_of__nat__zero__less__power__iff,axiom,
% 5.82/6.05 ! [X2: nat,N: nat] :
% 5.82/6.05 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_zero_less_power_iff
% 5.82/6.05 thf(fact_1813_of__nat__zero__less__power__iff,axiom,
% 5.82/6.05 ! [X2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_zero_less_power_iff
% 5.82/6.05 thf(fact_1814_of__nat__zero__less__power__iff,axiom,
% 5.82/6.05 ! [X2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_zero_less_power_iff
% 5.82/6.05 thf(fact_1815_of__nat__zero__less__power__iff,axiom,
% 5.82/6.05 ! [X2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_zero_less_power_iff
% 5.82/6.05 thf(fact_1816_of__nat__zero__less__power__iff,axiom,
% 5.82/6.05 ! [X2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 5.82/6.05 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.05 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % of_nat_zero_less_power_iff
% 5.82/6.05 thf(fact_1817_int__diff__cases,axiom,
% 5.82/6.05 ! [Z: int] :
% 5.82/6.05 ~ ! [M5: nat,N3: nat] :
% 5.82/6.05 ( Z
% 5.82/6.05 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % int_diff_cases
% 5.82/6.05 thf(fact_1818_power__0__left,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ( N = zero_zero_nat )
% 5.82/6.05 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.82/6.05 = one_one_rat ) )
% 5.82/6.05 & ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.82/6.05 = zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_left
% 5.82/6.05 thf(fact_1819_power__0__left,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ( N = zero_zero_nat )
% 5.82/6.05 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.82/6.05 = one_one_nat ) )
% 5.82/6.05 & ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.82/6.05 = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_left
% 5.82/6.05 thf(fact_1820_power__0__left,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ( N = zero_zero_nat )
% 5.82/6.05 => ( ( power_power_real @ zero_zero_real @ N )
% 5.82/6.05 = one_one_real ) )
% 5.82/6.05 & ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ( power_power_real @ zero_zero_real @ N )
% 5.82/6.05 = zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_left
% 5.82/6.05 thf(fact_1821_power__0__left,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ( N = zero_zero_nat )
% 5.82/6.05 => ( ( power_power_int @ zero_zero_int @ N )
% 5.82/6.05 = one_one_int ) )
% 5.82/6.05 & ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ( power_power_int @ zero_zero_int @ N )
% 5.82/6.05 = zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_left
% 5.82/6.05 thf(fact_1822_power__0__left,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ( N = zero_zero_nat )
% 5.82/6.05 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.82/6.05 = one_one_complex ) )
% 5.82/6.05 & ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.82/6.05 = zero_zero_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_left
% 5.82/6.05 thf(fact_1823_power__0__left,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ( N = zero_zero_nat )
% 5.82/6.05 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 5.82/6.05 = one_one_Code_integer ) )
% 5.82/6.05 & ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 5.82/6.05 = zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_0_left
% 5.82/6.05 thf(fact_1824_zero__power,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.82/6.05 = zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_power
% 5.82/6.05 thf(fact_1825_zero__power,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.82/6.05 = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_power
% 5.82/6.05 thf(fact_1826_zero__power,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( power_power_real @ zero_zero_real @ N )
% 5.82/6.05 = zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_power
% 5.82/6.05 thf(fact_1827_zero__power,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( power_power_int @ zero_zero_int @ N )
% 5.82/6.05 = zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_power
% 5.82/6.05 thf(fact_1828_zero__power,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.82/6.05 = zero_zero_complex ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_power
% 5.82/6.05 thf(fact_1829_zero__power,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 5.82/6.05 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_power
% 5.82/6.05 thf(fact_1830_le__numeral__extra_I3_J,axiom,
% 5.82/6.05 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.82/6.05
% 5.82/6.05 % le_numeral_extra(3)
% 5.82/6.05 thf(fact_1831_le__numeral__extra_I3_J,axiom,
% 5.82/6.05 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.82/6.05
% 5.82/6.05 % le_numeral_extra(3)
% 5.82/6.05 thf(fact_1832_le__numeral__extra_I3_J,axiom,
% 5.82/6.05 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.82/6.05
% 5.82/6.05 % le_numeral_extra(3)
% 5.82/6.05 thf(fact_1833_le__numeral__extra_I3_J,axiom,
% 5.82/6.05 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.82/6.05
% 5.82/6.05 % le_numeral_extra(3)
% 5.82/6.05 thf(fact_1834_less__numeral__extra_I3_J,axiom,
% 5.82/6.05 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % less_numeral_extra(3)
% 5.82/6.05 thf(fact_1835_less__numeral__extra_I3_J,axiom,
% 5.82/6.05 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % less_numeral_extra(3)
% 5.82/6.05 thf(fact_1836_less__numeral__extra_I3_J,axiom,
% 5.82/6.05 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % less_numeral_extra(3)
% 5.82/6.05 thf(fact_1837_less__numeral__extra_I3_J,axiom,
% 5.82/6.05 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % less_numeral_extra(3)
% 5.82/6.05 thf(fact_1838_field__lbound__gt__zero,axiom,
% 5.82/6.05 ! [D1: real,D22: real] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.82/6.05 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.82/6.05 => ? [E2: real] :
% 5.82/6.05 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.82/6.05 & ( ord_less_real @ E2 @ D1 )
% 5.82/6.05 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % field_lbound_gt_zero
% 5.82/6.05 thf(fact_1839_field__lbound__gt__zero,axiom,
% 5.82/6.05 ! [D1: rat,D22: rat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.82/6.05 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.82/6.05 => ? [E2: rat] :
% 5.82/6.05 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.82/6.05 & ( ord_less_rat @ E2 @ D1 )
% 5.82/6.05 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % field_lbound_gt_zero
% 5.82/6.05 thf(fact_1840_zero__neq__numeral,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ( zero_zero_complex
% 5.82/6.05 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_numeral
% 5.82/6.05 thf(fact_1841_zero__neq__numeral,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ( zero_zero_real
% 5.82/6.05 != ( numeral_numeral_real @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_numeral
% 5.82/6.05 thf(fact_1842_zero__neq__numeral,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ( zero_zero_rat
% 5.82/6.05 != ( numeral_numeral_rat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_numeral
% 5.82/6.05 thf(fact_1843_zero__neq__numeral,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ( zero_zero_nat
% 5.82/6.05 != ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_numeral
% 5.82/6.05 thf(fact_1844_zero__neq__numeral,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ( zero_zero_int
% 5.82/6.05 != ( numeral_numeral_int @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_numeral
% 5.82/6.05 thf(fact_1845_zero__neq__one,axiom,
% 5.82/6.05 zero_zero_complex != one_one_complex ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_one
% 5.82/6.05 thf(fact_1846_zero__neq__one,axiom,
% 5.82/6.05 zero_zero_real != one_one_real ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_one
% 5.82/6.05 thf(fact_1847_zero__neq__one,axiom,
% 5.82/6.05 zero_zero_rat != one_one_rat ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_one
% 5.82/6.05 thf(fact_1848_zero__neq__one,axiom,
% 5.82/6.05 zero_zero_nat != one_one_nat ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_one
% 5.82/6.05 thf(fact_1849_zero__neq__one,axiom,
% 5.82/6.05 zero_zero_int != one_one_int ).
% 5.82/6.05
% 5.82/6.05 % zero_neq_one
% 5.82/6.05 thf(fact_1850_mult__right__cancel,axiom,
% 5.82/6.05 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.05 ( ( C2 != zero_zero_complex )
% 5.82/6.05 => ( ( ( times_times_complex @ A2 @ C2 )
% 5.82/6.05 = ( times_times_complex @ B2 @ C2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_cancel
% 5.82/6.05 thf(fact_1851_mult__right__cancel,axiom,
% 5.82/6.05 ! [C2: real,A2: real,B2: real] :
% 5.82/6.05 ( ( C2 != zero_zero_real )
% 5.82/6.05 => ( ( ( times_times_real @ A2 @ C2 )
% 5.82/6.05 = ( times_times_real @ B2 @ C2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_cancel
% 5.82/6.05 thf(fact_1852_mult__right__cancel,axiom,
% 5.82/6.05 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.05 ( ( C2 != zero_zero_rat )
% 5.82/6.05 => ( ( ( times_times_rat @ A2 @ C2 )
% 5.82/6.05 = ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_cancel
% 5.82/6.05 thf(fact_1853_mult__right__cancel,axiom,
% 5.82/6.05 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( C2 != zero_zero_nat )
% 5.82/6.05 => ( ( ( times_times_nat @ A2 @ C2 )
% 5.82/6.05 = ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_cancel
% 5.82/6.05 thf(fact_1854_mult__right__cancel,axiom,
% 5.82/6.05 ! [C2: int,A2: int,B2: int] :
% 5.82/6.05 ( ( C2 != zero_zero_int )
% 5.82/6.05 => ( ( ( times_times_int @ A2 @ C2 )
% 5.82/6.05 = ( times_times_int @ B2 @ C2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_cancel
% 5.82/6.05 thf(fact_1855_mult__left__cancel,axiom,
% 5.82/6.05 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.05 ( ( C2 != zero_zero_complex )
% 5.82/6.05 => ( ( ( times_times_complex @ C2 @ A2 )
% 5.82/6.05 = ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_cancel
% 5.82/6.05 thf(fact_1856_mult__left__cancel,axiom,
% 5.82/6.05 ! [C2: real,A2: real,B2: real] :
% 5.82/6.05 ( ( C2 != zero_zero_real )
% 5.82/6.05 => ( ( ( times_times_real @ C2 @ A2 )
% 5.82/6.05 = ( times_times_real @ C2 @ B2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_cancel
% 5.82/6.05 thf(fact_1857_mult__left__cancel,axiom,
% 5.82/6.05 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.05 ( ( C2 != zero_zero_rat )
% 5.82/6.05 => ( ( ( times_times_rat @ C2 @ A2 )
% 5.82/6.05 = ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_cancel
% 5.82/6.05 thf(fact_1858_mult__left__cancel,axiom,
% 5.82/6.05 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( C2 != zero_zero_nat )
% 5.82/6.05 => ( ( ( times_times_nat @ C2 @ A2 )
% 5.82/6.05 = ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_cancel
% 5.82/6.05 thf(fact_1859_mult__left__cancel,axiom,
% 5.82/6.05 ! [C2: int,A2: int,B2: int] :
% 5.82/6.05 ( ( C2 != zero_zero_int )
% 5.82/6.05 => ( ( ( times_times_int @ C2 @ A2 )
% 5.82/6.05 = ( times_times_int @ C2 @ B2 ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_cancel
% 5.82/6.05 thf(fact_1860_no__zero__divisors,axiom,
% 5.82/6.05 ! [A2: complex,B2: complex] :
% 5.82/6.05 ( ( A2 != zero_zero_complex )
% 5.82/6.05 => ( ( B2 != zero_zero_complex )
% 5.82/6.05 => ( ( times_times_complex @ A2 @ B2 )
% 5.82/6.05 != zero_zero_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % no_zero_divisors
% 5.82/6.05 thf(fact_1861_no__zero__divisors,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( A2 != zero_zero_real )
% 5.82/6.05 => ( ( B2 != zero_zero_real )
% 5.82/6.05 => ( ( times_times_real @ A2 @ B2 )
% 5.82/6.05 != zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % no_zero_divisors
% 5.82/6.05 thf(fact_1862_no__zero__divisors,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( A2 != zero_zero_rat )
% 5.82/6.05 => ( ( B2 != zero_zero_rat )
% 5.82/6.05 => ( ( times_times_rat @ A2 @ B2 )
% 5.82/6.05 != zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % no_zero_divisors
% 5.82/6.05 thf(fact_1863_no__zero__divisors,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_nat )
% 5.82/6.05 => ( ( B2 != zero_zero_nat )
% 5.82/6.05 => ( ( times_times_nat @ A2 @ B2 )
% 5.82/6.05 != zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % no_zero_divisors
% 5.82/6.05 thf(fact_1864_no__zero__divisors,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( A2 != zero_zero_int )
% 5.82/6.05 => ( ( B2 != zero_zero_int )
% 5.82/6.05 => ( ( times_times_int @ A2 @ B2 )
% 5.82/6.05 != zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % no_zero_divisors
% 5.82/6.05 thf(fact_1865_divisors__zero,axiom,
% 5.82/6.05 ! [A2: complex,B2: complex] :
% 5.82/6.05 ( ( ( times_times_complex @ A2 @ B2 )
% 5.82/6.05 = zero_zero_complex )
% 5.82/6.05 => ( ( A2 = zero_zero_complex )
% 5.82/6.05 | ( B2 = zero_zero_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divisors_zero
% 5.82/6.05 thf(fact_1866_divisors__zero,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ( times_times_real @ A2 @ B2 )
% 5.82/6.05 = zero_zero_real )
% 5.82/6.05 => ( ( A2 = zero_zero_real )
% 5.82/6.05 | ( B2 = zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divisors_zero
% 5.82/6.05 thf(fact_1867_divisors__zero,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ( times_times_rat @ A2 @ B2 )
% 5.82/6.05 = zero_zero_rat )
% 5.82/6.05 => ( ( A2 = zero_zero_rat )
% 5.82/6.05 | ( B2 = zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divisors_zero
% 5.82/6.05 thf(fact_1868_divisors__zero,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ A2 @ B2 )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 => ( ( A2 = zero_zero_nat )
% 5.82/6.05 | ( B2 = zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divisors_zero
% 5.82/6.05 thf(fact_1869_divisors__zero,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ( times_times_int @ A2 @ B2 )
% 5.82/6.05 = zero_zero_int )
% 5.82/6.05 => ( ( A2 = zero_zero_int )
% 5.82/6.05 | ( B2 = zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % divisors_zero
% 5.82/6.05 thf(fact_1870_mult__not__zero,axiom,
% 5.82/6.05 ! [A2: complex,B2: complex] :
% 5.82/6.05 ( ( ( times_times_complex @ A2 @ B2 )
% 5.82/6.05 != zero_zero_complex )
% 5.82/6.05 => ( ( A2 != zero_zero_complex )
% 5.82/6.05 & ( B2 != zero_zero_complex ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_not_zero
% 5.82/6.05 thf(fact_1871_mult__not__zero,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ( times_times_real @ A2 @ B2 )
% 5.82/6.05 != zero_zero_real )
% 5.82/6.05 => ( ( A2 != zero_zero_real )
% 5.82/6.05 & ( B2 != zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_not_zero
% 5.82/6.05 thf(fact_1872_mult__not__zero,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ( times_times_rat @ A2 @ B2 )
% 5.82/6.05 != zero_zero_rat )
% 5.82/6.05 => ( ( A2 != zero_zero_rat )
% 5.82/6.05 & ( B2 != zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_not_zero
% 5.82/6.05 thf(fact_1873_mult__not__zero,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ A2 @ B2 )
% 5.82/6.05 != zero_zero_nat )
% 5.82/6.05 => ( ( A2 != zero_zero_nat )
% 5.82/6.05 & ( B2 != zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_not_zero
% 5.82/6.05 thf(fact_1874_mult__not__zero,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ( times_times_int @ A2 @ B2 )
% 5.82/6.05 != zero_zero_int )
% 5.82/6.05 => ( ( A2 != zero_zero_int )
% 5.82/6.05 & ( B2 != zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_not_zero
% 5.82/6.05 thf(fact_1875_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 5.82/6.05 ! [A2: rat,N: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_rat )
% 5.82/6.05 => ( ( power_power_rat @ A2 @ N )
% 5.82/6.05 != zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_no_zero_divisors_class.power_not_zero
% 5.82/6.05 thf(fact_1876_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 5.82/6.05 ! [A2: nat,N: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_nat )
% 5.82/6.05 => ( ( power_power_nat @ A2 @ N )
% 5.82/6.05 != zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_no_zero_divisors_class.power_not_zero
% 5.82/6.05 thf(fact_1877_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 5.82/6.05 ! [A2: real,N: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_real )
% 5.82/6.05 => ( ( power_power_real @ A2 @ N )
% 5.82/6.05 != zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_no_zero_divisors_class.power_not_zero
% 5.82/6.05 thf(fact_1878_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 5.82/6.05 ! [A2: int,N: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_int )
% 5.82/6.05 => ( ( power_power_int @ A2 @ N )
% 5.82/6.05 != zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_no_zero_divisors_class.power_not_zero
% 5.82/6.05 thf(fact_1879_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 5.82/6.05 ! [A2: complex,N: nat] :
% 5.82/6.05 ( ( A2 != zero_zero_complex )
% 5.82/6.05 => ( ( power_power_complex @ A2 @ N )
% 5.82/6.05 != zero_zero_complex ) ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_no_zero_divisors_class.power_not_zero
% 5.82/6.05 thf(fact_1880_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 5.82/6.05 ! [A2: code_integer,N: nat] :
% 5.82/6.05 ( ( A2 != zero_z3403309356797280102nteger )
% 5.82/6.05 => ( ( power_8256067586552552935nteger @ A2 @ N )
% 5.82/6.05 != zero_z3403309356797280102nteger ) ) ).
% 5.82/6.05
% 5.82/6.05 % semiring_1_no_zero_divisors_class.power_not_zero
% 5.82/6.05 thf(fact_1881_num_Osize_I4_J,axiom,
% 5.82/6.05 ( ( size_size_num @ one )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % num.size(4)
% 5.82/6.05 thf(fact_1882_not0__implies__Suc,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( N != zero_zero_nat )
% 5.82/6.05 => ? [M5: nat] :
% 5.82/6.05 ( N
% 5.82/6.05 = ( suc @ M5 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % not0_implies_Suc
% 5.82/6.05 thf(fact_1883_Zero__not__Suc,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( zero_zero_nat
% 5.82/6.05 != ( suc @ M ) ) ).
% 5.82/6.05
% 5.82/6.05 % Zero_not_Suc
% 5.82/6.05 thf(fact_1884_Zero__neq__Suc,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( zero_zero_nat
% 5.82/6.05 != ( suc @ M ) ) ).
% 5.82/6.05
% 5.82/6.05 % Zero_neq_Suc
% 5.82/6.05 thf(fact_1885_Suc__neq__Zero,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( suc @ M )
% 5.82/6.05 != zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % Suc_neq_Zero
% 5.82/6.05 thf(fact_1886_zero__induct,axiom,
% 5.82/6.05 ! [P: nat > $o,K: nat] :
% 5.82/6.05 ( ( P @ K )
% 5.82/6.05 => ( ! [N3: nat] :
% 5.82/6.05 ( ( P @ ( suc @ N3 ) )
% 5.82/6.05 => ( P @ N3 ) )
% 5.82/6.05 => ( P @ zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_induct
% 5.82/6.05 thf(fact_1887_diff__induct,axiom,
% 5.82/6.05 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.82/6.05 ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 5.82/6.05 => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 5.82/6.05 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.05 ( ( P @ X4 @ Y4 )
% 5.82/6.05 => ( P @ ( suc @ X4 ) @ ( suc @ Y4 ) ) )
% 5.82/6.05 => ( P @ M @ N ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % diff_induct
% 5.82/6.05 thf(fact_1888_nat__induct,axiom,
% 5.82/6.05 ! [P: nat > $o,N: nat] :
% 5.82/6.05 ( ( P @ zero_zero_nat )
% 5.82/6.05 => ( ! [N3: nat] :
% 5.82/6.05 ( ( P @ N3 )
% 5.82/6.05 => ( P @ ( suc @ N3 ) ) )
% 5.82/6.05 => ( P @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_induct
% 5.82/6.05 thf(fact_1889_old_Onat_Oexhaust,axiom,
% 5.82/6.05 ! [Y3: nat] :
% 5.82/6.05 ( ( Y3 != zero_zero_nat )
% 5.82/6.05 => ~ ! [Nat3: nat] :
% 5.82/6.05 ( Y3
% 5.82/6.05 != ( suc @ Nat3 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % old.nat.exhaust
% 5.82/6.05 thf(fact_1890_nat_OdiscI,axiom,
% 5.82/6.05 ! [Nat: nat,X22: nat] :
% 5.82/6.05 ( ( Nat
% 5.82/6.05 = ( suc @ X22 ) )
% 5.82/6.05 => ( Nat != zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat.discI
% 5.82/6.05 thf(fact_1891_old_Onat_Odistinct_I1_J,axiom,
% 5.82/6.05 ! [Nat2: nat] :
% 5.82/6.05 ( zero_zero_nat
% 5.82/6.05 != ( suc @ Nat2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % old.nat.distinct(1)
% 5.82/6.05 thf(fact_1892_old_Onat_Odistinct_I2_J,axiom,
% 5.82/6.05 ! [Nat2: nat] :
% 5.82/6.05 ( ( suc @ Nat2 )
% 5.82/6.05 != zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % old.nat.distinct(2)
% 5.82/6.05 thf(fact_1893_nat_Odistinct_I1_J,axiom,
% 5.82/6.05 ! [X22: nat] :
% 5.82/6.05 ( zero_zero_nat
% 5.82/6.05 != ( suc @ X22 ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat.distinct(1)
% 5.82/6.05 thf(fact_1894_infinite__descent0,axiom,
% 5.82/6.05 ! [P: nat > $o,N: nat] :
% 5.82/6.05 ( ( P @ zero_zero_nat )
% 5.82/6.05 => ( ! [N3: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.05 => ( ~ ( P @ N3 )
% 5.82/6.05 => ? [M3: nat] :
% 5.82/6.05 ( ( ord_less_nat @ M3 @ N3 )
% 5.82/6.05 & ~ ( P @ M3 ) ) ) )
% 5.82/6.05 => ( P @ N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % infinite_descent0
% 5.82/6.05 thf(fact_1895_gr__implies__not0,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ M @ N )
% 5.82/6.05 => ( N != zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % gr_implies_not0
% 5.82/6.05 thf(fact_1896_less__zeroE,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % less_zeroE
% 5.82/6.05 thf(fact_1897_not__less0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % not_less0
% 5.82/6.05 thf(fact_1898_not__gr0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.82/6.05 = ( N = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % not_gr0
% 5.82/6.05 thf(fact_1899_gr0I,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( N != zero_zero_nat )
% 5.82/6.05 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % gr0I
% 5.82/6.05 thf(fact_1900_bot__nat__0_Oextremum__strict,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ~ ( ord_less_nat @ A2 @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % bot_nat_0.extremum_strict
% 5.82/6.05 thf(fact_1901_add__eq__self__zero,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( plus_plus_nat @ M @ N )
% 5.82/6.05 = M )
% 5.82/6.05 => ( N = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % add_eq_self_zero
% 5.82/6.05 thf(fact_1902_plus__nat_Oadd__0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.82/6.05 = N ) ).
% 5.82/6.05
% 5.82/6.05 % plus_nat.add_0
% 5.82/6.05 thf(fact_1903_less__eq__nat_Osimps_I1_J,axiom,
% 5.82/6.05 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.82/6.05
% 5.82/6.05 % less_eq_nat.simps(1)
% 5.82/6.05 thf(fact_1904_bot__nat__0_Oextremum__unique,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 = ( A2 = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % bot_nat_0.extremum_unique
% 5.82/6.05 thf(fact_1905_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.82/6.05 ! [A2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 => ( A2 = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % bot_nat_0.extremum_uniqueI
% 5.82/6.05 thf(fact_1906_le__0__eq,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.82/6.05 = ( N = zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % le_0_eq
% 5.82/6.05 thf(fact_1907_diffs0__imp__equal,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ( minus_minus_nat @ M @ N )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 => ( ( ( minus_minus_nat @ N @ M )
% 5.82/6.05 = zero_zero_nat )
% 5.82/6.05 => ( M = N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % diffs0_imp_equal
% 5.82/6.05 thf(fact_1908_minus__nat_Odiff__0,axiom,
% 5.82/6.05 ! [M: nat] :
% 5.82/6.05 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.82/6.05 = M ) ).
% 5.82/6.05
% 5.82/6.05 % minus_nat.diff_0
% 5.82/6.05 thf(fact_1909_nat__mult__eq__cancel__disj,axiom,
% 5.82/6.05 ! [K: nat,M: nat,N: nat] :
% 5.82/6.05 ( ( ( times_times_nat @ K @ M )
% 5.82/6.05 = ( times_times_nat @ K @ N ) )
% 5.82/6.05 = ( ( K = zero_zero_nat )
% 5.82/6.05 | ( M = N ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % nat_mult_eq_cancel_disj
% 5.82/6.05 thf(fact_1910_mult__0,axiom,
% 5.82/6.05 ! [N: nat] :
% 5.82/6.05 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.82/6.05 = zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % mult_0
% 5.82/6.05 thf(fact_1911_zmult__zless__mono2__lemma,axiom,
% 5.82/6.05 ! [I: int,J: int,K: nat] :
% 5.82/6.05 ( ( ord_less_int @ I @ J )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.05 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % zmult_zless_mono2_lemma
% 5.82/6.05 thf(fact_1912_power__eq__iff__eq__base,axiom,
% 5.82/6.05 ! [N: nat,A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ( ( power_power_real @ A2 @ N )
% 5.82/6.05 = ( power_power_real @ B2 @ N ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_iff_eq_base
% 5.82/6.05 thf(fact_1913_power__eq__iff__eq__base,axiom,
% 5.82/6.05 ! [N: nat,A2: code_integer,B2: code_integer] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.05 => ( ( ( power_8256067586552552935nteger @ A2 @ N )
% 5.82/6.05 = ( power_8256067586552552935nteger @ B2 @ N ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_iff_eq_base
% 5.82/6.05 thf(fact_1914_power__eq__iff__eq__base,axiom,
% 5.82/6.05 ! [N: nat,A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ( ( power_power_rat @ A2 @ N )
% 5.82/6.05 = ( power_power_rat @ B2 @ N ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_iff_eq_base
% 5.82/6.05 thf(fact_1915_power__eq__iff__eq__base,axiom,
% 5.82/6.05 ! [N: nat,A2: nat,B2: nat] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ( ( power_power_nat @ A2 @ N )
% 5.82/6.05 = ( power_power_nat @ B2 @ N ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_iff_eq_base
% 5.82/6.05 thf(fact_1916_power__eq__iff__eq__base,axiom,
% 5.82/6.05 ! [N: nat,A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ( ( power_power_int @ A2 @ N )
% 5.82/6.05 = ( power_power_int @ B2 @ N ) )
% 5.82/6.05 = ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_iff_eq_base
% 5.82/6.05 thf(fact_1917_power__eq__imp__eq__base,axiom,
% 5.82/6.05 ! [A2: real,N: nat,B2: real] :
% 5.82/6.05 ( ( ( power_power_real @ A2 @ N )
% 5.82/6.05 = ( power_power_real @ B2 @ N ) )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_imp_eq_base
% 5.82/6.05 thf(fact_1918_power__eq__imp__eq__base,axiom,
% 5.82/6.05 ! [A2: code_integer,N: nat,B2: code_integer] :
% 5.82/6.05 ( ( ( power_8256067586552552935nteger @ A2 @ N )
% 5.82/6.05 = ( power_8256067586552552935nteger @ B2 @ N ) )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_imp_eq_base
% 5.82/6.05 thf(fact_1919_power__eq__imp__eq__base,axiom,
% 5.82/6.05 ! [A2: rat,N: nat,B2: rat] :
% 5.82/6.05 ( ( ( power_power_rat @ A2 @ N )
% 5.82/6.05 = ( power_power_rat @ B2 @ N ) )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_imp_eq_base
% 5.82/6.05 thf(fact_1920_power__eq__imp__eq__base,axiom,
% 5.82/6.05 ! [A2: nat,N: nat,B2: nat] :
% 5.82/6.05 ( ( ( power_power_nat @ A2 @ N )
% 5.82/6.05 = ( power_power_nat @ B2 @ N ) )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_imp_eq_base
% 5.82/6.05 thf(fact_1921_power__eq__imp__eq__base,axiom,
% 5.82/6.05 ! [A2: int,N: nat,B2: int] :
% 5.82/6.05 ( ( ( power_power_int @ A2 @ N )
% 5.82/6.05 = ( power_power_int @ B2 @ N ) )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( A2 = B2 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_eq_imp_eq_base
% 5.82/6.05 thf(fact_1922_VEBT__internal_OT__vebt__buildupi_Osimps_I2_J,axiom,
% 5.82/6.05 ( ( vEBT_V441764108873111860ildupi @ ( suc @ zero_zero_nat ) )
% 5.82/6.05 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % VEBT_internal.T_vebt_buildupi.simps(2)
% 5.82/6.05 thf(fact_1923_VEBT__internal_OT__vebt__buildupi_Osimps_I1_J,axiom,
% 5.82/6.05 ( ( vEBT_V441764108873111860ildupi @ zero_zero_nat )
% 5.82/6.05 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % VEBT_internal.T_vebt_buildupi.simps(1)
% 5.82/6.05 thf(fact_1924_lambda__zero,axiom,
% 5.82/6.05 ( ( ^ [H: complex] : zero_zero_complex )
% 5.82/6.05 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.82/6.05
% 5.82/6.05 % lambda_zero
% 5.82/6.05 thf(fact_1925_lambda__zero,axiom,
% 5.82/6.05 ( ( ^ [H: real] : zero_zero_real )
% 5.82/6.05 = ( times_times_real @ zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % lambda_zero
% 5.82/6.05 thf(fact_1926_lambda__zero,axiom,
% 5.82/6.05 ( ( ^ [H: rat] : zero_zero_rat )
% 5.82/6.05 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % lambda_zero
% 5.82/6.05 thf(fact_1927_lambda__zero,axiom,
% 5.82/6.05 ( ( ^ [H: nat] : zero_zero_nat )
% 5.82/6.05 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % lambda_zero
% 5.82/6.05 thf(fact_1928_lambda__zero,axiom,
% 5.82/6.05 ( ( ^ [H: int] : zero_zero_int )
% 5.82/6.05 = ( times_times_int @ zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % lambda_zero
% 5.82/6.05 thf(fact_1929_power__strict__mono,axiom,
% 5.82/6.05 ! [A2: code_integer,B2: code_integer,N: nat] :
% 5.82/6.05 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_mono
% 5.82/6.05 thf(fact_1930_power__strict__mono,axiom,
% 5.82/6.05 ! [A2: real,B2: real,N: nat] :
% 5.82/6.05 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_mono
% 5.82/6.05 thf(fact_1931_power__strict__mono,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.05 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_mono
% 5.82/6.05 thf(fact_1932_power__strict__mono,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_mono
% 5.82/6.05 thf(fact_1933_power__strict__mono,axiom,
% 5.82/6.05 ! [A2: int,B2: int,N: nat] :
% 5.82/6.05 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.05 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % power_strict_mono
% 5.82/6.05 thf(fact_1934_zle__int,axiom,
% 5.82/6.05 ! [M: nat,N: nat] :
% 5.82/6.05 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.05 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zle_int
% 5.82/6.05 thf(fact_1935_zadd__int__left,axiom,
% 5.82/6.05 ! [M: nat,N: nat,Z: int] :
% 5.82/6.05 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.82/6.05 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.82/6.05
% 5.82/6.05 % zadd_int_left
% 5.82/6.05 thf(fact_1936_zle__iff__zadd,axiom,
% 5.82/6.05 ( ord_less_eq_int
% 5.82/6.05 = ( ^ [W2: int,Z4: int] :
% 5.82/6.05 ? [N4: nat] :
% 5.82/6.05 ( Z4
% 5.82/6.05 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % zle_iff_zadd
% 5.82/6.05 thf(fact_1937_zdiv__int,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A2 @ B2 ) )
% 5.82/6.05 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % zdiv_int
% 5.82/6.05 thf(fact_1938_zero__le__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_numeral
% 5.82/6.05 thf(fact_1939_zero__le__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_numeral
% 5.82/6.05 thf(fact_1940_zero__le__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_numeral
% 5.82/6.05 thf(fact_1941_zero__le__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_numeral
% 5.82/6.05 thf(fact_1942_not__numeral__le__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_le_zero
% 5.82/6.05 thf(fact_1943_not__numeral__le__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_le_zero
% 5.82/6.05 thf(fact_1944_not__numeral__le__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_le_zero
% 5.82/6.05 thf(fact_1945_not__numeral__le__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_le_zero
% 5.82/6.05 thf(fact_1946_not__numeral__less__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_less_zero
% 5.82/6.05 thf(fact_1947_not__numeral__less__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_less_zero
% 5.82/6.05 thf(fact_1948_not__numeral__less__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_less_zero
% 5.82/6.05 thf(fact_1949_not__numeral__less__zero,axiom,
% 5.82/6.05 ! [N: num] :
% 5.82/6.05 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % not_numeral_less_zero
% 5.82/6.05 thf(fact_1950_zero__less__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_numeral
% 5.82/6.05 thf(fact_1951_zero__less__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_numeral
% 5.82/6.05 thf(fact_1952_zero__less__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_numeral
% 5.82/6.05 thf(fact_1953_zero__less__numeral,axiom,
% 5.82/6.05 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_less_numeral
% 5.82/6.05 thf(fact_1954_not__one__le__zero,axiom,
% 5.82/6.05 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.82/6.05
% 5.82/6.05 % not_one_le_zero
% 5.82/6.05 thf(fact_1955_not__one__le__zero,axiom,
% 5.82/6.05 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.82/6.05
% 5.82/6.05 % not_one_le_zero
% 5.82/6.05 thf(fact_1956_not__one__le__zero,axiom,
% 5.82/6.05 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.82/6.05
% 5.82/6.05 % not_one_le_zero
% 5.82/6.05 thf(fact_1957_not__one__le__zero,axiom,
% 5.82/6.05 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.82/6.05
% 5.82/6.05 % not_one_le_zero
% 5.82/6.05 thf(fact_1958_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.82/6.05
% 5.82/6.05 % linordered_nonzero_semiring_class.zero_le_one
% 5.82/6.05 thf(fact_1959_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.82/6.05
% 5.82/6.05 % linordered_nonzero_semiring_class.zero_le_one
% 5.82/6.05 thf(fact_1960_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.82/6.05
% 5.82/6.05 % linordered_nonzero_semiring_class.zero_le_one
% 5.82/6.05 thf(fact_1961_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.82/6.05
% 5.82/6.05 % linordered_nonzero_semiring_class.zero_le_one
% 5.82/6.05 thf(fact_1962_zero__less__one__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.82/6.05
% 5.82/6.05 % zero_less_one_class.zero_le_one
% 5.82/6.05 thf(fact_1963_zero__less__one__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.82/6.05
% 5.82/6.05 % zero_less_one_class.zero_le_one
% 5.82/6.05 thf(fact_1964_zero__less__one__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.82/6.05
% 5.82/6.05 % zero_less_one_class.zero_le_one
% 5.82/6.05 thf(fact_1965_zero__less__one__class_Ozero__le__one,axiom,
% 5.82/6.05 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.82/6.05
% 5.82/6.05 % zero_less_one_class.zero_le_one
% 5.82/6.05 thf(fact_1966_mult__mono,axiom,
% 5.82/6.05 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono
% 5.82/6.05 thf(fact_1967_mult__mono,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono
% 5.82/6.05 thf(fact_1968_mult__mono,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono
% 5.82/6.05 thf(fact_1969_mult__mono,axiom,
% 5.82/6.05 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono
% 5.82/6.05 thf(fact_1970_mult__mono_H,axiom,
% 5.82/6.05 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono'
% 5.82/6.05 thf(fact_1971_mult__mono_H,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono'
% 5.82/6.05 thf(fact_1972_mult__mono_H,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono'
% 5.82/6.05 thf(fact_1973_mult__mono_H,axiom,
% 5.82/6.05 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ C2 @ D2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_mono'
% 5.82/6.05 thf(fact_1974_zero__le__square,axiom,
% 5.82/6.05 ! [A2: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_square
% 5.82/6.05 thf(fact_1975_zero__le__square,axiom,
% 5.82/6.05 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_square
% 5.82/6.05 thf(fact_1976_zero__le__square,axiom,
% 5.82/6.05 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ A2 ) ) ).
% 5.82/6.05
% 5.82/6.05 % zero_le_square
% 5.82/6.05 thf(fact_1977_split__mult__pos__le,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 5.82/6.05 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.05 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) )
% 5.82/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_pos_le
% 5.82/6.05 thf(fact_1978_split__mult__pos__le,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 5.82/6.05 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) )
% 5.82/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_pos_le
% 5.82/6.05 thf(fact_1979_split__mult__pos__le,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 5.82/6.05 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.05 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) )
% 5.82/6.05 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_pos_le
% 5.82/6.05 thf(fact_1980_mult__left__mono__neg,axiom,
% 5.82/6.05 ! [B2: real,A2: real,C2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono_neg
% 5.82/6.05 thf(fact_1981_mult__left__mono__neg,axiom,
% 5.82/6.05 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono_neg
% 5.82/6.05 thf(fact_1982_mult__left__mono__neg,axiom,
% 5.82/6.05 ! [B2: int,A2: int,C2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono_neg
% 5.82/6.05 thf(fact_1983_mult__nonpos__nonpos,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.05 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.82/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonpos_nonpos
% 5.82/6.05 thf(fact_1984_mult__nonpos__nonpos,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.82/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonpos_nonpos
% 5.82/6.05 thf(fact_1985_mult__nonpos__nonpos,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.05 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.82/6.05 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonpos_nonpos
% 5.82/6.05 thf(fact_1986_mult__left__mono,axiom,
% 5.82/6.05 ! [A2: real,B2: real,C2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono
% 5.82/6.05 thf(fact_1987_mult__left__mono,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono
% 5.82/6.05 thf(fact_1988_mult__left__mono,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono
% 5.82/6.05 thf(fact_1989_mult__left__mono,axiom,
% 5.82/6.05 ! [A2: int,B2: int,C2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_left_mono
% 5.82/6.05 thf(fact_1990_mult__right__mono__neg,axiom,
% 5.82/6.05 ! [B2: real,A2: real,C2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono_neg
% 5.82/6.05 thf(fact_1991_mult__right__mono__neg,axiom,
% 5.82/6.05 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono_neg
% 5.82/6.05 thf(fact_1992_mult__right__mono__neg,axiom,
% 5.82/6.05 ! [B2: int,A2: int,C2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono_neg
% 5.82/6.05 thf(fact_1993_mult__right__mono,axiom,
% 5.82/6.05 ! [A2: real,B2: real,C2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono
% 5.82/6.05 thf(fact_1994_mult__right__mono,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono
% 5.82/6.05 thf(fact_1995_mult__right__mono,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono
% 5.82/6.05 thf(fact_1996_mult__right__mono,axiom,
% 5.82/6.05 ! [A2: int,B2: int,C2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_right_mono
% 5.82/6.05 thf(fact_1997_mult__le__0__iff,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real )
% 5.82/6.05 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 5.82/6.05 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.05 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_le_0_iff
% 5.82/6.05 thf(fact_1998_mult__le__0__iff,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat )
% 5.82/6.05 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 5.82/6.05 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_le_0_iff
% 5.82/6.05 thf(fact_1999_mult__le__0__iff,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int )
% 5.82/6.05 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 5.82/6.05 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.05 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_le_0_iff
% 5.82/6.05 thf(fact_2000_split__mult__neg__le,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 5.82/6.05 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.05 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_neg_le
% 5.82/6.05 thf(fact_2001_split__mult__neg__le,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 5.82/6.05 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_neg_le
% 5.82/6.05 thf(fact_2002_split__mult__neg__le,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 & ( ord_less_eq_nat @ B2 @ zero_zero_nat ) )
% 5.82/6.05 | ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.05 & ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) )
% 5.82/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_neg_le
% 5.82/6.05 thf(fact_2003_split__mult__neg__le,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 5.82/6.05 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.05 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ).
% 5.82/6.05
% 5.82/6.05 % split_mult_neg_le
% 5.82/6.05 thf(fact_2004_mult__nonneg__nonneg,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonneg
% 5.82/6.05 thf(fact_2005_mult__nonneg__nonneg,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonneg
% 5.82/6.05 thf(fact_2006_mult__nonneg__nonneg,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.05 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonneg
% 5.82/6.05 thf(fact_2007_mult__nonneg__nonneg,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.05 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonneg
% 5.82/6.05 thf(fact_2008_mult__nonneg__nonpos,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonpos
% 5.82/6.05 thf(fact_2009_mult__nonneg__nonpos,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonpos
% 5.82/6.05 thf(fact_2010_mult__nonneg__nonpos,axiom,
% 5.82/6.05 ! [A2: nat,B2: nat] :
% 5.82/6.05 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.82/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonpos
% 5.82/6.05 thf(fact_2011_mult__nonneg__nonpos,axiom,
% 5.82/6.05 ! [A2: int,B2: int] :
% 5.82/6.05 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.05 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.82/6.05 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonneg_nonpos
% 5.82/6.05 thf(fact_2012_mult__nonpos__nonneg,axiom,
% 5.82/6.05 ! [A2: real,B2: real] :
% 5.82/6.05 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.05 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.05 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.05
% 5.82/6.05 % mult_nonpos_nonneg
% 5.82/6.05 thf(fact_2013_mult__nonpos__nonneg,axiom,
% 5.82/6.05 ! [A2: rat,B2: rat] :
% 5.82/6.05 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.05 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonpos_nonneg
% 5.82/6.06 thf(fact_2014_mult__nonpos__nonneg,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonpos_nonneg
% 5.82/6.06 thf(fact_2015_mult__nonpos__nonneg,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonpos_nonneg
% 5.82/6.06 thf(fact_2016_mult__nonneg__nonpos2,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ B2 @ A2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonneg_nonpos2
% 5.82/6.06 thf(fact_2017_mult__nonneg__nonpos2,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ B2 @ A2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonneg_nonpos2
% 5.82/6.06 thf(fact_2018_mult__nonneg__nonpos2,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.82/6.06 => ( ord_less_eq_nat @ ( times_times_nat @ B2 @ A2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonneg_nonpos2
% 5.82/6.06 thf(fact_2019_mult__nonneg__nonpos2,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ B2 @ A2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_nonneg_nonpos2
% 5.82/6.06 thf(fact_2020_zero__le__mult__iff,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 5.82/6.06 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.06 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_mult_iff
% 5.82/6.06 thf(fact_2021_zero__le__mult__iff,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 5.82/6.06 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.06 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_mult_iff
% 5.82/6.06 thf(fact_2022_zero__le__mult__iff,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 5.82/6.06 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.06 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_mult_iff
% 5.82/6.06 thf(fact_2023_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.82/6.06 thf(fact_2024_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.82/6.06 thf(fact_2025_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.82/6.06 thf(fact_2026_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.82/6.06 thf(fact_2027_add__less__zeroD,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] :
% 5.82/6.06 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y3 ) @ zero_zero_real )
% 5.82/6.06 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.06 | ( ord_less_real @ Y3 @ zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % add_less_zeroD
% 5.82/6.06 thf(fact_2028_add__less__zeroD,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ zero_zero_rat )
% 5.82/6.06 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.82/6.06 | ( ord_less_rat @ Y3 @ zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % add_less_zeroD
% 5.82/6.06 thf(fact_2029_add__less__zeroD,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] :
% 5.82/6.06 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y3 ) @ zero_zero_int )
% 5.82/6.06 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.82/6.06 | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % add_less_zeroD
% 5.82/6.06 thf(fact_2030_zero__less__one,axiom,
% 5.82/6.06 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.82/6.06
% 5.82/6.06 % zero_less_one
% 5.82/6.06 thf(fact_2031_zero__less__one,axiom,
% 5.82/6.06 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.82/6.06
% 5.82/6.06 % zero_less_one
% 5.82/6.06 thf(fact_2032_zero__less__one,axiom,
% 5.82/6.06 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.82/6.06
% 5.82/6.06 % zero_less_one
% 5.82/6.06 thf(fact_2033_zero__less__one,axiom,
% 5.82/6.06 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.82/6.06
% 5.82/6.06 % zero_less_one
% 5.82/6.06 thf(fact_2034_not__one__less__zero,axiom,
% 5.82/6.06 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.82/6.06
% 5.82/6.06 % not_one_less_zero
% 5.82/6.06 thf(fact_2035_not__one__less__zero,axiom,
% 5.82/6.06 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.82/6.06
% 5.82/6.06 % not_one_less_zero
% 5.82/6.06 thf(fact_2036_not__one__less__zero,axiom,
% 5.82/6.06 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.82/6.06
% 5.82/6.06 % not_one_less_zero
% 5.82/6.06 thf(fact_2037_not__one__less__zero,axiom,
% 5.82/6.06 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.82/6.06
% 5.82/6.06 % not_one_less_zero
% 5.82/6.06 thf(fact_2038_less__numeral__extra_I1_J,axiom,
% 5.82/6.06 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.82/6.06
% 5.82/6.06 % less_numeral_extra(1)
% 5.82/6.06 thf(fact_2039_less__numeral__extra_I1_J,axiom,
% 5.82/6.06 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.82/6.06
% 5.82/6.06 % less_numeral_extra(1)
% 5.82/6.06 thf(fact_2040_less__numeral__extra_I1_J,axiom,
% 5.82/6.06 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.82/6.06
% 5.82/6.06 % less_numeral_extra(1)
% 5.82/6.06 thf(fact_2041_less__numeral__extra_I1_J,axiom,
% 5.82/6.06 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.82/6.06
% 5.82/6.06 % less_numeral_extra(1)
% 5.82/6.06 thf(fact_2042_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.82/6.06 thf(fact_2043_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.82/6.06 thf(fact_2044_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.82/6.06 thf(fact_2045_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.82/6.06 thf(fact_2046_mult__less__cancel__right__disj,axiom,
% 5.82/6.06 ! [A2: real,C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 & ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.06 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 & ( ord_less_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right_disj
% 5.82/6.06 thf(fact_2047_mult__less__cancel__right__disj,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 & ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.06 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 & ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right_disj
% 5.82/6.06 thf(fact_2048_mult__less__cancel__right__disj,axiom,
% 5.82/6.06 ! [A2: int,C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 & ( ord_less_int @ A2 @ B2 ) )
% 5.82/6.06 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 & ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right_disj
% 5.82/6.06 thf(fact_2049_mult__strict__right__mono,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono
% 5.82/6.06 thf(fact_2050_mult__strict__right__mono,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono
% 5.82/6.06 thf(fact_2051_mult__strict__right__mono,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono
% 5.82/6.06 thf(fact_2052_mult__strict__right__mono,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono
% 5.82/6.06 thf(fact_2053_mult__strict__right__mono__neg,axiom,
% 5.82/6.06 ! [B2: real,A2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono_neg
% 5.82/6.06 thf(fact_2054_mult__strict__right__mono__neg,axiom,
% 5.82/6.06 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono_neg
% 5.82/6.06 thf(fact_2055_mult__strict__right__mono__neg,axiom,
% 5.82/6.06 ! [B2: int,A2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_right_mono_neg
% 5.82/6.06 thf(fact_2056_mult__less__cancel__left__disj,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 & ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.06 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 & ( ord_less_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_disj
% 5.82/6.06 thf(fact_2057_mult__less__cancel__left__disj,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 & ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.06 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 & ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_disj
% 5.82/6.06 thf(fact_2058_mult__less__cancel__left__disj,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 & ( ord_less_int @ A2 @ B2 ) )
% 5.82/6.06 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 & ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_disj
% 5.82/6.06 thf(fact_2059_mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono
% 5.82/6.06 thf(fact_2060_mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono
% 5.82/6.06 thf(fact_2061_mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono
% 5.82/6.06 thf(fact_2062_mult__strict__left__mono,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono
% 5.82/6.06 thf(fact_2063_mult__strict__left__mono__neg,axiom,
% 5.82/6.06 ! [B2: real,A2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono_neg
% 5.82/6.06 thf(fact_2064_mult__strict__left__mono__neg,axiom,
% 5.82/6.06 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono_neg
% 5.82/6.06 thf(fact_2065_mult__strict__left__mono__neg,axiom,
% 5.82/6.06 ! [B2: int,A2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_left_mono_neg
% 5.82/6.06 thf(fact_2066_mult__less__cancel__left__pos,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_pos
% 5.82/6.06 thf(fact_2067_mult__less__cancel__left__pos,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_pos
% 5.82/6.06 thf(fact_2068_mult__less__cancel__left__pos,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_pos
% 5.82/6.06 thf(fact_2069_mult__less__cancel__left__neg,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_real @ B2 @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_neg
% 5.82/6.06 thf(fact_2070_mult__less__cancel__left__neg,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_rat @ B2 @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_neg
% 5.82/6.06 thf(fact_2071_mult__less__cancel__left__neg,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_int @ B2 @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left_neg
% 5.82/6.06 thf(fact_2072_zero__less__mult__pos2,axiom,
% 5.82/6.06 ! [B2: real,A2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B2 @ A2 ) )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos2
% 5.82/6.06 thf(fact_2073_zero__less__mult__pos2,axiom,
% 5.82/6.06 ! [B2: rat,A2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B2 @ A2 ) )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos2
% 5.82/6.06 thf(fact_2074_zero__less__mult__pos2,axiom,
% 5.82/6.06 ! [B2: nat,A2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B2 @ A2 ) )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos2
% 5.82/6.06 thf(fact_2075_zero__less__mult__pos2,axiom,
% 5.82/6.06 ! [B2: int,A2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B2 @ A2 ) )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos2
% 5.82/6.06 thf(fact_2076_zero__less__mult__pos,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos
% 5.82/6.06 thf(fact_2077_zero__less__mult__pos,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos
% 5.82/6.06 thf(fact_2078_zero__less__mult__pos,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos
% 5.82/6.06 thf(fact_2079_zero__less__mult__pos,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_pos
% 5.82/6.06 thf(fact_2080_zero__less__mult__iff,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 & ( ord_less_real @ zero_zero_real @ B2 ) )
% 5.82/6.06 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.06 & ( ord_less_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_iff
% 5.82/6.06 thf(fact_2081_zero__less__mult__iff,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 & ( ord_less_rat @ zero_zero_rat @ B2 ) )
% 5.82/6.06 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.06 & ( ord_less_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_iff
% 5.82/6.06 thf(fact_2082_zero__less__mult__iff,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 & ( ord_less_int @ zero_zero_int @ B2 ) )
% 5.82/6.06 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.06 & ( ord_less_int @ B2 @ zero_zero_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_mult_iff
% 5.82/6.06 thf(fact_2083_mult__pos__neg2,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ B2 @ A2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg2
% 5.82/6.06 thf(fact_2084_mult__pos__neg2,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ B2 @ A2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg2
% 5.82/6.06 thf(fact_2085_mult__pos__neg2,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ B2 @ A2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg2
% 5.82/6.06 thf(fact_2086_mult__pos__neg2,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ B2 @ A2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg2
% 5.82/6.06 thf(fact_2087_mult__pos__pos,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_pos
% 5.82/6.06 thf(fact_2088_mult__pos__pos,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_pos
% 5.82/6.06 thf(fact_2089_mult__pos__pos,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_pos
% 5.82/6.06 thf(fact_2090_mult__pos__pos,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_pos
% 5.82/6.06 thf(fact_2091_mult__pos__neg,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg
% 5.82/6.06 thf(fact_2092_mult__pos__neg,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg
% 5.82/6.06 thf(fact_2093_mult__pos__neg,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg
% 5.82/6.06 thf(fact_2094_mult__pos__neg,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_pos_neg
% 5.82/6.06 thf(fact_2095_mult__neg__pos,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_pos
% 5.82/6.06 thf(fact_2096_mult__neg__pos,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_pos
% 5.82/6.06 thf(fact_2097_mult__neg__pos,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_pos
% 5.82/6.06 thf(fact_2098_mult__neg__pos,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_pos
% 5.82/6.06 thf(fact_2099_mult__less__0__iff,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ A2 @ B2 ) @ zero_zero_real )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 & ( ord_less_real @ B2 @ zero_zero_real ) )
% 5.82/6.06 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.06 & ( ord_less_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_0_iff
% 5.82/6.06 thf(fact_2100_mult__less__0__iff,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 & ( ord_less_rat @ B2 @ zero_zero_rat ) )
% 5.82/6.06 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.06 & ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_0_iff
% 5.82/6.06 thf(fact_2101_mult__less__0__iff,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 & ( ord_less_int @ B2 @ zero_zero_int ) )
% 5.82/6.06 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.06 & ( ord_less_int @ zero_zero_int @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_0_iff
% 5.82/6.06 thf(fact_2102_not__square__less__zero,axiom,
% 5.82/6.06 ! [A2: real] :
% 5.82/6.06 ~ ( ord_less_real @ ( times_times_real @ A2 @ A2 ) @ zero_zero_real ) ).
% 5.82/6.06
% 5.82/6.06 % not_square_less_zero
% 5.82/6.06 thf(fact_2103_not__square__less__zero,axiom,
% 5.82/6.06 ! [A2: rat] :
% 5.82/6.06 ~ ( ord_less_rat @ ( times_times_rat @ A2 @ A2 ) @ zero_zero_rat ) ).
% 5.82/6.06
% 5.82/6.06 % not_square_less_zero
% 5.82/6.06 thf(fact_2104_not__square__less__zero,axiom,
% 5.82/6.06 ! [A2: int] :
% 5.82/6.06 ~ ( ord_less_int @ ( times_times_int @ A2 @ A2 ) @ zero_zero_int ) ).
% 5.82/6.06
% 5.82/6.06 % not_square_less_zero
% 5.82/6.06 thf(fact_2105_mult__neg__neg,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.06 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_neg
% 5.82/6.06 thf(fact_2106_mult__neg__neg,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.06 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_neg
% 5.82/6.06 thf(fact_2107_mult__neg__neg,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.06 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_neg_neg
% 5.82/6.06 thf(fact_2108_power__mono,axiom,
% 5.82/6.06 ! [A2: real,B2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_mono
% 5.82/6.06 thf(fact_2109_power__mono,axiom,
% 5.82/6.06 ! [A2: code_integer,B2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_mono
% 5.82/6.06 thf(fact_2110_power__mono,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_mono
% 5.82/6.06 thf(fact_2111_power__mono,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_mono
% 5.82/6.06 thf(fact_2112_power__mono,axiom,
% 5.82/6.06 ! [A2: int,B2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_mono
% 5.82/6.06 thf(fact_2113_zero__le__power,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_power
% 5.82/6.06 thf(fact_2114_zero__le__power,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_power
% 5.82/6.06 thf(fact_2115_zero__le__power,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_power
% 5.82/6.06 thf(fact_2116_zero__le__power,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_power
% 5.82/6.06 thf(fact_2117_zero__le__power,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_le_power
% 5.82/6.06 thf(fact_2118_zero__less__power,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_power
% 5.82/6.06 thf(fact_2119_zero__less__power,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_power
% 5.82/6.06 thf(fact_2120_zero__less__power,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_power
% 5.82/6.06 thf(fact_2121_zero__less__power,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_power
% 5.82/6.06 thf(fact_2122_zero__less__power,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_power
% 5.82/6.06 thf(fact_2123_of__nat__0__le__iff,axiom,
% 5.82/6.06 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_0_le_iff
% 5.82/6.06 thf(fact_2124_of__nat__0__le__iff,axiom,
% 5.82/6.06 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_0_le_iff
% 5.82/6.06 thf(fact_2125_of__nat__0__le__iff,axiom,
% 5.82/6.06 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_0_le_iff
% 5.82/6.06 thf(fact_2126_of__nat__0__le__iff,axiom,
% 5.82/6.06 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_0_le_iff
% 5.82/6.06 thf(fact_2127_of__nat__less__0__iff,axiom,
% 5.82/6.06 ! [M: nat] :
% 5.82/6.06 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_less_0_iff
% 5.82/6.06 thf(fact_2128_of__nat__less__0__iff,axiom,
% 5.82/6.06 ! [M: nat] :
% 5.82/6.06 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_less_0_iff
% 5.82/6.06 thf(fact_2129_of__nat__less__0__iff,axiom,
% 5.82/6.06 ! [M: nat] :
% 5.82/6.06 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_less_0_iff
% 5.82/6.06 thf(fact_2130_of__nat__less__0__iff,axiom,
% 5.82/6.06 ! [M: nat] :
% 5.82/6.06 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.82/6.06
% 5.82/6.06 % of_nat_less_0_iff
% 5.82/6.06 thf(fact_2131_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.82/6.06 != zero_zero_complex ) ).
% 5.82/6.06
% 5.82/6.06 % semiring_char_0_class.of_nat_neq_0
% 5.82/6.06 thf(fact_2132_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.82/6.06 != zero_zero_rat ) ).
% 5.82/6.06
% 5.82/6.06 % semiring_char_0_class.of_nat_neq_0
% 5.82/6.06 thf(fact_2133_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.82/6.06 != zero_zero_real ) ).
% 5.82/6.06
% 5.82/6.06 % semiring_char_0_class.of_nat_neq_0
% 5.82/6.06 thf(fact_2134_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.82/6.06 != zero_zero_int ) ).
% 5.82/6.06
% 5.82/6.06 % semiring_char_0_class.of_nat_neq_0
% 5.82/6.06 thf(fact_2135_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.82/6.06 != zero_zero_nat ) ).
% 5.82/6.06
% 5.82/6.06 % semiring_char_0_class.of_nat_neq_0
% 5.82/6.06 thf(fact_2136_power__0,axiom,
% 5.82/6.06 ! [A2: assn] :
% 5.82/6.06 ( ( power_power_assn @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_assn ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2137_power__0,axiom,
% 5.82/6.06 ! [A2: rat] :
% 5.82/6.06 ( ( power_power_rat @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_rat ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2138_power__0,axiom,
% 5.82/6.06 ! [A2: nat] :
% 5.82/6.06 ( ( power_power_nat @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_nat ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2139_power__0,axiom,
% 5.82/6.06 ! [A2: real] :
% 5.82/6.06 ( ( power_power_real @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_real ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2140_power__0,axiom,
% 5.82/6.06 ! [A2: int] :
% 5.82/6.06 ( ( power_power_int @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_int ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2141_power__0,axiom,
% 5.82/6.06 ! [A2: complex] :
% 5.82/6.06 ( ( power_power_complex @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_complex ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2142_power__0,axiom,
% 5.82/6.06 ! [A2: code_integer] :
% 5.82/6.06 ( ( power_8256067586552552935nteger @ A2 @ zero_zero_nat )
% 5.82/6.06 = one_one_Code_integer ) ).
% 5.82/6.06
% 5.82/6.06 % power_0
% 5.82/6.06 thf(fact_2143_less__Suc__eq__0__disj,axiom,
% 5.82/6.06 ! [M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.82/6.06 = ( ( M = zero_zero_nat )
% 5.82/6.06 | ? [J3: nat] :
% 5.82/6.06 ( ( M
% 5.82/6.06 = ( suc @ J3 ) )
% 5.82/6.06 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % less_Suc_eq_0_disj
% 5.82/6.06 thf(fact_2144_gr0__implies__Suc,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ? [M5: nat] :
% 5.82/6.06 ( N
% 5.82/6.06 = ( suc @ M5 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % gr0_implies_Suc
% 5.82/6.06 thf(fact_2145_All__less__Suc2,axiom,
% 5.82/6.06 ! [N: nat,P: nat > $o] :
% 5.82/6.06 ( ( ! [I4: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.82/6.06 => ( P @ I4 ) ) )
% 5.82/6.06 = ( ( P @ zero_zero_nat )
% 5.82/6.06 & ! [I4: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I4 @ N )
% 5.82/6.06 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % All_less_Suc2
% 5.82/6.06 thf(fact_2146_gr0__conv__Suc,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 = ( ? [M6: nat] :
% 5.82/6.06 ( N
% 5.82/6.06 = ( suc @ M6 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % gr0_conv_Suc
% 5.82/6.06 thf(fact_2147_Ex__less__Suc2,axiom,
% 5.82/6.06 ! [N: nat,P: nat > $o] :
% 5.82/6.06 ( ( ? [I4: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.82/6.06 & ( P @ I4 ) ) )
% 5.82/6.06 = ( ( P @ zero_zero_nat )
% 5.82/6.06 | ? [I4: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I4 @ N )
% 5.82/6.06 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % Ex_less_Suc2
% 5.82/6.06 thf(fact_2148_add__is__1,axiom,
% 5.82/6.06 ! [M: nat,N: nat] :
% 5.82/6.06 ( ( ( plus_plus_nat @ M @ N )
% 5.82/6.06 = ( suc @ zero_zero_nat ) )
% 5.82/6.06 = ( ( ( M
% 5.82/6.06 = ( suc @ zero_zero_nat ) )
% 5.82/6.06 & ( N = zero_zero_nat ) )
% 5.82/6.06 | ( ( M = zero_zero_nat )
% 5.82/6.06 & ( N
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % add_is_1
% 5.82/6.06 thf(fact_2149_one__is__add,axiom,
% 5.82/6.06 ! [M: nat,N: nat] :
% 5.82/6.06 ( ( ( suc @ zero_zero_nat )
% 5.82/6.06 = ( plus_plus_nat @ M @ N ) )
% 5.82/6.06 = ( ( ( M
% 5.82/6.06 = ( suc @ zero_zero_nat ) )
% 5.82/6.06 & ( N = zero_zero_nat ) )
% 5.82/6.06 | ( ( M = zero_zero_nat )
% 5.82/6.06 & ( N
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_is_add
% 5.82/6.06 thf(fact_2150_nat__compl__induct,axiom,
% 5.82/6.06 ! [P: nat > $o,N: nat] :
% 5.82/6.06 ( ( P @ zero_zero_nat )
% 5.82/6.06 => ( ! [N3: nat] :
% 5.82/6.06 ( ! [Nn: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ Nn @ N3 )
% 5.82/6.06 => ( P @ Nn ) )
% 5.82/6.06 => ( P @ ( suc @ N3 ) ) )
% 5.82/6.06 => ( P @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_compl_induct
% 5.82/6.06 thf(fact_2151_nat__compl__induct_H,axiom,
% 5.82/6.06 ! [P: nat > $o,N: nat] :
% 5.82/6.06 ( ( P @ zero_zero_nat )
% 5.82/6.06 => ( ! [N3: nat] :
% 5.82/6.06 ( ! [Nn: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ Nn @ N3 )
% 5.82/6.06 => ( P @ Nn ) )
% 5.82/6.06 => ( P @ ( suc @ N3 ) ) )
% 5.82/6.06 => ( P @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_compl_induct'
% 5.82/6.06 thf(fact_2152_option_Osize_I4_J,axiom,
% 5.82/6.06 ! [X22: product_prod_nat_nat] :
% 5.82/6.06 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % option.size(4)
% 5.82/6.06 thf(fact_2153_option_Osize_I4_J,axiom,
% 5.82/6.06 ! [X22: nat] :
% 5.82/6.06 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % option.size(4)
% 5.82/6.06 thf(fact_2154_One__nat__def,axiom,
% 5.82/6.06 ( one_one_nat
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % One_nat_def
% 5.82/6.06 thf(fact_2155_option_Osize_I3_J,axiom,
% 5.82/6.06 ( ( size_size_option_nat @ none_nat )
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % option.size(3)
% 5.82/6.06 thf(fact_2156_option_Osize_I3_J,axiom,
% 5.82/6.06 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % option.size(3)
% 5.82/6.06 thf(fact_2157_less__imp__add__positive,axiom,
% 5.82/6.06 ! [I: nat,J: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I @ J )
% 5.82/6.06 => ? [K2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.82/6.06 & ( ( plus_plus_nat @ I @ K2 )
% 5.82/6.06 = J ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % less_imp_add_positive
% 5.82/6.06 thf(fact_2158_ex__least__nat__le,axiom,
% 5.82/6.06 ! [P: nat > $o,N: nat] :
% 5.82/6.06 ( ( P @ N )
% 5.82/6.06 => ( ~ ( P @ zero_zero_nat )
% 5.82/6.06 => ? [K2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ K2 @ N )
% 5.82/6.06 & ! [I5: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I5 @ K2 )
% 5.82/6.06 => ~ ( P @ I5 ) )
% 5.82/6.06 & ( P @ K2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % ex_least_nat_le
% 5.82/6.06 thf(fact_2159_Suc__to__right,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ( suc @ N )
% 5.82/6.06 = M )
% 5.82/6.06 => ( N
% 5.82/6.06 = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % Suc_to_right
% 5.82/6.06 thf(fact_2160_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.82/6.06 ! [M: nat,N: nat] :
% 5.82/6.06 ( ( ( divide_divide_nat @ M @ N )
% 5.82/6.06 = zero_zero_nat )
% 5.82/6.06 = ( ( ord_less_nat @ M @ N )
% 5.82/6.06 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % Euclidean_Division.div_eq_0_iff
% 5.82/6.06 thf(fact_2161_diff__less,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.06 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % diff_less
% 5.82/6.06 thf(fact_2162_nat__geq__1__eq__neqz,axiom,
% 5.82/6.06 ! [X2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ one_one_nat @ X2 )
% 5.82/6.06 = ( X2 != zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_geq_1_eq_neqz
% 5.82/6.06 thf(fact_2163_nat__mult__eq__cancel1,axiom,
% 5.82/6.06 ! [K: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ( ( times_times_nat @ K @ M )
% 5.82/6.06 = ( times_times_nat @ K @ N ) )
% 5.82/6.06 = ( M = N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_mult_eq_cancel1
% 5.82/6.06 thf(fact_2164_nat__mult__less__cancel1,axiom,
% 5.82/6.06 ! [K: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.06 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_mult_less_cancel1
% 5.82/6.06 thf(fact_2165_mult__less__mono1,axiom,
% 5.82/6.06 ! [I: nat,J: nat,K: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I @ J )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_mono1
% 5.82/6.06 thf(fact_2166_mult__less__mono2,axiom,
% 5.82/6.06 ! [I: nat,J: nat,K: nat] :
% 5.82/6.06 ( ( ord_less_nat @ I @ J )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_mono2
% 5.82/6.06 thf(fact_2167_diff__add__0,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.82/6.06 = zero_zero_nat ) ).
% 5.82/6.06
% 5.82/6.06 % diff_add_0
% 5.82/6.06 thf(fact_2168_nat__power__less__imp__less,axiom,
% 5.82/6.06 ! [I: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.82/6.06 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.82/6.06 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_power_less_imp_less
% 5.82/6.06 thf(fact_2169_mult__eq__self__implies__10,axiom,
% 5.82/6.06 ! [M: nat,N: nat] :
% 5.82/6.06 ( ( M
% 5.82/6.06 = ( times_times_nat @ M @ N ) )
% 5.82/6.06 => ( ( N = one_one_nat )
% 5.82/6.06 | ( M = zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_eq_self_implies_10
% 5.82/6.06 thf(fact_2170_vebt__insert_Osimps_I2_J,axiom,
% 5.82/6.06 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) @ X2 )
% 5.82/6.06 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) ) ).
% 5.82/6.06
% 5.82/6.06 % vebt_insert.simps(2)
% 5.82/6.06 thf(fact_2171_zless__iff__Suc__zadd,axiom,
% 5.82/6.06 ( ord_less_int
% 5.82/6.06 = ( ^ [W2: int,Z4: int] :
% 5.82/6.06 ? [N4: nat] :
% 5.82/6.06 ( Z4
% 5.82/6.06 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % zless_iff_Suc_zadd
% 5.82/6.06 thf(fact_2172_mult__less__le__imp__less,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_le_imp_less
% 5.82/6.06 thf(fact_2173_mult__less__le__imp__less,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_le_imp_less
% 5.82/6.06 thf(fact_2174_mult__less__le__imp__less,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_le_imp_less
% 5.82/6.06 thf(fact_2175_mult__less__le__imp__less,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_le_imp_less
% 5.82/6.06 thf(fact_2176_mult__le__less__imp__less,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_less_imp_less
% 5.82/6.06 thf(fact_2177_mult__le__less__imp__less,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_less_imp_less
% 5.82/6.06 thf(fact_2178_mult__le__less__imp__less,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_less_imp_less
% 5.82/6.06 thf(fact_2179_mult__le__less__imp__less,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_less_imp_less
% 5.82/6.06 thf(fact_2180_mult__right__le__imp__le,axiom,
% 5.82/6.06 ! [A2: real,C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_imp_le
% 5.82/6.06 thf(fact_2181_mult__right__le__imp__le,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_imp_le
% 5.82/6.06 thf(fact_2182_mult__right__le__imp__le,axiom,
% 5.82/6.06 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_imp_le
% 5.82/6.06 thf(fact_2183_mult__right__le__imp__le,axiom,
% 5.82/6.06 ! [A2: int,C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_imp_le
% 5.82/6.06 thf(fact_2184_mult__left__le__imp__le,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_imp_le
% 5.82/6.06 thf(fact_2185_mult__left__le__imp__le,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_imp_le
% 5.82/6.06 thf(fact_2186_mult__left__le__imp__le,axiom,
% 5.82/6.06 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_imp_le
% 5.82/6.06 thf(fact_2187_mult__left__le__imp__le,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_imp_le
% 5.82/6.06 thf(fact_2188_mult__le__cancel__left__pos,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left_pos
% 5.82/6.06 thf(fact_2189_mult__le__cancel__left__pos,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left_pos
% 5.82/6.06 thf(fact_2190_mult__le__cancel__left__pos,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left_pos
% 5.82/6.06 thf(fact_2191_mult__le__cancel__left__neg,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_eq_real @ B2 @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left_neg
% 5.82/6.06 thf(fact_2192_mult__le__cancel__left__neg,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_eq_rat @ B2 @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left_neg
% 5.82/6.06 thf(fact_2193_mult__le__cancel__left__neg,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ord_less_eq_int @ B2 @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left_neg
% 5.82/6.06 thf(fact_2194_mult__less__cancel__right,axiom,
% 5.82/6.06 ! [A2: real,C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right
% 5.82/6.06 thf(fact_2195_mult__less__cancel__right,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right
% 5.82/6.06 thf(fact_2196_mult__less__cancel__right,axiom,
% 5.82/6.06 ! [A2: int,C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right
% 5.82/6.06 thf(fact_2197_mult__strict__mono_H,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono'
% 5.82/6.06 thf(fact_2198_mult__strict__mono_H,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono'
% 5.82/6.06 thf(fact_2199_mult__strict__mono_H,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono'
% 5.82/6.06 thf(fact_2200_mult__strict__mono_H,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono'
% 5.82/6.06 thf(fact_2201_mult__right__less__imp__less,axiom,
% 5.82/6.06 ! [A2: real,C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_less_imp_less
% 5.82/6.06 thf(fact_2202_mult__right__less__imp__less,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_less_imp_less
% 5.82/6.06 thf(fact_2203_mult__right__less__imp__less,axiom,
% 5.82/6.06 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_less_imp_less
% 5.82/6.06 thf(fact_2204_mult__right__less__imp__less,axiom,
% 5.82/6.06 ! [A2: int,C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_less_imp_less
% 5.82/6.06 thf(fact_2205_mult__less__cancel__left,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left
% 5.82/6.06 thf(fact_2206_mult__less__cancel__left,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left
% 5.82/6.06 thf(fact_2207_mult__less__cancel__left,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left
% 5.82/6.06 thf(fact_2208_mult__strict__mono,axiom,
% 5.82/6.06 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.06 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono
% 5.82/6.06 thf(fact_2209_mult__strict__mono,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono
% 5.82/6.06 thf(fact_2210_mult__strict__mono,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono
% 5.82/6.06 thf(fact_2211_mult__strict__mono,axiom,
% 5.82/6.06 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.06 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_strict_mono
% 5.82/6.06 thf(fact_2212_mult__left__less__imp__less,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_less_imp_less
% 5.82/6.06 thf(fact_2213_mult__left__less__imp__less,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_less_imp_less
% 5.82/6.06 thf(fact_2214_mult__left__less__imp__less,axiom,
% 5.82/6.06 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_less_imp_less
% 5.82/6.06 thf(fact_2215_mult__left__less__imp__less,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_less_imp_less
% 5.82/6.06 thf(fact_2216_mult__le__cancel__right,axiom,
% 5.82/6.06 ! [A2: real,C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right
% 5.82/6.06 thf(fact_2217_mult__le__cancel__right,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right
% 5.82/6.06 thf(fact_2218_mult__le__cancel__right,axiom,
% 5.82/6.06 ! [A2: int,C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right
% 5.82/6.06 thf(fact_2219_mult__le__cancel__left,axiom,
% 5.82/6.06 ! [C2: real,A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left
% 5.82/6.06 thf(fact_2220_mult__le__cancel__left,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left
% 5.82/6.06 thf(fact_2221_mult__le__cancel__left,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ B2 ) )
% 5.82/6.06 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left
% 5.82/6.06 thf(fact_2222_sum__squares__ge__zero,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_ge_zero
% 5.82/6.06 thf(fact_2223_sum__squares__ge__zero,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_ge_zero
% 5.82/6.06 thf(fact_2224_sum__squares__ge__zero,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_ge_zero
% 5.82/6.06 thf(fact_2225_sum__squares__le__zero__iff,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real )
% 5.82/6.06 = ( ( X2 = zero_zero_real )
% 5.82/6.06 & ( Y3 = zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_le_zero_iff
% 5.82/6.06 thf(fact_2226_sum__squares__le__zero__iff,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat )
% 5.82/6.06 = ( ( X2 = zero_zero_rat )
% 5.82/6.06 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_le_zero_iff
% 5.82/6.06 thf(fact_2227_sum__squares__le__zero__iff,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int )
% 5.82/6.06 = ( ( X2 = zero_zero_int )
% 5.82/6.06 & ( Y3 = zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_le_zero_iff
% 5.82/6.06 thf(fact_2228_mult__left__le__one__le,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.06 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ Y3 @ X2 ) @ X2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_one_le
% 5.82/6.06 thf(fact_2229_mult__left__le__one__le,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ Y3 @ X2 ) @ X2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_one_le
% 5.82/6.06 thf(fact_2230_mult__left__le__one__le,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.06 => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ Y3 @ X2 ) @ X2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le_one_le
% 5.82/6.06 thf(fact_2231_mult__right__le__one__le,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.06 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_one_le
% 5.82/6.06 thf(fact_2232_mult__right__le__one__le,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_one_le
% 5.82/6.06 thf(fact_2233_mult__right__le__one__le,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.06 => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_right_le_one_le
% 5.82/6.06 thf(fact_2234_mult__le__one,axiom,
% 5.82/6.06 ! [A2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ B2 @ one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B2 ) @ one_one_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_one
% 5.82/6.06 thf(fact_2235_mult__le__one,axiom,
% 5.82/6.06 ! [A2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ B2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ one_one_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_one
% 5.82/6.06 thf(fact_2236_mult__le__one,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ B2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ one_one_nat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_one
% 5.82/6.06 thf(fact_2237_mult__le__one,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ B2 @ one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ one_one_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_one
% 5.82/6.06 thf(fact_2238_mult__left__le,axiom,
% 5.82/6.06 ! [C2: real,A2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ C2 @ one_one_real )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le
% 5.82/6.06 thf(fact_2239_mult__left__le,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le
% 5.82/6.06 thf(fact_2240_mult__left__le,axiom,
% 5.82/6.06 ! [C2: nat,A2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le
% 5.82/6.06 thf(fact_2241_mult__left__le,axiom,
% 5.82/6.06 ! [C2: int,A2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_left_le
% 5.82/6.06 thf(fact_2242_div__positive,axiom,
% 5.82/6.06 ! [B2: nat,A2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_positive
% 5.82/6.06 thf(fact_2243_div__positive,axiom,
% 5.82/6.06 ! [B2: int,A2: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.06 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_positive
% 5.82/6.06 thf(fact_2244_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.82/6.06 ! [A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( ( divide_divide_nat @ A2 @ B2 )
% 5.82/6.06 = zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % unique_euclidean_semiring_numeral_class.div_less
% 5.82/6.06 thf(fact_2245_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.82/6.06 ! [A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.06 => ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.06 = zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % unique_euclidean_semiring_numeral_class.div_less
% 5.82/6.06 thf(fact_2246_zero__less__two,axiom,
% 5.82/6.06 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_two
% 5.82/6.06 thf(fact_2247_zero__less__two,axiom,
% 5.82/6.06 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_two
% 5.82/6.06 thf(fact_2248_zero__less__two,axiom,
% 5.82/6.06 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_two
% 5.82/6.06 thf(fact_2249_zero__less__two,axiom,
% 5.82/6.06 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.82/6.06
% 5.82/6.06 % zero_less_two
% 5.82/6.06 thf(fact_2250_not__sum__squares__lt__zero,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] :
% 5.82/6.06 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real ) ).
% 5.82/6.06
% 5.82/6.06 % not_sum_squares_lt_zero
% 5.82/6.06 thf(fact_2251_not__sum__squares__lt__zero,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] :
% 5.82/6.06 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat ) ).
% 5.82/6.06
% 5.82/6.06 % not_sum_squares_lt_zero
% 5.82/6.06 thf(fact_2252_not__sum__squares__lt__zero,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] :
% 5.82/6.06 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int ) ).
% 5.82/6.06
% 5.82/6.06 % not_sum_squares_lt_zero
% 5.82/6.06 thf(fact_2253_sum__squares__gt__zero__iff,axiom,
% 5.82/6.06 ! [X2: real,Y3: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) )
% 5.82/6.06 = ( ( X2 != zero_zero_real )
% 5.82/6.06 | ( Y3 != zero_zero_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_gt_zero_iff
% 5.82/6.06 thf(fact_2254_sum__squares__gt__zero__iff,axiom,
% 5.82/6.06 ! [X2: rat,Y3: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) )
% 5.82/6.06 = ( ( X2 != zero_zero_rat )
% 5.82/6.06 | ( Y3 != zero_zero_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_gt_zero_iff
% 5.82/6.06 thf(fact_2255_sum__squares__gt__zero__iff,axiom,
% 5.82/6.06 ! [X2: int,Y3: int] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) )
% 5.82/6.06 = ( ( X2 != zero_zero_int )
% 5.82/6.06 | ( Y3 != zero_zero_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % sum_squares_gt_zero_iff
% 5.82/6.06 thf(fact_2256_power__less__imp__less__base,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat,B2: code_integer] :
% 5.82/6.06 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.06 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_less_imp_less_base
% 5.82/6.06 thf(fact_2257_power__less__imp__less__base,axiom,
% 5.82/6.06 ! [A2: real,N: nat,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_less_imp_less_base
% 5.82/6.06 thf(fact_2258_power__less__imp__less__base,axiom,
% 5.82/6.06 ! [A2: rat,N: nat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_less_imp_less_base
% 5.82/6.06 thf(fact_2259_power__less__imp__less__base,axiom,
% 5.82/6.06 ! [A2: nat,N: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_less_imp_less_base
% 5.82/6.06 thf(fact_2260_power__less__imp__less__base,axiom,
% 5.82/6.06 ! [A2: int,N: nat,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_less_imp_less_base
% 5.82/6.06 thf(fact_2261_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.82/6.06 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.06 = ( divide_divide_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.82/6.06 thf(fact_2262_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.82/6.06 ! [C2: int,A2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.82/6.06 thf(fact_2263_power__le__one,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ one_one_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_one
% 5.82/6.06 thf(fact_2264_power__le__one,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ one_one_Code_integer ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_one
% 5.82/6.06 thf(fact_2265_power__le__one,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ one_one_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_one
% 5.82/6.06 thf(fact_2266_power__le__one,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ one_one_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_one
% 5.82/6.06 thf(fact_2267_power__le__one,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ one_one_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_one
% 5.82/6.06 thf(fact_2268_eq__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: complex,C2: complex] :
% 5.82/6.06 ( ( ( numera6690914467698888265omplex @ W )
% 5.82/6.06 = ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( C2 != zero_zero_complex )
% 5.82/6.06 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C2 )
% 5.82/6.06 = B2 ) )
% 5.82/6.06 & ( ( C2 = zero_zero_complex )
% 5.82/6.06 => ( ( numera6690914467698888265omplex @ W )
% 5.82/6.06 = zero_zero_complex ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % eq_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2269_eq__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: real,C2: real] :
% 5.82/6.06 ( ( ( numeral_numeral_real @ W )
% 5.82/6.06 = ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( C2 != zero_zero_real )
% 5.82/6.06 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 )
% 5.82/6.06 = B2 ) )
% 5.82/6.06 & ( ( C2 = zero_zero_real )
% 5.82/6.06 => ( ( numeral_numeral_real @ W )
% 5.82/6.06 = zero_zero_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % eq_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2270_eq__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ( numeral_numeral_rat @ W )
% 5.82/6.06 = ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( C2 != zero_zero_rat )
% 5.82/6.06 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 )
% 5.82/6.06 = B2 ) )
% 5.82/6.06 & ( ( C2 = zero_zero_rat )
% 5.82/6.06 => ( ( numeral_numeral_rat @ W )
% 5.82/6.06 = zero_zero_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % eq_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2271_divide__eq__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: complex,C2: complex,W: num] :
% 5.82/6.06 ( ( ( divide1717551699836669952omplex @ B2 @ C2 )
% 5.82/6.06 = ( numera6690914467698888265omplex @ W ) )
% 5.82/6.06 = ( ( ( C2 != zero_zero_complex )
% 5.82/6.06 => ( B2
% 5.82/6.06 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ( C2 = zero_zero_complex )
% 5.82/6.06 => ( ( numera6690914467698888265omplex @ W )
% 5.82/6.06 = zero_zero_complex ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_eq_eq_numeral(1)
% 5.82/6.06 thf(fact_2272_divide__eq__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: real,C2: real,W: num] :
% 5.82/6.06 ( ( ( divide_divide_real @ B2 @ C2 )
% 5.82/6.06 = ( numeral_numeral_real @ W ) )
% 5.82/6.06 = ( ( ( C2 != zero_zero_real )
% 5.82/6.06 => ( B2
% 5.82/6.06 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ( C2 = zero_zero_real )
% 5.82/6.06 => ( ( numeral_numeral_real @ W )
% 5.82/6.06 = zero_zero_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_eq_eq_numeral(1)
% 5.82/6.06 thf(fact_2273_divide__eq__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: rat,C2: rat,W: num] :
% 5.82/6.06 ( ( ( divide_divide_rat @ B2 @ C2 )
% 5.82/6.06 = ( numeral_numeral_rat @ W ) )
% 5.82/6.06 = ( ( ( C2 != zero_zero_rat )
% 5.82/6.06 => ( B2
% 5.82/6.06 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ( C2 = zero_zero_rat )
% 5.82/6.06 => ( ( numeral_numeral_rat @ W )
% 5.82/6.06 = zero_zero_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_eq_eq_numeral(1)
% 5.82/6.06 thf(fact_2274_power__inject__base,axiom,
% 5.82/6.06 ! [A2: real,N: nat,B2: real] :
% 5.82/6.06 ( ( ( power_power_real @ A2 @ ( suc @ N ) )
% 5.82/6.06 = ( power_power_real @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_inject_base
% 5.82/6.06 thf(fact_2275_power__inject__base,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat,B2: code_integer] :
% 5.82/6.06 ( ( ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) )
% 5.82/6.06 = ( power_8256067586552552935nteger @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.06 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_inject_base
% 5.82/6.06 thf(fact_2276_power__inject__base,axiom,
% 5.82/6.06 ! [A2: rat,N: nat,B2: rat] :
% 5.82/6.06 ( ( ( power_power_rat @ A2 @ ( suc @ N ) )
% 5.82/6.06 = ( power_power_rat @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_inject_base
% 5.82/6.06 thf(fact_2277_power__inject__base,axiom,
% 5.82/6.06 ! [A2: nat,N: nat,B2: nat] :
% 5.82/6.06 ( ( ( power_power_nat @ A2 @ ( suc @ N ) )
% 5.82/6.06 = ( power_power_nat @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_inject_base
% 5.82/6.06 thf(fact_2278_power__inject__base,axiom,
% 5.82/6.06 ! [A2: int,N: nat,B2: int] :
% 5.82/6.06 ( ( ( power_power_int @ A2 @ ( suc @ N ) )
% 5.82/6.06 = ( power_power_int @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_inject_base
% 5.82/6.06 thf(fact_2279_power__le__imp__le__base,axiom,
% 5.82/6.06 ! [A2: real,N: nat,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( power_power_real @ A2 @ ( suc @ N ) ) @ ( power_power_real @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_imp_le_base
% 5.82/6.06 thf(fact_2280_power__le__imp__le__base,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat,B2: code_integer] :
% 5.82/6.06 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_imp_le_base
% 5.82/6.06 thf(fact_2281_power__le__imp__le__base,axiom,
% 5.82/6.06 ! [A2: rat,N: nat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) @ ( power_power_rat @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_imp_le_base
% 5.82/6.06 thf(fact_2282_power__le__imp__le__base,axiom,
% 5.82/6.06 ! [A2: nat,N: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) @ ( power_power_nat @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_imp_le_base
% 5.82/6.06 thf(fact_2283_power__le__imp__le__base,axiom,
% 5.82/6.06 ! [A2: int,N: nat,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( power_power_int @ A2 @ ( suc @ N ) ) @ ( power_power_int @ B2 @ ( suc @ N ) ) )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_le_imp_le_base
% 5.82/6.06 thf(fact_2284_VEBT__internal_OTb_H_Osimps_I1_J,axiom,
% 5.82/6.06 ( ( vEBT_VEBT_Tb2 @ zero_zero_nat )
% 5.82/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % VEBT_internal.Tb'.simps(1)
% 5.82/6.06 thf(fact_2285_div__add__self2,axiom,
% 5.82/6.06 ! [B2: nat,A2: nat] :
% 5.82/6.06 ( ( B2 != zero_zero_nat )
% 5.82/6.06 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.06 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ B2 ) @ one_one_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_add_self2
% 5.82/6.06 thf(fact_2286_div__add__self2,axiom,
% 5.82/6.06 ! [B2: int,A2: int] :
% 5.82/6.06 ( ( B2 != zero_zero_int )
% 5.82/6.06 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.06 = ( plus_plus_int @ ( divide_divide_int @ A2 @ B2 ) @ one_one_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_add_self2
% 5.82/6.06 thf(fact_2287_div__add__self1,axiom,
% 5.82/6.06 ! [B2: nat,A2: nat] :
% 5.82/6.06 ( ( B2 != zero_zero_nat )
% 5.82/6.06 => ( ( divide_divide_nat @ ( plus_plus_nat @ B2 @ A2 ) @ B2 )
% 5.82/6.06 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ B2 ) @ one_one_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_add_self1
% 5.82/6.06 thf(fact_2288_div__add__self1,axiom,
% 5.82/6.06 ! [B2: int,A2: int] :
% 5.82/6.06 ( ( B2 != zero_zero_int )
% 5.82/6.06 => ( ( divide_divide_int @ ( plus_plus_int @ B2 @ A2 ) @ B2 )
% 5.82/6.06 = ( plus_plus_int @ ( divide_divide_int @ A2 @ B2 ) @ one_one_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_add_self1
% 5.82/6.06 thf(fact_2289_numeral__1__eq__Suc__0,axiom,
% 5.82/6.06 ( ( numeral_numeral_nat @ one )
% 5.82/6.06 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.06
% 5.82/6.06 % numeral_1_eq_Suc_0
% 5.82/6.06 thf(fact_2290_num_Osize_I5_J,axiom,
% 5.82/6.06 ! [X22: num] :
% 5.82/6.06 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.82/6.06 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % num.size(5)
% 5.82/6.06 thf(fact_2291_ex__least__nat__less,axiom,
% 5.82/6.06 ! [P: nat > $o,N: nat] :
% 5.82/6.06 ( ( P @ N )
% 5.82/6.06 => ( ~ ( P @ zero_zero_nat )
% 5.82/6.06 => ? [K2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ K2 @ N )
% 5.82/6.06 & ! [I5: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ I5 @ K2 )
% 5.82/6.06 => ~ ( P @ I5 ) )
% 5.82/6.06 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % ex_least_nat_less
% 5.82/6.06 thf(fact_2292_nat__induct__non__zero,axiom,
% 5.82/6.06 ! [N: nat,P: nat > $o] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ( P @ one_one_nat )
% 5.82/6.06 => ( ! [N3: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.06 => ( ( P @ N3 )
% 5.82/6.06 => ( P @ ( suc @ N3 ) ) ) )
% 5.82/6.06 => ( P @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_induct_non_zero
% 5.82/6.06 thf(fact_2293_num_Osize_I6_J,axiom,
% 5.82/6.06 ! [X33: num] :
% 5.82/6.06 ( ( size_size_num @ ( bit1 @ X33 ) )
% 5.82/6.06 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % num.size(6)
% 5.82/6.06 thf(fact_2294_diff__Suc__less,axiom,
% 5.82/6.06 ! [N: nat,I: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.82/6.06
% 5.82/6.06 % diff_Suc_less
% 5.82/6.06 thf(fact_2295_n__less__n__mult__m,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.82/6.06 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % n_less_n_mult_m
% 5.82/6.06 thf(fact_2296_n__less__m__mult__n,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.82/6.06 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % n_less_m_mult_n
% 5.82/6.06 thf(fact_2297_one__less__mult,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.06 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.82/6.06 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_less_mult
% 5.82/6.06 thf(fact_2298_power__gt__expt,axiom,
% 5.82/6.06 ! [N: nat,K: nat] :
% 5.82/6.06 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.06 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_gt_expt
% 5.82/6.06 thf(fact_2299_div__greater__zero__iff,axiom,
% 5.82/6.06 ! [M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.06 = ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_greater_zero_iff
% 5.82/6.06 thf(fact_2300_div__le__mono2,axiom,
% 5.82/6.06 ! [M: nat,N: nat,K: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.06 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.06 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_le_mono2
% 5.82/6.06 thf(fact_2301_nat__diff__split,axiom,
% 5.82/6.06 ! [P: nat > $o,A2: nat,B2: nat] :
% 5.82/6.06 ( ( P @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 => ( P @ zero_zero_nat ) )
% 5.82/6.06 & ! [D3: nat] :
% 5.82/6.06 ( ( A2
% 5.82/6.06 = ( plus_plus_nat @ B2 @ D3 ) )
% 5.82/6.06 => ( P @ D3 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_diff_split
% 5.82/6.06 thf(fact_2302_nat__diff__split__asm,axiom,
% 5.82/6.06 ! [P: nat > $o,A2: nat,B2: nat] :
% 5.82/6.06 ( ( P @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.06 = ( ~ ( ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.06 & ~ ( P @ zero_zero_nat ) )
% 5.82/6.06 | ? [D3: nat] :
% 5.82/6.06 ( ( A2
% 5.82/6.06 = ( plus_plus_nat @ B2 @ D3 ) )
% 5.82/6.06 & ~ ( P @ D3 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_diff_split_asm
% 5.82/6.06 thf(fact_2303_div__less__dividend,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ one_one_nat @ N )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.06 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_less_dividend
% 5.82/6.06 thf(fact_2304_nat__one__le__power,axiom,
% 5.82/6.06 ! [I: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.82/6.06 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_one_le_power
% 5.82/6.06 thf(fact_2305_length__pos__if__in__set,axiom,
% 5.82/6.06 ! [X2: int,Xs: list_int] :
% 5.82/6.06 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % length_pos_if_in_set
% 5.82/6.06 thf(fact_2306_length__pos__if__in__set,axiom,
% 5.82/6.06 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.82/6.06 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % length_pos_if_in_set
% 5.82/6.06 thf(fact_2307_length__pos__if__in__set,axiom,
% 5.82/6.06 ! [X2: real,Xs: list_real] :
% 5.82/6.06 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % length_pos_if_in_set
% 5.82/6.06 thf(fact_2308_length__pos__if__in__set,axiom,
% 5.82/6.06 ! [X2: $o,Xs: list_o] :
% 5.82/6.06 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % length_pos_if_in_set
% 5.82/6.06 thf(fact_2309_length__pos__if__in__set,axiom,
% 5.82/6.06 ! [X2: nat,Xs: list_nat] :
% 5.82/6.06 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % length_pos_if_in_set
% 5.82/6.06 thf(fact_2310_length__pos__if__in__set,axiom,
% 5.82/6.06 ! [X2: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 5.82/6.06 ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.06 => ( ord_less_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % length_pos_if_in_set
% 5.82/6.06 thf(fact_2311_nat__mult__le__cancel1,axiom,
% 5.82/6.06 ! [K: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.06 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_mult_le_cancel1
% 5.82/6.06 thf(fact_2312_nat__mult__div__cancel1,axiom,
% 5.82/6.06 ! [K: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.06 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_mult_div_cancel1
% 5.82/6.06 thf(fact_2313_div__less__iff__less__mult,axiom,
% 5.82/6.06 ! [Q3: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.82/6.06 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 5.82/6.06 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_less_iff_less_mult
% 5.82/6.06 thf(fact_2314_td__gal__lt,axiom,
% 5.82/6.06 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ( ord_less_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.06 = ( ord_less_nat @ ( divide_divide_nat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % td_gal_lt
% 5.82/6.06 thf(fact_2315_vebt__insert_Osimps_I3_J,axiom,
% 5.82/6.06 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ X2 )
% 5.82/6.06 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) ) ).
% 5.82/6.06
% 5.82/6.06 % vebt_insert.simps(3)
% 5.82/6.06 thf(fact_2316_vebt__member_Osimps_I3_J,axiom,
% 5.82/6.06 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 ) ).
% 5.82/6.06
% 5.82/6.06 % vebt_member.simps(3)
% 5.82/6.06 thf(fact_2317_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 5.82/6.06 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) @ X2 )
% 5.82/6.06 = one_one_nat ) ).
% 5.82/6.06
% 5.82/6.06 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 5.82/6.06 thf(fact_2318_VEBT__internal_OTb_H_Osimps_I2_J,axiom,
% 5.82/6.06 ( ( vEBT_VEBT_Tb2 @ ( suc @ zero_zero_nat ) )
% 5.82/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % VEBT_internal.Tb'.simps(2)
% 5.82/6.06 thf(fact_2319_mult__less__cancel__right2,axiom,
% 5.82/6.06 ! [A2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ one_one_real ) )
% 5.82/6.06 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ one_one_real @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right2
% 5.82/6.06 thf(fact_2320_mult__less__cancel__right2,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 5.82/6.06 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right2
% 5.82/6.06 thf(fact_2321_mult__less__cancel__right2,axiom,
% 5.82/6.06 ! [A2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ A2 @ C2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ one_one_int ) )
% 5.82/6.06 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right2
% 5.82/6.06 thf(fact_2322_mult__less__cancel__right1,axiom,
% 5.82/6.06 ! [C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ C2 @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ one_one_real @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ B2 @ one_one_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right1
% 5.82/6.06 thf(fact_2323_mult__less__cancel__right1,axiom,
% 5.82/6.06 ! [C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ one_one_rat @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right1
% 5.82/6.06 thf(fact_2324_mult__less__cancel__right1,axiom,
% 5.82/6.06 ! [C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ C2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ one_one_int @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_right1
% 5.82/6.06 thf(fact_2325_mult__less__cancel__left2,axiom,
% 5.82/6.06 ! [C2: real,A2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( times_times_real @ C2 @ A2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ A2 @ one_one_real ) )
% 5.82/6.06 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ one_one_real @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left2
% 5.82/6.06 thf(fact_2326_mult__less__cancel__left2,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 5.82/6.06 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left2
% 5.82/6.06 thf(fact_2327_mult__less__cancel__left2,axiom,
% 5.82/6.06 ! [C2: int,A2: int] :
% 5.82/6.06 ( ( ord_less_int @ ( times_times_int @ C2 @ A2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ A2 @ one_one_int ) )
% 5.82/6.06 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left2
% 5.82/6.06 thf(fact_2328_mult__less__cancel__left1,axiom,
% 5.82/6.06 ! [C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_real @ C2 @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ one_one_real @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ B2 @ one_one_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left1
% 5.82/6.06 thf(fact_2329_mult__less__cancel__left1,axiom,
% 5.82/6.06 ! [C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ one_one_rat @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left1
% 5.82/6.06 thf(fact_2330_mult__less__cancel__left1,axiom,
% 5.82/6.06 ! [C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_int @ one_one_int @ B2 ) )
% 5.82/6.06 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_less_cancel_left1
% 5.82/6.06 thf(fact_2331_mult__le__cancel__right2,axiom,
% 5.82/6.06 ! [A2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ one_one_real ) )
% 5.82/6.06 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ one_one_real @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right2
% 5.82/6.06 thf(fact_2332_mult__le__cancel__right2,axiom,
% 5.82/6.06 ! [A2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 5.82/6.06 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right2
% 5.82/6.06 thf(fact_2333_mult__le__cancel__right2,axiom,
% 5.82/6.06 ! [A2: int,C2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 5.82/6.06 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right2
% 5.82/6.06 thf(fact_2334_mult__le__cancel__right1,axiom,
% 5.82/6.06 ! [C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ one_one_real @ B2 ) )
% 5.82/6.06 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ B2 @ one_one_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right1
% 5.82/6.06 thf(fact_2335_mult__le__cancel__right1,axiom,
% 5.82/6.06 ! [C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ one_one_rat @ B2 ) )
% 5.82/6.06 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right1
% 5.82/6.06 thf(fact_2336_mult__le__cancel__right1,axiom,
% 5.82/6.06 ! [C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 5.82/6.06 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_right1
% 5.82/6.06 thf(fact_2337_mult__le__cancel__left2,axiom,
% 5.82/6.06 ! [C2: real,A2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ one_one_real ) )
% 5.82/6.06 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ one_one_real @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left2
% 5.82/6.06 thf(fact_2338_mult__le__cancel__left2,axiom,
% 5.82/6.06 ! [C2: rat,A2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 5.82/6.06 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left2
% 5.82/6.06 thf(fact_2339_mult__le__cancel__left2,axiom,
% 5.82/6.06 ! [C2: int,A2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A2 ) @ C2 )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 5.82/6.06 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left2
% 5.82/6.06 thf(fact_2340_mult__le__cancel__left1,axiom,
% 5.82/6.06 ! [C2: real,B2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ one_one_real @ B2 ) )
% 5.82/6.06 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ B2 @ one_one_real ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left1
% 5.82/6.06 thf(fact_2341_mult__le__cancel__left1,axiom,
% 5.82/6.06 ! [C2: rat,B2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ one_one_rat @ B2 ) )
% 5.82/6.06 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left1
% 5.82/6.06 thf(fact_2342_mult__le__cancel__left1,axiom,
% 5.82/6.06 ! [C2: int,B2: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.06 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 5.82/6.06 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 5.82/6.06 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 5.82/6.06 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_le_cancel_left1
% 5.82/6.06 thf(fact_2343_convex__bound__le,axiom,
% 5.82/6.06 ! [X2: real,A2: real,Y3: real,U: real,V: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ X2 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ Y3 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.82/6.06 => ( ( ( plus_plus_real @ U @ V )
% 5.82/6.06 = one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % convex_bound_le
% 5.82/6.06 thf(fact_2344_convex__bound__le,axiom,
% 5.82/6.06 ! [X2: rat,A2: rat,Y3: rat,U: rat,V: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ X2 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ Y3 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.82/6.06 => ( ( ( plus_plus_rat @ U @ V )
% 5.82/6.06 = one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % convex_bound_le
% 5.82/6.06 thf(fact_2345_convex__bound__le,axiom,
% 5.82/6.06 ! [X2: int,A2: int,Y3: int,U: int,V: int] :
% 5.82/6.06 ( ( ord_less_eq_int @ X2 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ Y3 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.82/6.06 => ( ( ( plus_plus_int @ U @ V )
% 5.82/6.06 = one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % convex_bound_le
% 5.82/6.06 thf(fact_2346_less__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % less_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2347_less__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % less_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2348_divide__less__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: real,C2: real,W: num] :
% 5.82/6.06 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C2 ) @ ( numeral_numeral_real @ W ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_less_eq_numeral(1)
% 5.82/6.06 thf(fact_2349_divide__less__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: rat,C2: rat,W: num] :
% 5.82/6.06 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C2 ) @ ( numeral_numeral_rat @ W ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_less_eq_numeral(1)
% 5.82/6.06 thf(fact_2350_power__Suc__less,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer )
% 5.82/6.06 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less
% 5.82/6.06 thf(fact_2351_power__Suc__less,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ord_less_real @ ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less
% 5.82/6.06 thf(fact_2352_power__Suc__less,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_rat @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less
% 5.82/6.06 thf(fact_2353_power__Suc__less,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less
% 5.82/6.06 thf(fact_2354_power__Suc__less,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ord_less_int @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less
% 5.82/6.06 thf(fact_2355_power__Suc__le__self,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( power_power_real @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_le_self
% 5.82/6.06 thf(fact_2356_power__Suc__le__self,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_le_self
% 5.82/6.06 thf(fact_2357_power__Suc__le__self,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_le_self
% 5.82/6.06 thf(fact_2358_power__Suc__le__self,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_le_self
% 5.82/6.06 thf(fact_2359_power__Suc__le__self,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( power_power_int @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_le_self
% 5.82/6.06 thf(fact_2360_power__Suc__less__one,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer )
% 5.82/6.06 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less_one
% 5.82/6.06 thf(fact_2361_power__Suc__less__one,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ord_less_real @ ( power_power_real @ A2 @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less_one
% 5.82/6.06 thf(fact_2362_power__Suc__less__one,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less_one
% 5.82/6.06 thf(fact_2363_power__Suc__less__one,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less_one
% 5.82/6.06 thf(fact_2364_power__Suc__less__one,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ord_less_int @ ( power_power_int @ A2 @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_Suc_less_one
% 5.82/6.06 thf(fact_2365_zero__power2,axiom,
% 5.82/6.06 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.06 = zero_zero_rat ) ).
% 5.82/6.06
% 5.82/6.06 % zero_power2
% 5.82/6.06 thf(fact_2366_zero__power2,axiom,
% 5.82/6.06 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.06 = zero_zero_nat ) ).
% 5.82/6.06
% 5.82/6.06 % zero_power2
% 5.82/6.06 thf(fact_2367_zero__power2,axiom,
% 5.82/6.06 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.06 = zero_zero_real ) ).
% 5.82/6.06
% 5.82/6.06 % zero_power2
% 5.82/6.06 thf(fact_2368_zero__power2,axiom,
% 5.82/6.06 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.06 = zero_zero_int ) ).
% 5.82/6.06
% 5.82/6.06 % zero_power2
% 5.82/6.06 thf(fact_2369_zero__power2,axiom,
% 5.82/6.06 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.06 = zero_zero_complex ) ).
% 5.82/6.06
% 5.82/6.06 % zero_power2
% 5.82/6.06 thf(fact_2370_zero__power2,axiom,
% 5.82/6.06 ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.06 = zero_z3403309356797280102nteger ) ).
% 5.82/6.06
% 5.82/6.06 % zero_power2
% 5.82/6.06 thf(fact_2371_power__strict__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: code_integer] :
% 5.82/6.06 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer )
% 5.82/6.06 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N7 ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_strict_decreasing
% 5.82/6.06 thf(fact_2372_power__strict__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: real] :
% 5.82/6.06 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ord_less_real @ ( power_power_real @ A2 @ N7 ) @ ( power_power_real @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_strict_decreasing
% 5.82/6.06 thf(fact_2373_power__strict__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: rat] :
% 5.82/6.06 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_rat @ ( power_power_rat @ A2 @ N7 ) @ ( power_power_rat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_strict_decreasing
% 5.82/6.06 thf(fact_2374_power__strict__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_nat @ ( power_power_nat @ A2 @ N7 ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_strict_decreasing
% 5.82/6.06 thf(fact_2375_power__strict__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: int] :
% 5.82/6.06 ( ( ord_less_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ord_less_int @ ( power_power_int @ A2 @ N7 ) @ ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_strict_decreasing
% 5.82/6.06 thf(fact_2376_power__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: real] :
% 5.82/6.06 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N7 ) @ ( power_power_real @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_decreasing
% 5.82/6.06 thf(fact_2377_power__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: code_integer] :
% 5.82/6.06 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.06 => ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N7 ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_decreasing
% 5.82/6.06 thf(fact_2378_power__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: rat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N7 ) @ ( power_power_rat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_decreasing
% 5.82/6.06 thf(fact_2379_power__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.82/6.06 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N7 ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_decreasing
% 5.82/6.06 thf(fact_2380_power__decreasing,axiom,
% 5.82/6.06 ! [N: nat,N7: nat,A2: int] :
% 5.82/6.06 ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.82/6.06 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N7 ) @ ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_decreasing
% 5.82/6.06 thf(fact_2381_numeral__2__eq__2,axiom,
% 5.82/6.06 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.06 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % numeral_2_eq_2
% 5.82/6.06 thf(fact_2382_self__le__power,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_real @ one_one_real @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_eq_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % self_le_power
% 5.82/6.06 thf(fact_2383_self__le__power,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_le3102999989581377725nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % self_le_power
% 5.82/6.06 thf(fact_2384_self__le__power,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_eq_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % self_le_power
% 5.82/6.06 thf(fact_2385_self__le__power,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_eq_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % self_le_power
% 5.82/6.06 thf(fact_2386_self__le__power,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_eq_int @ one_one_int @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_eq_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % self_le_power
% 5.82/6.06 thf(fact_2387_pos2,axiom,
% 5.82/6.06 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.82/6.06
% 5.82/6.06 % pos2
% 5.82/6.06 thf(fact_2388_power__diff,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat,M: nat] :
% 5.82/6.06 ( ( A2 != zero_z3403309356797280102nteger )
% 5.82/6.06 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 => ( ( power_8256067586552552935nteger @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.06 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_diff
% 5.82/6.06 thf(fact_2389_power__diff,axiom,
% 5.82/6.06 ! [A2: complex,N: nat,M: nat] :
% 5.82/6.06 ( ( A2 != zero_zero_complex )
% 5.82/6.06 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 => ( ( power_power_complex @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.06 = ( divide1717551699836669952omplex @ ( power_power_complex @ A2 @ M ) @ ( power_power_complex @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_diff
% 5.82/6.06 thf(fact_2390_power__diff,axiom,
% 5.82/6.06 ! [A2: real,N: nat,M: nat] :
% 5.82/6.06 ( ( A2 != zero_zero_real )
% 5.82/6.06 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 => ( ( power_power_real @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.06 = ( divide_divide_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_diff
% 5.82/6.06 thf(fact_2391_power__diff,axiom,
% 5.82/6.06 ! [A2: rat,N: nat,M: nat] :
% 5.82/6.06 ( ( A2 != zero_zero_rat )
% 5.82/6.06 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 => ( ( power_power_rat @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.06 = ( divide_divide_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_diff
% 5.82/6.06 thf(fact_2392_power__diff,axiom,
% 5.82/6.06 ! [A2: nat,N: nat,M: nat] :
% 5.82/6.06 ( ( A2 != zero_zero_nat )
% 5.82/6.06 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 => ( ( power_power_nat @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.06 = ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_diff
% 5.82/6.06 thf(fact_2393_power__diff,axiom,
% 5.82/6.06 ! [A2: int,N: nat,M: nat] :
% 5.82/6.06 ( ( A2 != zero_zero_int )
% 5.82/6.06 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.06 => ( ( power_power_int @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.06 = ( divide_divide_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % power_diff
% 5.82/6.06 thf(fact_2394_one__less__power,axiom,
% 5.82/6.06 ! [A2: code_integer,N: nat] :
% 5.82/6.06 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_less_power
% 5.82/6.06 thf(fact_2395_one__less__power,axiom,
% 5.82/6.06 ! [A2: real,N: nat] :
% 5.82/6.06 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_real @ one_one_real @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_less_power
% 5.82/6.06 thf(fact_2396_one__less__power,axiom,
% 5.82/6.06 ! [A2: rat,N: nat] :
% 5.82/6.06 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_less_power
% 5.82/6.06 thf(fact_2397_one__less__power,axiom,
% 5.82/6.06 ! [A2: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_less_power
% 5.82/6.06 thf(fact_2398_one__less__power,axiom,
% 5.82/6.06 ! [A2: int,N: nat] :
% 5.82/6.06 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.06 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_int @ one_one_int @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % one_less_power
% 5.82/6.06 thf(fact_2399_numeral__3__eq__3,axiom,
% 5.82/6.06 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.06 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % numeral_3_eq_3
% 5.82/6.06 thf(fact_2400_nz__le__conv__less,axiom,
% 5.82/6.06 ! [K: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.06 => ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.06 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nz_le_conv_less
% 5.82/6.06 thf(fact_2401_Suc__diff__eq__diff__pred,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.82/6.06 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % Suc_diff_eq_diff_pred
% 5.82/6.06 thf(fact_2402_Suc__pred_H,axiom,
% 5.82/6.06 ! [N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( N
% 5.82/6.06 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % Suc_pred'
% 5.82/6.06 thf(fact_2403_div__if,axiom,
% 5.82/6.06 ( divide_divide_nat
% 5.82/6.06 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.06 ( if_nat
% 5.82/6.06 @ ( ( ord_less_nat @ M6 @ N4 )
% 5.82/6.06 | ( N4 = zero_zero_nat ) )
% 5.82/6.06 @ zero_zero_nat
% 5.82/6.06 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_if
% 5.82/6.06 thf(fact_2404_div__geq,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ~ ( ord_less_nat @ M @ N )
% 5.82/6.06 => ( ( divide_divide_nat @ M @ N )
% 5.82/6.06 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % div_geq
% 5.82/6.06 thf(fact_2405_add__eq__if,axiom,
% 5.82/6.06 ( plus_plus_nat
% 5.82/6.06 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % add_eq_if
% 5.82/6.06 thf(fact_2406_msrevs_I1_J,axiom,
% 5.82/6.06 ! [N: nat,K: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 5.82/6.06 = ( plus_plus_nat @ ( divide_divide_nat @ M @ N ) @ K ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % msrevs(1)
% 5.82/6.06 thf(fact_2407_dividend__less__times__div,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % dividend_less_times_div
% 5.82/6.06 thf(fact_2408_dividend__less__div__times,axiom,
% 5.82/6.06 ! [N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.06 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % dividend_less_div_times
% 5.82/6.06 thf(fact_2409_split__div,axiom,
% 5.82/6.06 ! [P: nat > $o,M: nat,N: nat] :
% 5.82/6.06 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.06 = ( ( ( N = zero_zero_nat )
% 5.82/6.06 => ( P @ zero_zero_nat ) )
% 5.82/6.06 & ( ( N != zero_zero_nat )
% 5.82/6.06 => ! [I4: nat,J3: nat] :
% 5.82/6.06 ( ( ord_less_nat @ J3 @ N )
% 5.82/6.06 => ( ( M
% 5.82/6.06 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.82/6.06 => ( P @ I4 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % split_div
% 5.82/6.06 thf(fact_2410_less__eq__div__iff__mult__less__eq,axiom,
% 5.82/6.06 ! [Q3: nat,M: nat,N: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 5.82/6.06 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % less_eq_div_iff_mult_less_eq
% 5.82/6.06 thf(fact_2411_td__gal,axiom,
% 5.82/6.06 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.06 => ( ( ord_less_eq_nat @ ( times_times_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.06 = ( ord_less_eq_nat @ B2 @ ( divide_divide_nat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % td_gal
% 5.82/6.06 thf(fact_2412_mult__eq__if,axiom,
% 5.82/6.06 ( times_times_nat
% 5.82/6.06 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % mult_eq_if
% 5.82/6.06 thf(fact_2413_nat__mult__power__less__eq,axiom,
% 5.82/6.06 ! [B2: nat,A2: nat,N: nat,M: nat] :
% 5.82/6.06 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.06 => ( ( ord_less_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ B2 @ N ) ) @ ( power_power_nat @ B2 @ M ) )
% 5.82/6.06 = ( ord_less_nat @ A2 @ ( power_power_nat @ B2 @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % nat_mult_power_less_eq
% 5.82/6.06 thf(fact_2414_vebt__delete_Osimps_I5_J,axiom,
% 5.82/6.06 ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X2 )
% 5.82/6.06 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 5.82/6.06
% 5.82/6.06 % vebt_delete.simps(5)
% 5.82/6.06 thf(fact_2415_vebt__member_Osimps_I4_J,axiom,
% 5.82/6.06 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 ) ).
% 5.82/6.06
% 5.82/6.06 % vebt_member.simps(4)
% 5.82/6.06 thf(fact_2416_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 5.82/6.06 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.06 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ X2 )
% 5.82/6.06 = one_one_nat ) ).
% 5.82/6.06
% 5.82/6.06 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 5.82/6.06 thf(fact_2417_convex__bound__lt,axiom,
% 5.82/6.06 ! [X2: real,A2: real,Y3: real,U: real,V: real] :
% 5.82/6.06 ( ( ord_less_real @ X2 @ A2 )
% 5.82/6.06 => ( ( ord_less_real @ Y3 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.82/6.06 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.82/6.06 => ( ( ( plus_plus_real @ U @ V )
% 5.82/6.06 = one_one_real )
% 5.82/6.06 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % convex_bound_lt
% 5.82/6.06 thf(fact_2418_convex__bound__lt,axiom,
% 5.82/6.06 ! [X2: rat,A2: rat,Y3: rat,U: rat,V: rat] :
% 5.82/6.06 ( ( ord_less_rat @ X2 @ A2 )
% 5.82/6.06 => ( ( ord_less_rat @ Y3 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.82/6.06 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.82/6.06 => ( ( ( plus_plus_rat @ U @ V )
% 5.82/6.06 = one_one_rat )
% 5.82/6.06 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % convex_bound_lt
% 5.82/6.06 thf(fact_2419_convex__bound__lt,axiom,
% 5.82/6.06 ! [X2: int,A2: int,Y3: int,U: int,V: int] :
% 5.82/6.06 ( ( ord_less_int @ X2 @ A2 )
% 5.82/6.06 => ( ( ord_less_int @ Y3 @ A2 )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.82/6.06 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.82/6.06 => ( ( ( plus_plus_int @ U @ V )
% 5.82/6.06 = one_one_int )
% 5.82/6.06 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % convex_bound_lt
% 5.82/6.06 thf(fact_2420_le__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: real,C2: real] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % le_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2421_le__divide__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [W: num,B2: rat,C2: rat] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % le_divide_eq_numeral(1)
% 5.82/6.06 thf(fact_2422_divide__le__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: real,C2: real,W: num] :
% 5.82/6.06 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C2 ) @ ( numeral_numeral_real @ W ) )
% 5.82/6.06 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.06 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_le_eq_numeral(1)
% 5.82/6.06 thf(fact_2423_divide__le__eq__numeral_I1_J,axiom,
% 5.82/6.06 ! [B2: rat,C2: rat,W: num] :
% 5.82/6.06 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C2 ) @ ( numeral_numeral_rat @ W ) )
% 5.82/6.06 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.06 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C2 ) @ B2 ) )
% 5.82/6.06 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.82/6.06
% 5.82/6.06 % divide_le_eq_numeral(1)
% 5.82/6.06 thf(fact_2424_half__gt__zero__iff,axiom,
% 5.82/6.06 ! [A2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.06 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.06
% 5.82/6.06 % half_gt_zero_iff
% 5.82/6.06 thf(fact_2425_half__gt__zero__iff,axiom,
% 5.82/6.06 ! [A2: rat] :
% 5.82/6.06 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.82/6.06 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.06
% 5.82/6.06 % half_gt_zero_iff
% 5.82/6.06 thf(fact_2426_half__gt__zero,axiom,
% 5.82/6.06 ! [A2: real] :
% 5.82/6.06 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.06 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % half_gt_zero
% 5.82/6.07 thf(fact_2427_half__gt__zero,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % half_gt_zero
% 5.82/6.07 thf(fact_2428_power2__le__imp__le,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_le_imp_le
% 5.82/6.07 thf(fact_2429_power2__le__imp__le,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.07 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 5.82/6.07 => ( ord_le3102999989581377725nteger @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_le_imp_le
% 5.82/6.07 thf(fact_2430_power2__le__imp__le,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_le_imp_le
% 5.82/6.07 thf(fact_2431_power2__le__imp__le,axiom,
% 5.82/6.07 ! [X2: nat,Y3: nat] :
% 5.82/6.07 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_le_imp_le
% 5.82/6.07 thf(fact_2432_power2__le__imp__le,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.07 => ( ord_less_eq_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_le_imp_le
% 5.82/6.07 thf(fact_2433_power2__eq__imp__eq,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( X2 = Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_eq_imp_eq
% 5.82/6.07 thf(fact_2434_power2__eq__imp__eq,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.07 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.82/6.07 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 5.82/6.07 => ( X2 = Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_eq_imp_eq
% 5.82/6.07 thf(fact_2435_power2__eq__imp__eq,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( X2 = Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_eq_imp_eq
% 5.82/6.07 thf(fact_2436_power2__eq__imp__eq,axiom,
% 5.82/6.07 ! [X2: nat,Y3: nat] :
% 5.82/6.07 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.82/6.07 => ( X2 = Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_eq_imp_eq
% 5.82/6.07 thf(fact_2437_power2__eq__imp__eq,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] :
% 5.82/6.07 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.07 => ( X2 = Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_eq_imp_eq
% 5.82/6.07 thf(fact_2438_zero__le__power2,axiom,
% 5.82/6.07 ! [A2: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_power2
% 5.82/6.07 thf(fact_2439_zero__le__power2,axiom,
% 5.82/6.07 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_power2
% 5.82/6.07 thf(fact_2440_zero__le__power2,axiom,
% 5.82/6.07 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_power2
% 5.82/6.07 thf(fact_2441_zero__le__power2,axiom,
% 5.82/6.07 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_power2
% 5.82/6.07 thf(fact_2442_power2__less__0,axiom,
% 5.82/6.07 ! [A2: code_integer] :
% 5.82/6.07 ~ ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_0
% 5.82/6.07 thf(fact_2443_power2__less__0,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ~ ( ord_less_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_0
% 5.82/6.07 thf(fact_2444_power2__less__0,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ~ ( ord_less_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_0
% 5.82/6.07 thf(fact_2445_power2__less__0,axiom,
% 5.82/6.07 ! [A2: int] :
% 5.82/6.07 ~ ( ord_less_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_0
% 5.82/6.07 thf(fact_2446_exp__add__not__zero__imp__right,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.07 != zero_z3403309356797280102nteger )
% 5.82/6.07 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.82/6.07 != zero_z3403309356797280102nteger ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_add_not_zero_imp_right
% 5.82/6.07 thf(fact_2447_exp__add__not__zero__imp__right,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.07 != zero_zero_nat )
% 5.82/6.07 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.07 != zero_zero_nat ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_add_not_zero_imp_right
% 5.82/6.07 thf(fact_2448_exp__add__not__zero__imp__right,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.07 != zero_zero_int )
% 5.82/6.07 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.07 != zero_zero_int ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_add_not_zero_imp_right
% 5.82/6.07 thf(fact_2449_exp__add__not__zero__imp__left,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.07 != zero_z3403309356797280102nteger )
% 5.82/6.07 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.82/6.07 != zero_z3403309356797280102nteger ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_add_not_zero_imp_left
% 5.82/6.07 thf(fact_2450_exp__add__not__zero__imp__left,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.07 != zero_zero_nat )
% 5.82/6.07 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.82/6.07 != zero_zero_nat ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_add_not_zero_imp_left
% 5.82/6.07 thf(fact_2451_exp__add__not__zero__imp__left,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.82/6.07 != zero_zero_int )
% 5.82/6.07 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.82/6.07 != zero_zero_int ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_add_not_zero_imp_left
% 5.82/6.07 thf(fact_2452_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.82/6.07 != zero_z3403309356797280102nteger )
% 5.82/6.07 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.07 != zero_z3403309356797280102nteger ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_not_zero_imp_exp_diff_not_zero
% 5.82/6.07 thf(fact_2453_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.07 != zero_zero_nat )
% 5.82/6.07 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.07 != zero_zero_nat ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_not_zero_imp_exp_diff_not_zero
% 5.82/6.07 thf(fact_2454_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.07 != zero_zero_int )
% 5.82/6.07 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.07 != zero_zero_int ) ) ).
% 5.82/6.07
% 5.82/6.07 % exp_not_zero_imp_exp_diff_not_zero
% 5.82/6.07 thf(fact_2455_power__diff__power__eq,axiom,
% 5.82/6.07 ! [A2: code_integer,N: nat,M: nat] :
% 5.82/6.07 ( ( A2 != zero_z3403309356797280102nteger )
% 5.82/6.07 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.07 = ( power_8256067586552552935nteger @ A2 @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.82/6.07 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.07 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_diff_power_eq
% 5.82/6.07 thf(fact_2456_power__diff__power__eq,axiom,
% 5.82/6.07 ! [A2: nat,N: nat,M: nat] :
% 5.82/6.07 ( ( A2 != zero_zero_nat )
% 5.82/6.07 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.82/6.07 = ( power_power_nat @ A2 @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.82/6.07 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.82/6.07 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_diff_power_eq
% 5.82/6.07 thf(fact_2457_power__diff__power__eq,axiom,
% 5.82/6.07 ! [A2: int,N: nat,M: nat] :
% 5.82/6.07 ( ( A2 != zero_zero_int )
% 5.82/6.07 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide_divide_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.82/6.07 = ( power_power_int @ A2 @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.82/6.07 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide_divide_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.82/6.07 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_diff_power_eq
% 5.82/6.07 thf(fact_2458_less__2__cases__iff,axiom,
% 5.82/6.07 ! [N: nat] :
% 5.82/6.07 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( ( N = zero_zero_nat )
% 5.82/6.07 | ( N
% 5.82/6.07 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_2_cases_iff
% 5.82/6.07 thf(fact_2459_less__2__cases,axiom,
% 5.82/6.07 ! [N: nat] :
% 5.82/6.07 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 => ( ( N = zero_zero_nat )
% 5.82/6.07 | ( N
% 5.82/6.07 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_2_cases
% 5.82/6.07 thf(fact_2460_inverse__of__nat__le,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( N != zero_zero_nat )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % inverse_of_nat_le
% 5.82/6.07 thf(fact_2461_inverse__of__nat__le,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( N != zero_zero_nat )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % inverse_of_nat_le
% 5.82/6.07 thf(fact_2462_power__eq__if,axiom,
% 5.82/6.07 ( power_power_assn
% 5.82/6.07 = ( ^ [P4: assn,M6: nat] : ( if_assn @ ( M6 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P4 @ ( power_power_assn @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2463_power__eq__if,axiom,
% 5.82/6.07 ( power_power_complex
% 5.82/6.07 = ( ^ [P4: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P4 @ ( power_power_complex @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2464_power__eq__if,axiom,
% 5.82/6.07 ( power_8256067586552552935nteger
% 5.82/6.07 = ( ^ [P4: code_integer,M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P4 @ ( power_8256067586552552935nteger @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2465_power__eq__if,axiom,
% 5.82/6.07 ( power_power_real
% 5.82/6.07 = ( ^ [P4: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P4 @ ( power_power_real @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2466_power__eq__if,axiom,
% 5.82/6.07 ( power_power_rat
% 5.82/6.07 = ( ^ [P4: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P4 @ ( power_power_rat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2467_power__eq__if,axiom,
% 5.82/6.07 ( power_power_nat
% 5.82/6.07 = ( ^ [P4: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P4 @ ( power_power_nat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2468_power__eq__if,axiom,
% 5.82/6.07 ( power_power_int
% 5.82/6.07 = ( ^ [P4: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P4 @ ( power_power_int @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_eq_if
% 5.82/6.07 thf(fact_2469_power__minus__mult,axiom,
% 5.82/6.07 ! [N: nat,A2: complex] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( times_times_complex @ ( power_power_complex @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.82/6.07 = ( power_power_complex @ A2 @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_minus_mult
% 5.82/6.07 thf(fact_2470_power__minus__mult,axiom,
% 5.82/6.07 ! [N: nat,A2: code_integer] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.82/6.07 = ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_minus_mult
% 5.82/6.07 thf(fact_2471_power__minus__mult,axiom,
% 5.82/6.07 ! [N: nat,A2: real] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( times_times_real @ ( power_power_real @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.82/6.07 = ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_minus_mult
% 5.82/6.07 thf(fact_2472_power__minus__mult,axiom,
% 5.82/6.07 ! [N: nat,A2: rat] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( times_times_rat @ ( power_power_rat @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.82/6.07 = ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_minus_mult
% 5.82/6.07 thf(fact_2473_power__minus__mult,axiom,
% 5.82/6.07 ! [N: nat,A2: nat] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( times_times_nat @ ( power_power_nat @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.82/6.07 = ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_minus_mult
% 5.82/6.07 thf(fact_2474_power__minus__mult,axiom,
% 5.82/6.07 ! [N: nat,A2: int] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( times_times_int @ ( power_power_int @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.82/6.07 = ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_minus_mult
% 5.82/6.07 thf(fact_2475_le__div__geq,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( divide_divide_nat @ M @ N )
% 5.82/6.07 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % le_div_geq
% 5.82/6.07 thf(fact_2476_split__div_H,axiom,
% 5.82/6.07 ! [P: nat > $o,M: nat,N: nat] :
% 5.82/6.07 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.07 = ( ( ( N = zero_zero_nat )
% 5.82/6.07 & ( P @ zero_zero_nat ) )
% 5.82/6.07 | ? [Q5: nat] :
% 5.82/6.07 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M )
% 5.82/6.07 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 5.82/6.07 & ( P @ Q5 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % split_div'
% 5.82/6.07 thf(fact_2477_power__sub,axiom,
% 5.82/6.07 ! [N: nat,M: nat,A2: nat] :
% 5.82/6.07 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.07 => ( ( power_power_nat @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.07 = ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power_sub
% 5.82/6.07 thf(fact_2478_vebt__delete_Osimps_I6_J,axiom,
% 5.82/6.07 ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X2 )
% 5.82/6.07 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 5.82/6.07
% 5.82/6.07 % vebt_delete.simps(6)
% 5.82/6.07 thf(fact_2479_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,
% 5.82/6.07 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X2 )
% 5.82/6.07 = one_one_nat ) ).
% 5.82/6.07
% 5.82/6.07 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(5)
% 5.82/6.07 thf(fact_2480_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,
% 5.82/6.07 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X2 )
% 5.82/6.07 = one_one_nat ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(5)
% 5.82/6.07 thf(fact_2481_power2__less__imp__less,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.07 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 5.82/6.07 => ( ord_le6747313008572928689nteger @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_imp_less
% 5.82/6.07 thf(fact_2482_power2__less__imp__less,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_imp_less
% 5.82/6.07 thf(fact_2483_power2__less__imp__less,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_imp_less
% 5.82/6.07 thf(fact_2484_power2__less__imp__less,axiom,
% 5.82/6.07 ! [X2: nat,Y3: nat] :
% 5.82/6.07 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.82/6.07 => ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_imp_less
% 5.82/6.07 thf(fact_2485_power2__less__imp__less,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] :
% 5.82/6.07 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.07 => ( ord_less_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % power2_less_imp_less
% 5.82/6.07 thf(fact_2486_sum__power2__le__zero__iff,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.82/6.07 = ( ( X2 = zero_zero_real )
% 5.82/6.07 & ( Y3 = zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_le_zero_iff
% 5.82/6.07 thf(fact_2487_sum__power2__le__zero__iff,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.07 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger )
% 5.82/6.07 = ( ( X2 = zero_z3403309356797280102nteger )
% 5.82/6.07 & ( Y3 = zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_le_zero_iff
% 5.82/6.07 thf(fact_2488_sum__power2__le__zero__iff,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.82/6.07 = ( ( X2 = zero_zero_rat )
% 5.82/6.07 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_le_zero_iff
% 5.82/6.07 thf(fact_2489_sum__power2__le__zero__iff,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.82/6.07 = ( ( X2 = zero_zero_int )
% 5.82/6.07 & ( Y3 = zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_le_zero_iff
% 5.82/6.07 thf(fact_2490_sum__power2__ge__zero,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_ge_zero
% 5.82/6.07 thf(fact_2491_sum__power2__ge__zero,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_ge_zero
% 5.82/6.07 thf(fact_2492_sum__power2__ge__zero,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_ge_zero
% 5.82/6.07 thf(fact_2493_sum__power2__ge__zero,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_ge_zero
% 5.82/6.07 thf(fact_2494_sum__power2__gt__zero__iff,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.07 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.07 = ( ( X2 != zero_z3403309356797280102nteger )
% 5.82/6.07 | ( Y3 != zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_gt_zero_iff
% 5.82/6.07 thf(fact_2495_sum__power2__gt__zero__iff,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.07 = ( ( X2 != zero_zero_real )
% 5.82/6.07 | ( Y3 != zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_gt_zero_iff
% 5.82/6.07 thf(fact_2496_sum__power2__gt__zero__iff,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.07 = ( ( X2 != zero_zero_rat )
% 5.82/6.07 | ( Y3 != zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_gt_zero_iff
% 5.82/6.07 thf(fact_2497_sum__power2__gt__zero__iff,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.07 = ( ( X2 != zero_zero_int )
% 5.82/6.07 | ( Y3 != zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % sum_power2_gt_zero_iff
% 5.82/6.07 thf(fact_2498_not__sum__power2__lt__zero,axiom,
% 5.82/6.07 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.07 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger ) ).
% 5.82/6.07
% 5.82/6.07 % not_sum_power2_lt_zero
% 5.82/6.07 thf(fact_2499_not__sum__power2__lt__zero,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.82/6.07
% 5.82/6.07 % not_sum_power2_lt_zero
% 5.82/6.07 thf(fact_2500_not__sum__power2__lt__zero,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.82/6.07
% 5.82/6.07 % not_sum_power2_lt_zero
% 5.82/6.07 thf(fact_2501_not__sum__power2__lt__zero,axiom,
% 5.82/6.07 ! [X2: int,Y3: int] :
% 5.82/6.07 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.82/6.07
% 5.82/6.07 % not_sum_power2_lt_zero
% 5.82/6.07 thf(fact_2502_zero__le__even__power_H,axiom,
% 5.82/6.07 ! [A2: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_even_power'
% 5.82/6.07 thf(fact_2503_zero__le__even__power_H,axiom,
% 5.82/6.07 ! [A2: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_even_power'
% 5.82/6.07 thf(fact_2504_zero__le__even__power_H,axiom,
% 5.82/6.07 ! [A2: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_even_power'
% 5.82/6.07 thf(fact_2505_zero__le__even__power_H,axiom,
% 5.82/6.07 ! [A2: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_even_power'
% 5.82/6.07 thf(fact_2506_Suc__n__div__2__gt__zero,axiom,
% 5.82/6.07 ! [N: nat] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % Suc_n_div_2_gt_zero
% 5.82/6.07 thf(fact_2507_div__2__gt__zero,axiom,
% 5.82/6.07 ! [N: nat] :
% 5.82/6.07 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.07 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_2_gt_zero
% 5.82/6.07 thf(fact_2508_nat__bit__induct,axiom,
% 5.82/6.07 ! [P: nat > $o,N: nat] :
% 5.82/6.07 ( ( P @ zero_zero_nat )
% 5.82/6.07 => ( ! [N3: nat] :
% 5.82/6.07 ( ( P @ N3 )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.07 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.82/6.07 => ( ! [N3: nat] :
% 5.82/6.07 ( ( P @ N3 )
% 5.82/6.07 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.82/6.07 => ( P @ N ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nat_bit_induct
% 5.82/6.07 thf(fact_2509_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 5.82/6.07 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.82/6.07 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 5.82/6.07 thf(fact_2510_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,
% 5.82/6.07 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.07 = one_one_nat ) ).
% 5.82/6.07
% 5.82/6.07 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(6)
% 5.82/6.07 thf(fact_2511_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,
% 5.82/6.07 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.07 = one_one_nat ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(6)
% 5.82/6.07 thf(fact_2512_odd__0__le__power__imp__0__le,axiom,
% 5.82/6.07 ! [A2: real,N: nat] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.07 => ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_0_le_power_imp_0_le
% 5.82/6.07 thf(fact_2513_odd__0__le__power__imp__0__le,axiom,
% 5.82/6.07 ! [A2: code_integer,N: nat] :
% 5.82/6.07 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.07 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_0_le_power_imp_0_le
% 5.82/6.07 thf(fact_2514_odd__0__le__power__imp__0__le,axiom,
% 5.82/6.07 ! [A2: rat,N: nat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.07 => ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_0_le_power_imp_0_le
% 5.82/6.07 thf(fact_2515_odd__0__le__power__imp__0__le,axiom,
% 5.82/6.07 ! [A2: int,N: nat] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.07 => ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_0_le_power_imp_0_le
% 5.82/6.07 thf(fact_2516_odd__power__less__zero,axiom,
% 5.82/6.07 ! [A2: code_integer,N: nat] :
% 5.82/6.07 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 5.82/6.07 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_z3403309356797280102nteger ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_power_less_zero
% 5.82/6.07 thf(fact_2517_odd__power__less__zero,axiom,
% 5.82/6.07 ! [A2: real,N: nat] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ ( power_power_real @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_power_less_zero
% 5.82/6.07 thf(fact_2518_odd__power__less__zero,axiom,
% 5.82/6.07 ! [A2: rat,N: nat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ ( power_power_rat @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_power_less_zero
% 5.82/6.07 thf(fact_2519_odd__power__less__zero,axiom,
% 5.82/6.07 ! [A2: int,N: nat] :
% 5.82/6.07 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.07 => ( ord_less_int @ ( power_power_int @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_power_less_zero
% 5.82/6.07 thf(fact_2520_VEBTi_Oexhaust,axiom,
% 5.82/6.07 ! [Y3: vEBT_VEBTi] :
% 5.82/6.07 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: array_VEBT_VEBTi,X142: vEBT_VEBTi] :
% 5.82/6.07 ( Y3
% 5.82/6.07 != ( vEBT_Nodei @ X112 @ X122 @ X132 @ X142 ) )
% 5.82/6.07 => ~ ! [X212: $o,X223: $o] :
% 5.82/6.07 ( Y3
% 5.82/6.07 != ( vEBT_Leafi @ X212 @ X223 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBTi.exhaust
% 5.82/6.07 thf(fact_2521_VEBTi_Odistinct_I1_J,axiom,
% 5.82/6.07 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,X21: $o,X222: $o] :
% 5.82/6.07 ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 5.82/6.07 != ( vEBT_Leafi @ X21 @ X222 ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBTi.distinct(1)
% 5.82/6.07 thf(fact_2522_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.82/6.07 ! [X2: nat,N: nat,M: nat] :
% 5.82/6.07 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.07 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.exp_split_high_low(1)
% 5.82/6.07 thf(fact_2523_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.82/6.07 ! [X2: nat,N: nat,M: nat] :
% 5.82/6.07 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.07 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.exp_split_high_low(2)
% 5.82/6.07 thf(fact_2524_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 5.82/6.07 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.82/6.07 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.82/6.07 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 5.82/6.07 thf(fact_2525_nat__div__eq__Suc__0__iff,axiom,
% 5.82/6.07 ! [N: nat,M: nat] :
% 5.82/6.07 ( ( ( divide_divide_nat @ N @ M )
% 5.82/6.07 = ( suc @ zero_zero_nat ) )
% 5.82/6.07 = ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.07 & ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nat_div_eq_Suc_0_iff
% 5.82/6.07 thf(fact_2526_arith__geo__mean,axiom,
% 5.82/6.07 ! [U: real,X2: real,Y3: real] :
% 5.82/6.07 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( times_times_real @ X2 @ Y3 ) )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % arith_geo_mean
% 5.82/6.07 thf(fact_2527_arith__geo__mean,axiom,
% 5.82/6.07 ! [U: rat,X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.07 = ( times_times_rat @ X2 @ Y3 ) )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % arith_geo_mean
% 5.82/6.07 thf(fact_2528_member__bound__size__univ,axiom,
% 5.82/6.07 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.07 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.07 => ( ( U
% 5.82/6.07 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.07 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % member_bound_size_univ
% 5.82/6.07 thf(fact_2529_VEBT__internal_OminNulli_Ocases,axiom,
% 5.82/6.07 ! [X2: vEBT_VEBTi] :
% 5.82/6.07 ( ( X2
% 5.82/6.07 != ( vEBT_Leafi @ $false @ $false ) )
% 5.82/6.07 => ( ! [Uv2: $o] :
% 5.82/6.07 ( X2
% 5.82/6.07 != ( vEBT_Leafi @ $true @ Uv2 ) )
% 5.82/6.07 => ( ! [Uu2: $o] :
% 5.82/6.07 ( X2
% 5.82/6.07 != ( vEBT_Leafi @ Uu2 @ $true ) )
% 5.82/6.07 => ( ! [Uw2: nat,Ux2: array_VEBT_VEBTi,Uy2: vEBT_VEBTi] :
% 5.82/6.07 ( X2
% 5.82/6.07 != ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.07 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: array_VEBT_VEBTi,Vc2: vEBT_VEBTi] :
% 5.82/6.07 ( X2
% 5.82/6.07 != ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.minNulli.cases
% 5.82/6.07 thf(fact_2530_Tb__T__vebt__buildupi,axiom,
% 5.82/6.07 ! [N: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( vEBT_V441764108873111860ildupi @ N ) ) @ ( minus_minus_int @ ( vEBT_VEBT_Tb @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % Tb_T_vebt_buildupi
% 5.82/6.07 thf(fact_2531_le__divide__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % le_divide_eq_1_pos
% 5.82/6.07 thf(fact_2532_le__divide__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % le_divide_eq_1_pos
% 5.82/6.07 thf(fact_2533_le__divide__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_eq_real @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % le_divide_eq_1_neg
% 5.82/6.07 thf(fact_2534_le__divide__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_eq_rat @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % le_divide_eq_1_neg
% 5.82/6.07 thf(fact_2535_divide__le__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A2 ) @ one_one_real )
% 5.82/6.07 = ( ord_less_eq_real @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_eq_1_pos
% 5.82/6.07 thf(fact_2536_divide__le__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ A2 ) @ one_one_rat )
% 5.82/6.07 = ( ord_less_eq_rat @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_eq_1_pos
% 5.82/6.07 thf(fact_2537_divide__le__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A2 ) @ one_one_real )
% 5.82/6.07 = ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_eq_1_neg
% 5.82/6.07 thf(fact_2538_divide__le__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ A2 ) @ one_one_rat )
% 5.82/6.07 = ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_eq_1_neg
% 5.82/6.07 thf(fact_2539_log2__of__power__le,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.07 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log2_of_power_le
% 5.82/6.07 thf(fact_2540_log2__of__power__less,axiom,
% 5.82/6.07 ! [M: nat,N: nat] :
% 5.82/6.07 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.07 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.07 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log2_of_power_less
% 5.82/6.07 thf(fact_2541_TBOUND__minNulli,axiom,
% 5.82/6.07 ! [T: vEBT_VEBTi] : ( time_TBOUND_o @ ( vEBT_VEBT_minNulli @ T ) @ one_one_nat ) ).
% 5.82/6.07
% 5.82/6.07 % TBOUND_minNulli
% 5.82/6.07 thf(fact_2542_nonzero__divide__mult__cancel__right,axiom,
% 5.82/6.07 ! [B2: complex,A2: complex] :
% 5.82/6.07 ( ( B2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ B2 @ ( times_times_complex @ A2 @ B2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ one_one_complex @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_mult_cancel_right
% 5.82/6.07 thf(fact_2543_nonzero__divide__mult__cancel__right,axiom,
% 5.82/6.07 ! [B2: real,A2: real] :
% 5.82/6.07 ( ( B2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ B2 @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_real @ one_one_real @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_mult_cancel_right
% 5.82/6.07 thf(fact_2544_nonzero__divide__mult__cancel__right,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat] :
% 5.82/6.07 ( ( B2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ B2 @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_rat @ one_one_rat @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_mult_cancel_right
% 5.82/6.07 thf(fact_2545_nonzero__divide__mult__cancel__left,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex] :
% 5.82/6.07 ( ( A2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ A2 @ ( times_times_complex @ A2 @ B2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ one_one_complex @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_mult_cancel_left
% 5.82/6.07 thf(fact_2546_nonzero__divide__mult__cancel__left,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( A2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ A2 @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_real @ one_one_real @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_mult_cancel_left
% 5.82/6.07 thf(fact_2547_nonzero__divide__mult__cancel__left,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( A2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ A2 @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_rat @ one_one_rat @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_mult_cancel_left
% 5.82/6.07 thf(fact_2548_cnt__non__neg,axiom,
% 5.82/6.07 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ zero_zero_real @ ( vEBT_VEBT_cnt @ T ) ) ).
% 5.82/6.07
% 5.82/6.07 % cnt_non_neg
% 5.82/6.07 thf(fact_2549_Tb__Tb_H,axiom,
% 5.82/6.07 ( vEBT_VEBT_Tb
% 5.82/6.07 = ( ^ [T2: nat] : ( semiri1314217659103216013at_int @ ( vEBT_VEBT_Tb2 @ T2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % Tb_Tb'
% 5.82/6.07 thf(fact_2550_i0__less,axiom,
% 5.82/6.07 ! [N: extended_enat] :
% 5.82/6.07 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.82/6.07 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.82/6.07
% 5.82/6.07 % i0_less
% 5.82/6.07 thf(fact_2551_idiff__0,axiom,
% 5.82/6.07 ! [N: extended_enat] :
% 5.82/6.07 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.82/6.07 = zero_z5237406670263579293d_enat ) ).
% 5.82/6.07
% 5.82/6.07 % idiff_0
% 5.82/6.07 thf(fact_2552_idiff__0__right,axiom,
% 5.82/6.07 ! [N: extended_enat] :
% 5.82/6.07 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.82/6.07 = N ) ).
% 5.82/6.07
% 5.82/6.07 % idiff_0_right
% 5.82/6.07 thf(fact_2553_divide__eq__0__iff,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex] :
% 5.82/6.07 ( ( ( divide1717551699836669952omplex @ A2 @ B2 )
% 5.82/6.07 = zero_zero_complex )
% 5.82/6.07 = ( ( A2 = zero_zero_complex )
% 5.82/6.07 | ( B2 = zero_zero_complex ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_0_iff
% 5.82/6.07 thf(fact_2554_divide__eq__0__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ A2 @ B2 )
% 5.82/6.07 = zero_zero_real )
% 5.82/6.07 = ( ( A2 = zero_zero_real )
% 5.82/6.07 | ( B2 = zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_0_iff
% 5.82/6.07 thf(fact_2555_divide__eq__0__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ A2 @ B2 )
% 5.82/6.07 = zero_zero_rat )
% 5.82/6.07 = ( ( A2 = zero_zero_rat )
% 5.82/6.07 | ( B2 = zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_0_iff
% 5.82/6.07 thf(fact_2556_divide__cancel__left,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( ( divide1717551699836669952omplex @ C2 @ A2 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ C2 @ B2 ) )
% 5.82/6.07 = ( ( C2 = zero_zero_complex )
% 5.82/6.07 | ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_cancel_left
% 5.82/6.07 thf(fact_2557_divide__cancel__left,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ C2 @ A2 )
% 5.82/6.07 = ( divide_divide_real @ C2 @ B2 ) )
% 5.82/6.07 = ( ( C2 = zero_zero_real )
% 5.82/6.07 | ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_cancel_left
% 5.82/6.07 thf(fact_2558_divide__cancel__left,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ C2 @ A2 )
% 5.82/6.07 = ( divide_divide_rat @ C2 @ B2 ) )
% 5.82/6.07 = ( ( C2 = zero_zero_rat )
% 5.82/6.07 | ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_cancel_left
% 5.82/6.07 thf(fact_2559_divide__cancel__right,axiom,
% 5.82/6.07 ! [A2: complex,C2: complex,B2: complex] :
% 5.82/6.07 ( ( ( divide1717551699836669952omplex @ A2 @ C2 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.07 = ( ( C2 = zero_zero_complex )
% 5.82/6.07 | ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_cancel_right
% 5.82/6.07 thf(fact_2560_divide__cancel__right,axiom,
% 5.82/6.07 ! [A2: real,C2: real,B2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ A2 @ C2 )
% 5.82/6.07 = ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ( C2 = zero_zero_real )
% 5.82/6.07 | ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_cancel_right
% 5.82/6.07 thf(fact_2561_divide__cancel__right,axiom,
% 5.82/6.07 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ A2 @ C2 )
% 5.82/6.07 = ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ( C2 = zero_zero_rat )
% 5.82/6.07 | ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_cancel_right
% 5.82/6.07 thf(fact_2562_division__ring__divide__zero,axiom,
% 5.82/6.07 ! [A2: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ A2 @ zero_zero_complex )
% 5.82/6.07 = zero_zero_complex ) ).
% 5.82/6.07
% 5.82/6.07 % division_ring_divide_zero
% 5.82/6.07 thf(fact_2563_division__ring__divide__zero,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( divide_divide_real @ A2 @ zero_zero_real )
% 5.82/6.07 = zero_zero_real ) ).
% 5.82/6.07
% 5.82/6.07 % division_ring_divide_zero
% 5.82/6.07 thf(fact_2564_division__ring__divide__zero,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 = zero_zero_rat ) ).
% 5.82/6.07
% 5.82/6.07 % division_ring_divide_zero
% 5.82/6.07 thf(fact_2565_times__divide__eq__left,axiom,
% 5.82/6.07 ! [B2: complex,C2: complex,A2: complex] :
% 5.82/6.07 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( times_times_complex @ B2 @ A2 ) @ C2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_eq_left
% 5.82/6.07 thf(fact_2566_times__divide__eq__left,axiom,
% 5.82/6.07 ! [B2: real,C2: real,A2: real] :
% 5.82/6.07 ( ( times_times_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( divide_divide_real @ ( times_times_real @ B2 @ A2 ) @ C2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_eq_left
% 5.82/6.07 thf(fact_2567_times__divide__eq__left,axiom,
% 5.82/6.07 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.07 ( ( times_times_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( divide_divide_rat @ ( times_times_rat @ B2 @ A2 ) @ C2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_eq_left
% 5.82/6.07 thf(fact_2568_divide__divide__eq__left,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ ( times_times_complex @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_left
% 5.82/6.07 thf(fact_2569_divide__divide__eq__left,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( divide_divide_real @ ( divide_divide_real @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( divide_divide_real @ A2 @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_left
% 5.82/6.07 thf(fact_2570_divide__divide__eq__left,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ ( divide_divide_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_left
% 5.82/6.07 thf(fact_2571_divide__divide__eq__right,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ A2 @ ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_right
% 5.82/6.07 thf(fact_2572_divide__divide__eq__right,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( divide_divide_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_right
% 5.82/6.07 thf(fact_2573_divide__divide__eq__right,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_right
% 5.82/6.07 thf(fact_2574_times__divide__eq__right,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( times_times_complex @ A2 @ ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_eq_right
% 5.82/6.07 thf(fact_2575_times__divide__eq__right,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( times_times_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_real @ ( times_times_real @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_eq_right
% 5.82/6.07 thf(fact_2576_times__divide__eq__right,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( times_times_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_rat @ ( times_times_rat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_eq_right
% 5.82/6.07 thf(fact_2577_log__one,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( log @ A2 @ one_one_real )
% 5.82/6.07 = zero_zero_real ) ).
% 5.82/6.07
% 5.82/6.07 % log_one
% 5.82/6.07 thf(fact_2578_divide__eq__1__iff,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex] :
% 5.82/6.07 ( ( ( divide1717551699836669952omplex @ A2 @ B2 )
% 5.82/6.07 = one_one_complex )
% 5.82/6.07 = ( ( B2 != zero_zero_complex )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_1_iff
% 5.82/6.07 thf(fact_2579_divide__eq__1__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ A2 @ B2 )
% 5.82/6.07 = one_one_real )
% 5.82/6.07 = ( ( B2 != zero_zero_real )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_1_iff
% 5.82/6.07 thf(fact_2580_divide__eq__1__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ A2 @ B2 )
% 5.82/6.07 = one_one_rat )
% 5.82/6.07 = ( ( B2 != zero_zero_rat )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_1_iff
% 5.82/6.07 thf(fact_2581_one__eq__divide__iff,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex] :
% 5.82/6.07 ( ( one_one_complex
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ B2 ) )
% 5.82/6.07 = ( ( B2 != zero_zero_complex )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_eq_divide_iff
% 5.82/6.07 thf(fact_2582_one__eq__divide__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( one_one_real
% 5.82/6.07 = ( divide_divide_real @ A2 @ B2 ) )
% 5.82/6.07 = ( ( B2 != zero_zero_real )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_eq_divide_iff
% 5.82/6.07 thf(fact_2583_one__eq__divide__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( one_one_rat
% 5.82/6.07 = ( divide_divide_rat @ A2 @ B2 ) )
% 5.82/6.07 = ( ( B2 != zero_zero_rat )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_eq_divide_iff
% 5.82/6.07 thf(fact_2584_divide__self,axiom,
% 5.82/6.07 ! [A2: complex] :
% 5.82/6.07 ( ( A2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.82/6.07 = one_one_complex ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_self
% 5.82/6.07 thf(fact_2585_divide__self,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( A2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ A2 @ A2 )
% 5.82/6.07 = one_one_real ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_self
% 5.82/6.07 thf(fact_2586_divide__self,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( A2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.82/6.07 = one_one_rat ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_self
% 5.82/6.07 thf(fact_2587_divide__self__if,axiom,
% 5.82/6.07 ! [A2: complex] :
% 5.82/6.07 ( ( ( A2 = zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.82/6.07 = zero_zero_complex ) )
% 5.82/6.07 & ( ( A2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.82/6.07 = one_one_complex ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_self_if
% 5.82/6.07 thf(fact_2588_divide__self__if,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ( A2 = zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ A2 @ A2 )
% 5.82/6.07 = zero_zero_real ) )
% 5.82/6.07 & ( ( A2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ A2 @ A2 )
% 5.82/6.07 = one_one_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_self_if
% 5.82/6.07 thf(fact_2589_divide__self__if,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ( A2 = zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.82/6.07 = zero_zero_rat ) )
% 5.82/6.07 & ( ( A2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.82/6.07 = one_one_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_self_if
% 5.82/6.07 thf(fact_2590_divide__eq__eq__1,axiom,
% 5.82/6.07 ! [B2: real,A2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ B2 @ A2 )
% 5.82/6.07 = one_one_real )
% 5.82/6.07 = ( ( A2 != zero_zero_real )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_eq_1
% 5.82/6.07 thf(fact_2591_divide__eq__eq__1,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ B2 @ A2 )
% 5.82/6.07 = one_one_rat )
% 5.82/6.07 = ( ( A2 != zero_zero_rat )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_eq_1
% 5.82/6.07 thf(fact_2592_eq__divide__eq__1,axiom,
% 5.82/6.07 ! [B2: real,A2: real] :
% 5.82/6.07 ( ( one_one_real
% 5.82/6.07 = ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.07 = ( ( A2 != zero_zero_real )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_eq_1
% 5.82/6.07 thf(fact_2593_eq__divide__eq__1,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat] :
% 5.82/6.07 ( ( one_one_rat
% 5.82/6.07 = ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.07 = ( ( A2 != zero_zero_rat )
% 5.82/6.07 & ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_eq_1
% 5.82/6.07 thf(fact_2594_one__divide__eq__0__iff,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ one_one_real @ A2 )
% 5.82/6.07 = zero_zero_real )
% 5.82/6.07 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_divide_eq_0_iff
% 5.82/6.07 thf(fact_2595_one__divide__eq__0__iff,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ one_one_rat @ A2 )
% 5.82/6.07 = zero_zero_rat )
% 5.82/6.07 = ( A2 = zero_zero_rat ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_divide_eq_0_iff
% 5.82/6.07 thf(fact_2596_zero__eq__1__divide__iff,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( zero_zero_real
% 5.82/6.07 = ( divide_divide_real @ one_one_real @ A2 ) )
% 5.82/6.07 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_eq_1_divide_iff
% 5.82/6.07 thf(fact_2597_zero__eq__1__divide__iff,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( zero_zero_rat
% 5.82/6.07 = ( divide_divide_rat @ one_one_rat @ A2 ) )
% 5.82/6.07 = ( A2 = zero_zero_rat ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_eq_1_divide_iff
% 5.82/6.07 thf(fact_2598_mult__divide__mult__cancel__left__if,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( ( C2 = zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A2 ) @ ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.07 = zero_zero_complex ) )
% 5.82/6.07 & ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A2 ) @ ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_divide_mult_cancel_left_if
% 5.82/6.07 thf(fact_2599_mult__divide__mult__cancel__left__if,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( ( C2 = zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.07 = zero_zero_real ) )
% 5.82/6.07 & ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_divide_mult_cancel_left_if
% 5.82/6.07 thf(fact_2600_mult__divide__mult__cancel__left__if,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( ( C2 = zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.07 = zero_zero_rat ) )
% 5.82/6.07 & ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_divide_mult_cancel_left_if
% 5.82/6.07 thf(fact_2601_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A2 ) @ ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_left
% 5.82/6.07 thf(fact_2602_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_left
% 5.82/6.07 thf(fact_2603_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_left
% 5.82/6.07 thf(fact_2604_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A2 ) @ ( times_times_complex @ B2 @ C2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_left2
% 5.82/6.07 thf(fact_2605_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_left2
% 5.82/6.07 thf(fact_2606_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_left2
% 5.82/6.07 thf(fact_2607_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ C2 ) @ ( times_times_complex @ B2 @ C2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_right
% 5.82/6.07 thf(fact_2608_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_right
% 5.82/6.07 thf(fact_2609_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_right
% 5.82/6.07 thf(fact_2610_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ C2 ) @ ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_right2
% 5.82/6.07 thf(fact_2611_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( divide_divide_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_right2
% 5.82/6.07 thf(fact_2612_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_mult_divide_mult_cancel_right2
% 5.82/6.07 thf(fact_2613_div__pos__pos__trivial,axiom,
% 5.82/6.07 ! [K: int,L: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.07 => ( ( ord_less_int @ K @ L )
% 5.82/6.07 => ( ( divide_divide_int @ K @ L )
% 5.82/6.07 = zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_pos_pos_trivial
% 5.82/6.07 thf(fact_2614_div__neg__neg__trivial,axiom,
% 5.82/6.07 ! [K: int,L: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_int @ L @ K )
% 5.82/6.07 => ( ( divide_divide_int @ K @ L )
% 5.82/6.07 = zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_neg_neg_trivial
% 5.82/6.07 thf(fact_2615_int__div__same__is__1,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.07 => ( ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( B2 = one_one_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % int_div_same_is_1
% 5.82/6.07 thf(fact_2616_log__eq__one,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( A2 != one_one_real )
% 5.82/6.07 => ( ( log @ A2 @ A2 )
% 5.82/6.07 = one_one_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_eq_one
% 5.82/6.07 thf(fact_2617_log__less__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) )
% 5.82/6.07 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_less_cancel_iff
% 5.82/6.07 thf(fact_2618_log__less__one__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ ( log @ A2 @ X2 ) @ one_one_real )
% 5.82/6.07 = ( ord_less_real @ X2 @ A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_less_one_cancel_iff
% 5.82/6.07 thf(fact_2619_one__less__log__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ one_one_real @ ( log @ A2 @ X2 ) )
% 5.82/6.07 = ( ord_less_real @ A2 @ X2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_less_log_cancel_iff
% 5.82/6.07 thf(fact_2620_log__less__zero__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ ( log @ A2 @ X2 ) @ zero_zero_real )
% 5.82/6.07 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_less_zero_cancel_iff
% 5.82/6.07 thf(fact_2621_zero__less__log__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ ( log @ A2 @ X2 ) )
% 5.82/6.07 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_less_log_cancel_iff
% 5.82/6.07 thf(fact_2622_zero__le__divide__1__iff,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A2 ) )
% 5.82/6.07 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_divide_1_iff
% 5.82/6.07 thf(fact_2623_zero__le__divide__1__iff,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) )
% 5.82/6.07 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_divide_1_iff
% 5.82/6.07 thf(fact_2624_divide__le__0__1__iff,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A2 ) @ zero_zero_real )
% 5.82/6.07 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_0_1_iff
% 5.82/6.07 thf(fact_2625_divide__le__0__1__iff,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) @ zero_zero_rat )
% 5.82/6.07 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_0_1_iff
% 5.82/6.07 thf(fact_2626_divide__less__0__1__iff,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A2 ) @ zero_zero_real )
% 5.82/6.07 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_0_1_iff
% 5.82/6.07 thf(fact_2627_divide__less__0__1__iff,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) @ zero_zero_rat )
% 5.82/6.07 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_0_1_iff
% 5.82/6.07 thf(fact_2628_divide__less__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ A2 ) @ one_one_real )
% 5.82/6.07 = ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq_1_neg
% 5.82/6.07 thf(fact_2629_divide__less__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ A2 ) @ one_one_rat )
% 5.82/6.07 = ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq_1_neg
% 5.82/6.07 thf(fact_2630_divide__less__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ A2 ) @ one_one_real )
% 5.82/6.07 = ( ord_less_real @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq_1_pos
% 5.82/6.07 thf(fact_2631_divide__less__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ A2 ) @ one_one_rat )
% 5.82/6.07 = ( ord_less_rat @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq_1_pos
% 5.82/6.07 thf(fact_2632_less__divide__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_real @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq_1_neg
% 5.82/6.07 thf(fact_2633_less__divide__eq__1__neg,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_rat @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq_1_neg
% 5.82/6.07 thf(fact_2634_less__divide__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq_1_pos
% 5.82/6.07 thf(fact_2635_less__divide__eq__1__pos,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.07 = ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq_1_pos
% 5.82/6.07 thf(fact_2636_zero__less__divide__1__iff,axiom,
% 5.82/6.07 ! [A2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A2 ) )
% 5.82/6.07 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_less_divide_1_iff
% 5.82/6.07 thf(fact_2637_zero__less__divide__1__iff,axiom,
% 5.82/6.07 ! [A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) )
% 5.82/6.07 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_less_divide_1_iff
% 5.82/6.07 thf(fact_2638_log__le__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( ord_less_eq_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) )
% 5.82/6.07 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_le_cancel_iff
% 5.82/6.07 thf(fact_2639_log__le__one__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ ( log @ A2 @ X2 ) @ one_one_real )
% 5.82/6.07 = ( ord_less_eq_real @ X2 @ A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_le_one_cancel_iff
% 5.82/6.07 thf(fact_2640_one__le__log__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A2 @ X2 ) )
% 5.82/6.07 = ( ord_less_eq_real @ A2 @ X2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % one_le_log_cancel_iff
% 5.82/6.07 thf(fact_2641_log__le__zero__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ ( log @ A2 @ X2 ) @ zero_zero_real )
% 5.82/6.07 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_le_zero_cancel_iff
% 5.82/6.07 thf(fact_2642_zero__le__log__cancel__iff,axiom,
% 5.82/6.07 ! [A2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A2 @ X2 ) )
% 5.82/6.07 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_log_cancel_iff
% 5.82/6.07 thf(fact_2643_half__nonnegative__int__iff,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.82/6.07 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.07
% 5.82/6.07 % half_nonnegative_int_iff
% 5.82/6.07 thf(fact_2644_half__negative__int__iff,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.82/6.07 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.82/6.07
% 5.82/6.07 % half_negative_int_iff
% 5.82/6.07 thf(fact_2645_log__pow__cancel,axiom,
% 5.82/6.07 ! [A2: real,B2: nat] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( A2 != one_one_real )
% 5.82/6.07 => ( ( log @ A2 @ ( power_power_real @ A2 @ B2 ) )
% 5.82/6.07 = ( semiri5074537144036343181t_real @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_pow_cancel
% 5.82/6.07 thf(fact_2646_less__eq__int__code_I1_J,axiom,
% 5.82/6.07 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.82/6.07
% 5.82/6.07 % less_eq_int_code(1)
% 5.82/6.07 thf(fact_2647_zero__le__imp__eq__int,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.07 => ? [N3: nat] :
% 5.82/6.07 ( K
% 5.82/6.07 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_imp_eq_int
% 5.82/6.07 thf(fact_2648_nonneg__int__cases,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.07 => ~ ! [N3: nat] :
% 5.82/6.07 ( K
% 5.82/6.07 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonneg_int_cases
% 5.82/6.07 thf(fact_2649_plus__int__code_I1_J,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.82/6.07 = K ) ).
% 5.82/6.07
% 5.82/6.07 % plus_int_code(1)
% 5.82/6.07 thf(fact_2650_plus__int__code_I2_J,axiom,
% 5.82/6.07 ! [L: int] :
% 5.82/6.07 ( ( plus_plus_int @ zero_zero_int @ L )
% 5.82/6.07 = L ) ).
% 5.82/6.07
% 5.82/6.07 % plus_int_code(2)
% 5.82/6.07 thf(fact_2651_minus__int__code_I1_J,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.82/6.07 = K ) ).
% 5.82/6.07
% 5.82/6.07 % minus_int_code(1)
% 5.82/6.07 thf(fact_2652_not__iless0,axiom,
% 5.82/6.07 ! [N: extended_enat] :
% 5.82/6.07 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.82/6.07
% 5.82/6.07 % not_iless0
% 5.82/6.07 thf(fact_2653_enat__0__less__mult__iff,axiom,
% 5.82/6.07 ! [M: extended_enat,N: extended_enat] :
% 5.82/6.07 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.82/6.07 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.82/6.07 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % enat_0_less_mult_iff
% 5.82/6.07 thf(fact_2654_iadd__is__0,axiom,
% 5.82/6.07 ! [M: extended_enat,N: extended_enat] :
% 5.82/6.07 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.82/6.07 = zero_z5237406670263579293d_enat )
% 5.82/6.07 = ( ( M = zero_z5237406670263579293d_enat )
% 5.82/6.07 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % iadd_is_0
% 5.82/6.07 thf(fact_2655_ile0__eq,axiom,
% 5.82/6.07 ! [N: extended_enat] :
% 5.82/6.07 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.82/6.07 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.82/6.07
% 5.82/6.07 % ile0_eq
% 5.82/6.07 thf(fact_2656_i0__lb,axiom,
% 5.82/6.07 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.82/6.07
% 5.82/6.07 % i0_lb
% 5.82/6.07 thf(fact_2657_odd__nonzero,axiom,
% 5.82/6.07 ! [Z: int] :
% 5.82/6.07 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.82/6.07 != zero_zero_int ) ).
% 5.82/6.07
% 5.82/6.07 % odd_nonzero
% 5.82/6.07 thf(fact_2658_linordered__field__no__lb,axiom,
% 5.82/6.07 ! [X8: real] :
% 5.82/6.07 ? [Y4: real] : ( ord_less_real @ Y4 @ X8 ) ).
% 5.82/6.07
% 5.82/6.07 % linordered_field_no_lb
% 5.82/6.07 thf(fact_2659_linordered__field__no__lb,axiom,
% 5.82/6.07 ! [X8: rat] :
% 5.82/6.07 ? [Y4: rat] : ( ord_less_rat @ Y4 @ X8 ) ).
% 5.82/6.07
% 5.82/6.07 % linordered_field_no_lb
% 5.82/6.07 thf(fact_2660_linordered__field__no__ub,axiom,
% 5.82/6.07 ! [X8: real] :
% 5.82/6.07 ? [X_1: real] : ( ord_less_real @ X8 @ X_1 ) ).
% 5.82/6.07
% 5.82/6.07 % linordered_field_no_ub
% 5.82/6.07 thf(fact_2661_linordered__field__no__ub,axiom,
% 5.82/6.07 ! [X8: rat] :
% 5.82/6.07 ? [X_1: rat] : ( ord_less_rat @ X8 @ X_1 ) ).
% 5.82/6.07
% 5.82/6.07 % linordered_field_no_ub
% 5.82/6.07 thf(fact_2662_log__base__change,axiom,
% 5.82/6.07 ! [A2: real,B2: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( A2 != one_one_real )
% 5.82/6.07 => ( ( log @ B2 @ X2 )
% 5.82/6.07 = ( divide_divide_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_base_change
% 5.82/6.07 thf(fact_2663_pos__int__cases,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.07 => ~ ! [N3: nat] :
% 5.82/6.07 ( ( K
% 5.82/6.07 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.82/6.07 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_int_cases
% 5.82/6.07 thf(fact_2664_zero__less__imp__eq__int,axiom,
% 5.82/6.07 ! [K: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.07 => ? [N3: nat] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.07 & ( K
% 5.82/6.07 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_less_imp_eq_int
% 5.82/6.07 thf(fact_2665_realpow__pos__nth2,axiom,
% 5.82/6.07 ! [A2: real,N: nat] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ? [R3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.82/6.07 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.82/6.07 = A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % realpow_pos_nth2
% 5.82/6.07 thf(fact_2666_real__arch__pow__inv,axiom,
% 5.82/6.07 ! [Y3: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.07 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N3 ) @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % real_arch_pow_inv
% 5.82/6.07 thf(fact_2667_int__one__le__iff__zero__less,axiom,
% 5.82/6.07 ! [Z: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.82/6.07 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.07
% 5.82/6.07 % int_one_le_iff_zero_less
% 5.82/6.07 thf(fact_2668_odd__less__0__iff,axiom,
% 5.82/6.07 ! [Z: int] :
% 5.82/6.07 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.82/6.07 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.07
% 5.82/6.07 % odd_less_0_iff
% 5.82/6.07 thf(fact_2669_pos__zmult__eq__1__iff,axiom,
% 5.82/6.07 ! [M: int,N: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ M )
% 5.82/6.07 => ( ( ( times_times_int @ M @ N )
% 5.82/6.07 = one_one_int )
% 5.82/6.07 = ( ( M = one_one_int )
% 5.82/6.07 & ( N = one_one_int ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_zmult_eq_1_iff
% 5.82/6.07 thf(fact_2670_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B2 ) )
% 5.82/6.07 = ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.07 & ( ord_less_int @ zero_zero_int @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonneg1_imp_zdiv_pos_iff
% 5.82/6.07 thf(fact_2671_pos__imp__zdiv__nonneg__iff,axiom,
% 5.82/6.07 ! [B2: int,A2: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B2 ) )
% 5.82/6.07 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_imp_zdiv_nonneg_iff
% 5.82/6.07 thf(fact_2672_neg__imp__zdiv__nonneg__iff,axiom,
% 5.82/6.07 ! [B2: int,A2: int] :
% 5.82/6.07 ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B2 ) )
% 5.82/6.07 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % neg_imp_zdiv_nonneg_iff
% 5.82/6.07 thf(fact_2673_pos__imp__zdiv__pos__iff,axiom,
% 5.82/6.07 ! [K: int,I: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.82/6.07 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_imp_zdiv_pos_iff
% 5.82/6.07 thf(fact_2674_div__nonpos__pos__le0,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_nonpos_pos_le0
% 5.82/6.07 thf(fact_2675_div__nonneg__neg__le0,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.07 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_nonneg_neg_le0
% 5.82/6.07 thf(fact_2676_div__positive__int,axiom,
% 5.82/6.07 ! [L: int,K: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ L @ K )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.07 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_positive_int
% 5.82/6.07 thf(fact_2677_div__int__pos__iff,axiom,
% 5.82/6.07 ! [K: int,L: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.82/6.07 = ( ( K = zero_zero_int )
% 5.82/6.07 | ( L = zero_zero_int )
% 5.82/6.07 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.07 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.82/6.07 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.82/6.07 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_int_pos_iff
% 5.82/6.07 thf(fact_2678_zdiv__mono2__neg,axiom,
% 5.82/6.07 ! [A2: int,B4: int,B2: int] :
% 5.82/6.07 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.82/6.07 => ( ( ord_less_eq_int @ B4 @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B4 ) @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mono2_neg
% 5.82/6.07 thf(fact_2679_zdiv__mono1__neg,axiom,
% 5.82/6.07 ! [A2: int,A4: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ A2 @ A4 )
% 5.82/6.07 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B2 ) @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mono1_neg
% 5.82/6.07 thf(fact_2680_zdiv__eq__0__iff,axiom,
% 5.82/6.07 ! [I: int,K: int] :
% 5.82/6.07 ( ( ( divide_divide_int @ I @ K )
% 5.82/6.07 = zero_zero_int )
% 5.82/6.07 = ( ( K = zero_zero_int )
% 5.82/6.07 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.82/6.07 & ( ord_less_int @ I @ K ) )
% 5.82/6.07 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.82/6.07 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_eq_0_iff
% 5.82/6.07 thf(fact_2681_zdiv__mono2,axiom,
% 5.82/6.07 ! [A2: int,B4: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.82/6.07 => ( ( ord_less_eq_int @ B4 @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B2 ) @ ( divide_divide_int @ A2 @ B4 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mono2
% 5.82/6.07 thf(fact_2682_zdiv__mono1,axiom,
% 5.82/6.07 ! [A2: int,A4: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ A2 @ A4 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B2 ) @ ( divide_divide_int @ A4 @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mono1
% 5.82/6.07 thf(fact_2683_zdiv__le__dividend,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B2 ) @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_le_dividend
% 5.82/6.07 thf(fact_2684_int__div__less__self,axiom,
% 5.82/6.07 ! [X2: int,K: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.82/6.07 => ( ( ord_less_int @ one_one_int @ K )
% 5.82/6.07 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % int_div_less_self
% 5.82/6.07 thf(fact_2685_zdiv__zmult2__eq,axiom,
% 5.82/6.07 ! [C2: int,A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.07 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.07 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_zmult2_eq
% 5.82/6.07 thf(fact_2686_zdiv__mult__self,axiom,
% 5.82/6.07 ! [M: int,A2: int,N: int] :
% 5.82/6.07 ( ( M != zero_zero_int )
% 5.82/6.07 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ ( times_times_int @ M @ N ) ) @ M )
% 5.82/6.07 = ( plus_plus_int @ ( divide_divide_int @ A2 @ M ) @ N ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mult_self
% 5.82/6.07 thf(fact_2687_log__mult,axiom,
% 5.82/6.07 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( A2 != one_one_real )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( log @ A2 @ ( times_times_real @ X2 @ Y3 ) )
% 5.82/6.07 = ( plus_plus_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_mult
% 5.82/6.07 thf(fact_2688_log__divide,axiom,
% 5.82/6.07 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ( ( A2 != one_one_real )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( log @ A2 @ ( divide_divide_real @ X2 @ Y3 ) )
% 5.82/6.07 = ( minus_minus_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % log_divide
% 5.82/6.07 thf(fact_2689_not__exp__less__eq__0__int,axiom,
% 5.82/6.07 ! [N: nat] :
% 5.82/6.07 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.82/6.07
% 5.82/6.07 % not_exp_less_eq_0_int
% 5.82/6.07 thf(fact_2690_realpow__pos__nth__unique,axiom,
% 5.82/6.07 ! [N: nat,A2: real] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ? [X4: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.82/6.07 & ( ( power_power_real @ X4 @ N )
% 5.82/6.07 = A2 )
% 5.82/6.07 & ! [Y5: real] :
% 5.82/6.07 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 5.82/6.07 & ( ( power_power_real @ Y5 @ N )
% 5.82/6.07 = A2 ) )
% 5.82/6.07 => ( Y5 = X4 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % realpow_pos_nth_unique
% 5.82/6.07 thf(fact_2691_realpow__pos__nth,axiom,
% 5.82/6.07 ! [N: nat,A2: real] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 => ? [R3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.82/6.07 & ( ( power_power_real @ R3 @ N )
% 5.82/6.07 = A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % realpow_pos_nth
% 5.82/6.07 thf(fact_2692_le__imp__0__less,axiom,
% 5.82/6.07 ! [Z: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.07 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % le_imp_0_less
% 5.82/6.07 thf(fact_2693_q__pos__lemma,axiom,
% 5.82/6.07 ! [B4: int,Q6: int,R4: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R4 ) )
% 5.82/6.07 => ( ( ord_less_int @ R4 @ B4 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.82/6.07 => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % q_pos_lemma
% 5.82/6.07 thf(fact_2694_zdiv__mono2__lemma,axiom,
% 5.82/6.07 ! [B2: int,Q3: int,R2: int,B4: int,Q6: int,R4: int] :
% 5.82/6.07 ( ( ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 )
% 5.82/6.07 = ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R4 ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R4 ) )
% 5.82/6.07 => ( ( ord_less_int @ R4 @ B4 )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.82/6.07 => ( ( ord_less_eq_int @ B4 @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ Q3 @ Q6 ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mono2_lemma
% 5.82/6.07 thf(fact_2695_zdiv__mono2__neg__lemma,axiom,
% 5.82/6.07 ! [B2: int,Q3: int,R2: int,B4: int,Q6: int,R4: int] :
% 5.82/6.07 ( ( ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 )
% 5.82/6.07 = ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R4 ) )
% 5.82/6.07 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R4 ) @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_int @ R2 @ B2 )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.82/6.07 => ( ( ord_less_eq_int @ B4 @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ Q6 @ Q3 ) ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zdiv_mono2_neg_lemma
% 5.82/6.07 thf(fact_2696_unique__quotient__lemma,axiom,
% 5.82/6.07 ! [B2: int,Q6: int,R4: int,Q3: int,R2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.82/6.07 => ( ( ord_less_int @ R4 @ B2 )
% 5.82/6.07 => ( ( ord_less_int @ R2 @ B2 )
% 5.82/6.07 => ( ord_less_eq_int @ Q6 @ Q3 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % unique_quotient_lemma
% 5.82/6.07 thf(fact_2697_unique__quotient__lemma__neg,axiom,
% 5.82/6.07 ! [B2: int,Q6: int,R4: int,Q3: int,R2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q6 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_int @ B2 @ R2 )
% 5.82/6.07 => ( ( ord_less_int @ B2 @ R4 )
% 5.82/6.07 => ( ord_less_eq_int @ Q3 @ Q6 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % unique_quotient_lemma_neg
% 5.82/6.07 thf(fact_2698_VEBT__internal_OTb_Osimps_I1_J,axiom,
% 5.82/6.07 ( ( vEBT_VEBT_Tb @ zero_zero_nat )
% 5.82/6.07 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.Tb.simps(1)
% 5.82/6.07 thf(fact_2699_real__archimedian__rdiv__eq__0,axiom,
% 5.82/6.07 ! [X2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ! [M5: nat] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 5.82/6.07 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X2 ) @ C2 ) )
% 5.82/6.07 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % real_archimedian_rdiv_eq_0
% 5.82/6.07 thf(fact_2700_split__zdiv,axiom,
% 5.82/6.07 ! [P: int > $o,N: int,K: int] :
% 5.82/6.07 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.82/6.07 = ( ( ( K = zero_zero_int )
% 5.82/6.07 => ( P @ zero_zero_int ) )
% 5.82/6.07 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.07 => ! [I4: int,J3: int] :
% 5.82/6.07 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.82/6.07 & ( ord_less_int @ J3 @ K )
% 5.82/6.07 & ( N
% 5.82/6.07 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.82/6.07 => ( P @ I4 ) ) )
% 5.82/6.07 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.82/6.07 => ! [I4: int,J3: int] :
% 5.82/6.07 ( ( ( ord_less_int @ K @ J3 )
% 5.82/6.07 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.82/6.07 & ( N
% 5.82/6.07 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.82/6.07 => ( P @ I4 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % split_zdiv
% 5.82/6.07 thf(fact_2701_int__div__neg__eq,axiom,
% 5.82/6.07 ! [A2: int,B2: int,Q3: int,R2: int] :
% 5.82/6.07 ( ( A2
% 5.82/6.07 = ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.82/6.07 => ( ( ord_less_int @ B2 @ R2 )
% 5.82/6.07 => ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.07 = Q3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % int_div_neg_eq
% 5.82/6.07 thf(fact_2702_int__div__pos__eq,axiom,
% 5.82/6.07 ! [A2: int,B2: int,Q3: int,R2: int] :
% 5.82/6.07 ( ( A2
% 5.82/6.07 = ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 ) )
% 5.82/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.82/6.07 => ( ( ord_less_int @ R2 @ B2 )
% 5.82/6.07 => ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.07 = Q3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % int_div_pos_eq
% 5.82/6.07 thf(fact_2703_real__of__nat__div2,axiom,
% 5.82/6.07 ! [N: nat,X2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % real_of_nat_div2
% 5.82/6.07 thf(fact_2704_int__power__div__base,axiom,
% 5.82/6.07 ! [M: nat,K: int] :
% 5.82/6.07 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.07 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.07 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.82/6.07 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % int_power_div_base
% 5.82/6.07 thf(fact_2705_axxdiv2,axiom,
% 5.82/6.07 ! [X2: int] :
% 5.82/6.07 ( ( ( divide_divide_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X2 ) @ X2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.07 = X2 )
% 5.82/6.07 & ( ( divide_divide_int @ ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ X2 ) @ X2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.07 = X2 ) ) ).
% 5.82/6.07
% 5.82/6.07 % axxdiv2
% 5.82/6.07 thf(fact_2706_add__divide__distrib,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A2 @ C2 ) @ ( divide1717551699836669952omplex @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_distrib
% 5.82/6.07 thf(fact_2707_add__divide__distrib,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( divide_divide_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( plus_plus_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_distrib
% 5.82/6.07 thf(fact_2708_add__divide__distrib,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( plus_plus_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_distrib
% 5.82/6.07 thf(fact_2709_times__divide__times__eq,axiom,
% 5.82/6.07 ! [X2: complex,Y3: complex,Z: complex,W: complex] :
% 5.82/6.07 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ Y3 @ W ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_times_eq
% 5.82/6.07 thf(fact_2710_times__divide__times__eq,axiom,
% 5.82/6.07 ! [X2: real,Y3: real,Z: real,W: real] :
% 5.82/6.07 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ Z @ W ) )
% 5.82/6.07 = ( divide_divide_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y3 @ W ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_times_eq
% 5.82/6.07 thf(fact_2711_times__divide__times__eq,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat,Z: rat,W: rat] :
% 5.82/6.07 ( ( times_times_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.82/6.07 = ( divide_divide_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y3 @ W ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % times_divide_times_eq
% 5.82/6.07 thf(fact_2712_divide__divide__times__eq,axiom,
% 5.82/6.07 ! [X2: complex,Y3: complex,Z: complex,W: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ W ) @ ( times_times_complex @ Y3 @ Z ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_times_eq
% 5.82/6.07 thf(fact_2713_divide__divide__times__eq,axiom,
% 5.82/6.07 ! [X2: real,Y3: real,Z: real,W: real] :
% 5.82/6.07 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ Z @ W ) )
% 5.82/6.07 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y3 @ Z ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_times_eq
% 5.82/6.07 thf(fact_2714_divide__divide__times__eq,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat,Z: rat,W: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.82/6.07 = ( divide_divide_rat @ ( times_times_rat @ X2 @ W ) @ ( times_times_rat @ Y3 @ Z ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_times_eq
% 5.82/6.07 thf(fact_2715_divide__divide__eq__left_H,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ A2 @ ( times_times_complex @ C2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_left'
% 5.82/6.07 thf(fact_2716_divide__divide__eq__left_H,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( divide_divide_real @ ( divide_divide_real @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( divide_divide_real @ A2 @ ( times_times_real @ C2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_left'
% 5.82/6.07 thf(fact_2717_divide__divide__eq__left_H,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ ( divide_divide_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( divide_divide_rat @ A2 @ ( times_times_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_divide_eq_left'
% 5.82/6.07 thf(fact_2718_diff__divide__distrib,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A2 @ C2 ) @ ( divide1717551699836669952omplex @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % diff_divide_distrib
% 5.82/6.07 thf(fact_2719_diff__divide__distrib,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( divide_divide_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( minus_minus_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % diff_divide_distrib
% 5.82/6.07 thf(fact_2720_diff__divide__distrib,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( divide_divide_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.07 = ( minus_minus_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % diff_divide_distrib
% 5.82/6.07 thf(fact_2721_div__pos__geq,axiom,
% 5.82/6.07 ! [L: int,K: int] :
% 5.82/6.07 ( ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.07 => ( ( ord_less_eq_int @ L @ K )
% 5.82/6.07 => ( ( divide_divide_int @ K @ L )
% 5.82/6.07 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % div_pos_geq
% 5.82/6.07 thf(fact_2722_VEBT__internal_OTb_Osimps_I2_J,axiom,
% 5.82/6.07 ( ( vEBT_VEBT_Tb @ ( suc @ zero_zero_nat ) )
% 5.82/6.07 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % VEBT_internal.Tb.simps(2)
% 5.82/6.07 thf(fact_2723_neg__zdiv__mult__2,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.07 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.07 = ( divide_divide_int @ ( plus_plus_int @ B2 @ one_one_int ) @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % neg_zdiv_mult_2
% 5.82/6.07 thf(fact_2724_pos__zdiv__mult__2,axiom,
% 5.82/6.07 ! [A2: int,B2: int] :
% 5.82/6.07 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.07 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.07 = ( divide_divide_int @ B2 @ A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_zdiv_mult_2
% 5.82/6.07 thf(fact_2725_divide__right__mono__neg,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C2 ) @ ( divide_divide_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_right_mono_neg
% 5.82/6.07 thf(fact_2726_divide__right__mono__neg,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C2 ) @ ( divide_divide_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_right_mono_neg
% 5.82/6.07 thf(fact_2727_divide__nonpos__nonpos,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_nonpos
% 5.82/6.07 thf(fact_2728_divide__nonpos__nonpos,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_nonpos
% 5.82/6.07 thf(fact_2729_divide__nonpos__nonneg,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_nonneg
% 5.82/6.07 thf(fact_2730_divide__nonpos__nonneg,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_nonneg
% 5.82/6.07 thf(fact_2731_divide__nonneg__nonpos,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_nonpos
% 5.82/6.07 thf(fact_2732_divide__nonneg__nonpos,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_nonpos
% 5.82/6.07 thf(fact_2733_divide__nonneg__nonneg,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_nonneg
% 5.82/6.07 thf(fact_2734_divide__nonneg__nonneg,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_nonneg
% 5.82/6.07 thf(fact_2735_zero__le__divide__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A2 @ B2 ) )
% 5.82/6.07 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.07 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 5.82/6.07 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.07 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_divide_iff
% 5.82/6.07 thf(fact_2736_zero__le__divide__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ B2 ) )
% 5.82/6.07 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 5.82/6.07 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_le_divide_iff
% 5.82/6.07 thf(fact_2737_divide__right__mono,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_right_mono
% 5.82/6.07 thf(fact_2738_divide__right__mono,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_right_mono
% 5.82/6.07 thf(fact_2739_divide__le__0__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ ( divide_divide_real @ A2 @ B2 ) @ zero_zero_real )
% 5.82/6.07 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.07 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 5.82/6.07 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.07 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_0_iff
% 5.82/6.07 thf(fact_2740_divide__le__0__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ B2 ) @ zero_zero_rat )
% 5.82/6.07 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 5.82/6.07 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_0_iff
% 5.82/6.07 thf(fact_2741_divide__neg__neg,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_neg_neg
% 5.82/6.07 thf(fact_2742_divide__neg__neg,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_neg_neg
% 5.82/6.07 thf(fact_2743_divide__neg__pos,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_neg_pos
% 5.82/6.07 thf(fact_2744_divide__neg__pos,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_neg_pos
% 5.82/6.07 thf(fact_2745_divide__pos__neg,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_pos_neg
% 5.82/6.07 thf(fact_2746_divide__pos__neg,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_pos_neg
% 5.82/6.07 thf(fact_2747_divide__pos__pos,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_pos_pos
% 5.82/6.07 thf(fact_2748_divide__pos__pos,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_pos_pos
% 5.82/6.07 thf(fact_2749_divide__less__0__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ ( divide_divide_real @ A2 @ B2 ) @ zero_zero_real )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 & ( ord_less_real @ B2 @ zero_zero_real ) )
% 5.82/6.07 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 & ( ord_less_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_0_iff
% 5.82/6.07 thf(fact_2750_divide__less__0__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ ( divide_divide_rat @ A2 @ B2 ) @ zero_zero_rat )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 & ( ord_less_rat @ B2 @ zero_zero_rat ) )
% 5.82/6.07 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 & ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_0_iff
% 5.82/6.07 thf(fact_2751_divide__less__cancel,axiom,
% 5.82/6.07 ! [A2: real,C2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.07 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ B2 @ A2 ) )
% 5.82/6.07 & ( C2 != zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_cancel
% 5.82/6.07 thf(fact_2752_divide__less__cancel,axiom,
% 5.82/6.07 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.07 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ B2 @ A2 ) )
% 5.82/6.07 & ( C2 != zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_cancel
% 5.82/6.07 thf(fact_2753_zero__less__divide__iff,axiom,
% 5.82/6.07 ! [A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A2 @ B2 ) )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 & ( ord_less_real @ zero_zero_real @ B2 ) )
% 5.82/6.07 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 & ( ord_less_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_less_divide_iff
% 5.82/6.07 thf(fact_2754_zero__less__divide__iff,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ B2 ) )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 & ( ord_less_rat @ zero_zero_rat @ B2 ) )
% 5.82/6.07 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 & ( ord_less_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % zero_less_divide_iff
% 5.82/6.07 thf(fact_2755_divide__strict__right__mono,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_right_mono
% 5.82/6.07 thf(fact_2756_divide__strict__right__mono,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_right_mono
% 5.82/6.07 thf(fact_2757_divide__strict__right__mono__neg,axiom,
% 5.82/6.07 ! [B2: real,A2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_right_mono_neg
% 5.82/6.07 thf(fact_2758_divide__strict__right__mono__neg,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.07 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_right_mono_neg
% 5.82/6.07 thf(fact_2759_right__inverse__eq,axiom,
% 5.82/6.07 ! [B2: complex,A2: complex] :
% 5.82/6.07 ( ( B2 != zero_zero_complex )
% 5.82/6.07 => ( ( ( divide1717551699836669952omplex @ A2 @ B2 )
% 5.82/6.07 = one_one_complex )
% 5.82/6.07 = ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % right_inverse_eq
% 5.82/6.07 thf(fact_2760_right__inverse__eq,axiom,
% 5.82/6.07 ! [B2: real,A2: real] :
% 5.82/6.07 ( ( B2 != zero_zero_real )
% 5.82/6.07 => ( ( ( divide_divide_real @ A2 @ B2 )
% 5.82/6.07 = one_one_real )
% 5.82/6.07 = ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % right_inverse_eq
% 5.82/6.07 thf(fact_2761_right__inverse__eq,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat] :
% 5.82/6.07 ( ( B2 != zero_zero_rat )
% 5.82/6.07 => ( ( ( divide_divide_rat @ A2 @ B2 )
% 5.82/6.07 = one_one_rat )
% 5.82/6.07 = ( A2 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % right_inverse_eq
% 5.82/6.07 thf(fact_2762_frac__eq__eq,axiom,
% 5.82/6.07 ! [Y3: complex,Z: complex,X2: complex,W: complex] :
% 5.82/6.07 ( ( Y3 != zero_zero_complex )
% 5.82/6.07 => ( ( Z != zero_zero_complex )
% 5.82/6.07 => ( ( ( divide1717551699836669952omplex @ X2 @ Y3 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.82/6.07 = ( ( times_times_complex @ X2 @ Z )
% 5.82/6.07 = ( times_times_complex @ W @ Y3 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_eq_eq
% 5.82/6.07 thf(fact_2763_frac__eq__eq,axiom,
% 5.82/6.07 ! [Y3: real,Z: real,X2: real,W: real] :
% 5.82/6.07 ( ( Y3 != zero_zero_real )
% 5.82/6.07 => ( ( Z != zero_zero_real )
% 5.82/6.07 => ( ( ( divide_divide_real @ X2 @ Y3 )
% 5.82/6.07 = ( divide_divide_real @ W @ Z ) )
% 5.82/6.07 = ( ( times_times_real @ X2 @ Z )
% 5.82/6.07 = ( times_times_real @ W @ Y3 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_eq_eq
% 5.82/6.07 thf(fact_2764_frac__eq__eq,axiom,
% 5.82/6.07 ! [Y3: rat,Z: rat,X2: rat,W: rat] :
% 5.82/6.07 ( ( Y3 != zero_zero_rat )
% 5.82/6.07 => ( ( Z != zero_zero_rat )
% 5.82/6.07 => ( ( ( divide_divide_rat @ X2 @ Y3 )
% 5.82/6.07 = ( divide_divide_rat @ W @ Z ) )
% 5.82/6.07 = ( ( times_times_rat @ X2 @ Z )
% 5.82/6.07 = ( times_times_rat @ W @ Y3 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_eq_eq
% 5.82/6.07 thf(fact_2765_divide__eq__eq,axiom,
% 5.82/6.07 ! [B2: complex,C2: complex,A2: complex] :
% 5.82/6.07 ( ( ( divide1717551699836669952omplex @ B2 @ C2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( B2
% 5.82/6.07 = ( times_times_complex @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ( C2 = zero_zero_complex )
% 5.82/6.07 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_eq
% 5.82/6.07 thf(fact_2766_divide__eq__eq,axiom,
% 5.82/6.07 ! [B2: real,C2: real,A2: real] :
% 5.82/6.07 ( ( ( divide_divide_real @ B2 @ C2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( B2
% 5.82/6.07 = ( times_times_real @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ( C2 = zero_zero_real )
% 5.82/6.07 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_eq
% 5.82/6.07 thf(fact_2767_divide__eq__eq,axiom,
% 5.82/6.07 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.07 ( ( ( divide_divide_rat @ B2 @ C2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( B2
% 5.82/6.07 = ( times_times_rat @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ( C2 = zero_zero_rat )
% 5.82/6.07 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_eq
% 5.82/6.07 thf(fact_2768_eq__divide__eq,axiom,
% 5.82/6.07 ! [A2: complex,B2: complex,C2: complex] :
% 5.82/6.07 ( ( A2
% 5.82/6.07 = ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( times_times_complex @ A2 @ C2 )
% 5.82/6.07 = B2 ) )
% 5.82/6.07 & ( ( C2 = zero_zero_complex )
% 5.82/6.07 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_eq
% 5.82/6.07 thf(fact_2769_eq__divide__eq,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( A2
% 5.82/6.07 = ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( times_times_real @ A2 @ C2 )
% 5.82/6.07 = B2 ) )
% 5.82/6.07 & ( ( C2 = zero_zero_real )
% 5.82/6.07 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_eq
% 5.82/6.07 thf(fact_2770_eq__divide__eq,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( A2
% 5.82/6.07 = ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( times_times_rat @ A2 @ C2 )
% 5.82/6.07 = B2 ) )
% 5.82/6.07 & ( ( C2 = zero_zero_rat )
% 5.82/6.07 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_eq
% 5.82/6.07 thf(fact_2771_divide__eq__imp,axiom,
% 5.82/6.07 ! [C2: complex,B2: complex,A2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( B2
% 5.82/6.07 = ( times_times_complex @ A2 @ C2 ) )
% 5.82/6.07 => ( ( divide1717551699836669952omplex @ B2 @ C2 )
% 5.82/6.07 = A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_imp
% 5.82/6.07 thf(fact_2772_divide__eq__imp,axiom,
% 5.82/6.07 ! [C2: real,B2: real,A2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( B2
% 5.82/6.07 = ( times_times_real @ A2 @ C2 ) )
% 5.82/6.07 => ( ( divide_divide_real @ B2 @ C2 )
% 5.82/6.07 = A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_imp
% 5.82/6.07 thf(fact_2773_divide__eq__imp,axiom,
% 5.82/6.07 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( B2
% 5.82/6.07 = ( times_times_rat @ A2 @ C2 ) )
% 5.82/6.07 => ( ( divide_divide_rat @ B2 @ C2 )
% 5.82/6.07 = A2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_eq_imp
% 5.82/6.07 thf(fact_2774_eq__divide__imp,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( ( times_times_complex @ A2 @ C2 )
% 5.82/6.07 = B2 )
% 5.82/6.07 => ( A2
% 5.82/6.07 = ( divide1717551699836669952omplex @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_imp
% 5.82/6.07 thf(fact_2775_eq__divide__imp,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( ( times_times_real @ A2 @ C2 )
% 5.82/6.07 = B2 )
% 5.82/6.07 => ( A2
% 5.82/6.07 = ( divide_divide_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_imp
% 5.82/6.07 thf(fact_2776_eq__divide__imp,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( ( times_times_rat @ A2 @ C2 )
% 5.82/6.07 = B2 )
% 5.82/6.07 => ( A2
% 5.82/6.07 = ( divide_divide_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % eq_divide_imp
% 5.82/6.07 thf(fact_2777_nonzero__divide__eq__eq,axiom,
% 5.82/6.07 ! [C2: complex,B2: complex,A2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( ( divide1717551699836669952omplex @ B2 @ C2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( B2
% 5.82/6.07 = ( times_times_complex @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_eq_eq
% 5.82/6.07 thf(fact_2778_nonzero__divide__eq__eq,axiom,
% 5.82/6.07 ! [C2: real,B2: real,A2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( ( divide_divide_real @ B2 @ C2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( B2
% 5.82/6.07 = ( times_times_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_eq_eq
% 5.82/6.07 thf(fact_2779_nonzero__divide__eq__eq,axiom,
% 5.82/6.07 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( ( divide_divide_rat @ B2 @ C2 )
% 5.82/6.07 = A2 )
% 5.82/6.07 = ( B2
% 5.82/6.07 = ( times_times_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_divide_eq_eq
% 5.82/6.07 thf(fact_2780_nonzero__eq__divide__eq,axiom,
% 5.82/6.07 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( C2 != zero_zero_complex )
% 5.82/6.07 => ( ( A2
% 5.82/6.07 = ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.07 = ( ( times_times_complex @ A2 @ C2 )
% 5.82/6.07 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_eq_divide_eq
% 5.82/6.07 thf(fact_2781_nonzero__eq__divide__eq,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( C2 != zero_zero_real )
% 5.82/6.07 => ( ( A2
% 5.82/6.07 = ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ( times_times_real @ A2 @ C2 )
% 5.82/6.07 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_eq_divide_eq
% 5.82/6.07 thf(fact_2782_nonzero__eq__divide__eq,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( C2 != zero_zero_rat )
% 5.82/6.07 => ( ( A2
% 5.82/6.07 = ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ( times_times_rat @ A2 @ C2 )
% 5.82/6.07 = B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % nonzero_eq_divide_eq
% 5.82/6.07 thf(fact_2783_field__le__epsilon,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ! [E2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.82/6.07 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y3 @ E2 ) ) )
% 5.82/6.07 => ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.07
% 5.82/6.07 % field_le_epsilon
% 5.82/6.07 thf(fact_2784_field__le__epsilon,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ! [E2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.82/6.07 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y3 @ E2 ) ) )
% 5.82/6.07 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.07
% 5.82/6.07 % field_le_epsilon
% 5.82/6.07 thf(fact_2785_frac__le,axiom,
% 5.82/6.07 ! [Y3: real,X2: real,W: real,Z: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.82/6.07 => ( ( ord_less_eq_real @ W @ Z )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_le
% 5.82/6.07 thf(fact_2786_frac__le,axiom,
% 5.82/6.07 ! [Y3: rat,X2: rat,W: rat,Z: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.82/6.07 => ( ( ord_less_eq_rat @ W @ Z )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_le
% 5.82/6.07 thf(fact_2787_frac__less,axiom,
% 5.82/6.07 ! [X2: real,Y3: real,W: real,Z: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.82/6.07 => ( ( ord_less_eq_real @ W @ Z )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_less
% 5.82/6.07 thf(fact_2788_frac__less,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat,W: rat,Z: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.82/6.07 => ( ( ord_less_eq_rat @ W @ Z )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_less
% 5.82/6.07 thf(fact_2789_frac__less2,axiom,
% 5.82/6.07 ! [X2: real,Y3: real,W: real,Z: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.82/6.07 => ( ( ord_less_real @ W @ Z )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_less2
% 5.82/6.07 thf(fact_2790_frac__less2,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat,W: rat,Z: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.82/6.07 => ( ( ord_less_rat @ W @ Z )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % frac_less2
% 5.82/6.07 thf(fact_2791_divide__le__cancel,axiom,
% 5.82/6.07 ! [A2: real,C2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ ( divide_divide_real @ A2 @ C2 ) @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ord_less_eq_real @ A2 @ B2 ) )
% 5.82/6.07 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_eq_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_cancel
% 5.82/6.07 thf(fact_2792_divide__le__cancel,axiom,
% 5.82/6.07 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ C2 ) @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ord_less_eq_rat @ A2 @ B2 ) )
% 5.82/6.07 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_le_cancel
% 5.82/6.07 thf(fact_2793_divide__nonneg__neg,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_neg
% 5.82/6.07 thf(fact_2794_divide__nonneg__neg,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_neg
% 5.82/6.07 thf(fact_2795_divide__nonneg__pos,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_pos
% 5.82/6.07 thf(fact_2796_divide__nonneg__pos,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonneg_pos
% 5.82/6.07 thf(fact_2797_divide__nonpos__neg,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_neg
% 5.82/6.07 thf(fact_2798_divide__nonpos__neg,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_neg
% 5.82/6.07 thf(fact_2799_divide__nonpos__pos,axiom,
% 5.82/6.07 ! [X2: real,Y3: real] :
% 5.82/6.07 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_pos
% 5.82/6.07 thf(fact_2800_divide__nonpos__pos,axiom,
% 5.82/6.07 ! [X2: rat,Y3: rat] :
% 5.82/6.07 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_nonpos_pos
% 5.82/6.07 thf(fact_2801_divide__less__eq__1,axiom,
% 5.82/6.07 ! [B2: real,A2: real] :
% 5.82/6.07 ( ( ord_less_real @ ( divide_divide_real @ B2 @ A2 ) @ one_one_real )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 & ( ord_less_real @ B2 @ A2 ) )
% 5.82/6.07 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 & ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.07 | ( A2 = zero_zero_real ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq_1
% 5.82/6.07 thf(fact_2802_divide__less__eq__1,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ A2 ) @ one_one_rat )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 & ( ord_less_rat @ B2 @ A2 ) )
% 5.82/6.07 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 & ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.07 | ( A2 = zero_zero_rat ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq_1
% 5.82/6.07 thf(fact_2803_less__divide__eq__1,axiom,
% 5.82/6.07 ! [B2: real,A2: real] :
% 5.82/6.07 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.07 & ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.07 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.07 & ( ord_less_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq_1
% 5.82/6.07 thf(fact_2804_less__divide__eq__1,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.07 & ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.07 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.07 & ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq_1
% 5.82/6.07 thf(fact_2805_divide__less__eq,axiom,
% 5.82/6.07 ! [B2: real,C2: real,A2: real] :
% 5.82/6.07 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ord_less_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) )
% 5.82/6.07 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ zero_zero_real @ A2 ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq
% 5.82/6.07 thf(fact_2806_divide__less__eq,axiom,
% 5.82/6.07 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ord_less_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) )
% 5.82/6.07 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ zero_zero_rat @ A2 ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_less_eq
% 5.82/6.07 thf(fact_2807_less__divide__eq,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) )
% 5.82/6.07 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ord_less_real @ A2 @ zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq
% 5.82/6.07 thf(fact_2808_less__divide__eq,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) )
% 5.82/6.07 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) )
% 5.82/6.07 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ord_less_rat @ A2 @ zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % less_divide_eq
% 5.82/6.07 thf(fact_2809_neg__divide__less__eq,axiom,
% 5.82/6.07 ! [C2: real,B2: real,A2: real] :
% 5.82/6.07 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % neg_divide_less_eq
% 5.82/6.07 thf(fact_2810_neg__divide__less__eq,axiom,
% 5.82/6.07 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % neg_divide_less_eq
% 5.82/6.07 thf(fact_2811_neg__less__divide__eq,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ord_less_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % neg_less_divide_eq
% 5.82/6.07 thf(fact_2812_neg__less__divide__eq,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ord_less_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % neg_less_divide_eq
% 5.82/6.07 thf(fact_2813_pos__divide__less__eq,axiom,
% 5.82/6.07 ! [C2: real,B2: real,A2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( ord_less_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_divide_less_eq
% 5.82/6.07 thf(fact_2814_pos__divide__less__eq,axiom,
% 5.82/6.07 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.07 = ( ord_less_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_divide_less_eq
% 5.82/6.07 thf(fact_2815_pos__less__divide__eq,axiom,
% 5.82/6.07 ! [C2: real,A2: real,B2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ( ord_less_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.07 = ( ord_less_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_less_divide_eq
% 5.82/6.07 thf(fact_2816_pos__less__divide__eq,axiom,
% 5.82/6.07 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.07 = ( ord_less_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % pos_less_divide_eq
% 5.82/6.07 thf(fact_2817_mult__imp__div__pos__less,axiom,
% 5.82/6.07 ! [Y3: real,X2: real,Z: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y3 ) )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_imp_div_pos_less
% 5.82/6.07 thf(fact_2818_mult__imp__div__pos__less,axiom,
% 5.82/6.07 ! [Y3: rat,X2: rat,Z: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_imp_div_pos_less
% 5.82/6.07 thf(fact_2819_mult__imp__less__div__pos,axiom,
% 5.82/6.07 ! [Y3: real,Z: real,X2: real] :
% 5.82/6.07 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.07 => ( ( ord_less_real @ ( times_times_real @ Z @ Y3 ) @ X2 )
% 5.82/6.07 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_imp_less_div_pos
% 5.82/6.07 thf(fact_2820_mult__imp__less__div__pos,axiom,
% 5.82/6.07 ! [Y3: rat,Z: rat,X2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.07 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y3 ) @ X2 )
% 5.82/6.07 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % mult_imp_less_div_pos
% 5.82/6.07 thf(fact_2821_divide__strict__left__mono,axiom,
% 5.82/6.07 ! [B2: real,A2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ C2 @ A2 ) @ ( divide_divide_real @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_left_mono
% 5.82/6.07 thf(fact_2822_divide__strict__left__mono,axiom,
% 5.82/6.07 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A2 ) @ ( divide_divide_rat @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_left_mono
% 5.82/6.07 thf(fact_2823_divide__strict__left__mono__neg,axiom,
% 5.82/6.07 ! [A2: real,B2: real,C2: real] :
% 5.82/6.07 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.07 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.07 => ( ord_less_real @ ( divide_divide_real @ C2 @ A2 ) @ ( divide_divide_real @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_left_mono_neg
% 5.82/6.07 thf(fact_2824_divide__strict__left__mono__neg,axiom,
% 5.82/6.07 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.07 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.07 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.07 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.07 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A2 ) @ ( divide_divide_rat @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % divide_strict_left_mono_neg
% 5.82/6.07 thf(fact_2825_add__divide__eq__if__simps_I2_J,axiom,
% 5.82/6.07 ! [Z: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( ( Z = zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A2 @ Z ) @ B2 )
% 5.82/6.07 = B2 ) )
% 5.82/6.07 & ( ( Z != zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A2 @ Z ) @ B2 )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A2 @ ( times_times_complex @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_eq_if_simps(2)
% 5.82/6.07 thf(fact_2826_add__divide__eq__if__simps_I2_J,axiom,
% 5.82/6.07 ! [Z: real,A2: real,B2: real] :
% 5.82/6.07 ( ( ( Z = zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ ( divide_divide_real @ A2 @ Z ) @ B2 )
% 5.82/6.07 = B2 ) )
% 5.82/6.07 & ( ( Z != zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ ( divide_divide_real @ A2 @ Z ) @ B2 )
% 5.82/6.07 = ( divide_divide_real @ ( plus_plus_real @ A2 @ ( times_times_real @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_eq_if_simps(2)
% 5.82/6.07 thf(fact_2827_add__divide__eq__if__simps_I2_J,axiom,
% 5.82/6.07 ! [Z: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( ( Z = zero_zero_rat )
% 5.82/6.07 => ( ( plus_plus_rat @ ( divide_divide_rat @ A2 @ Z ) @ B2 )
% 5.82/6.07 = B2 ) )
% 5.82/6.07 & ( ( Z != zero_zero_rat )
% 5.82/6.07 => ( ( plus_plus_rat @ ( divide_divide_rat @ A2 @ Z ) @ B2 )
% 5.82/6.07 = ( divide_divide_rat @ ( plus_plus_rat @ A2 @ ( times_times_rat @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_eq_if_simps(2)
% 5.82/6.07 thf(fact_2828_add__divide__eq__if__simps_I1_J,axiom,
% 5.82/6.07 ! [Z: complex,A2: complex,B2: complex] :
% 5.82/6.07 ( ( ( Z = zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ A2 @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.82/6.07 = A2 ) )
% 5.82/6.07 & ( ( Z != zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ A2 @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A2 @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_eq_if_simps(1)
% 5.82/6.07 thf(fact_2829_add__divide__eq__if__simps_I1_J,axiom,
% 5.82/6.07 ! [Z: real,A2: real,B2: real] :
% 5.82/6.07 ( ( ( Z = zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ A2 @ ( divide_divide_real @ B2 @ Z ) )
% 5.82/6.07 = A2 ) )
% 5.82/6.07 & ( ( Z != zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ A2 @ ( divide_divide_real @ B2 @ Z ) )
% 5.82/6.07 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A2 @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_eq_if_simps(1)
% 5.82/6.07 thf(fact_2830_add__divide__eq__if__simps_I1_J,axiom,
% 5.82/6.07 ! [Z: rat,A2: rat,B2: rat] :
% 5.82/6.07 ( ( ( Z = zero_zero_rat )
% 5.82/6.07 => ( ( plus_plus_rat @ A2 @ ( divide_divide_rat @ B2 @ Z ) )
% 5.82/6.07 = A2 ) )
% 5.82/6.07 & ( ( Z != zero_zero_rat )
% 5.82/6.07 => ( ( plus_plus_rat @ A2 @ ( divide_divide_rat @ B2 @ Z ) )
% 5.82/6.07 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_divide_eq_if_simps(1)
% 5.82/6.07 thf(fact_2831_add__frac__eq,axiom,
% 5.82/6.07 ! [Y3: complex,Z: complex,X2: complex,W: complex] :
% 5.82/6.07 ( ( Y3 != zero_zero_complex )
% 5.82/6.07 => ( ( Z != zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_frac_eq
% 5.82/6.07 thf(fact_2832_add__frac__eq,axiom,
% 5.82/6.07 ! [Y3: real,Z: real,X2: real,W: real] :
% 5.82/6.07 ( ( Y3 != zero_zero_real )
% 5.82/6.07 => ( ( Z != zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.82/6.07 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_frac_eq
% 5.82/6.07 thf(fact_2833_add__frac__eq,axiom,
% 5.82/6.07 ! [Y3: rat,Z: rat,X2: rat,W: rat] :
% 5.82/6.07 ( ( Y3 != zero_zero_rat )
% 5.82/6.07 => ( ( Z != zero_zero_rat )
% 5.82/6.07 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.82/6.07 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_frac_eq
% 5.82/6.07 thf(fact_2834_add__frac__num,axiom,
% 5.82/6.07 ! [Y3: complex,X2: complex,Z: complex] :
% 5.82/6.07 ( ( Y3 != zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ Z )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_frac_num
% 5.82/6.07 thf(fact_2835_add__frac__num,axiom,
% 5.82/6.07 ! [Y3: real,X2: real,Z: real] :
% 5.82/6.07 ( ( Y3 != zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y3 ) @ Z )
% 5.82/6.07 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_frac_num
% 5.82/6.07 thf(fact_2836_add__frac__num,axiom,
% 5.82/6.07 ! [Y3: rat,X2: rat,Z: rat] :
% 5.82/6.07 ( ( Y3 != zero_zero_rat )
% 5.82/6.07 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ Z )
% 5.82/6.07 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_frac_num
% 5.82/6.07 thf(fact_2837_add__num__frac,axiom,
% 5.82/6.07 ! [Y3: complex,Z: complex,X2: complex] :
% 5.82/6.07 ( ( Y3 != zero_zero_complex )
% 5.82/6.07 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y3 ) )
% 5.82/6.07 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.82/6.07
% 5.82/6.07 % add_num_frac
% 5.82/6.07 thf(fact_2838_add__num__frac,axiom,
% 5.82/6.07 ! [Y3: real,Z: real,X2: real] :
% 5.82/6.07 ( ( Y3 != zero_zero_real )
% 5.82/6.07 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y3 ) )
% 5.82/6.08 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_num_frac
% 5.82/6.08 thf(fact_2839_add__num__frac,axiom,
% 5.82/6.08 ! [Y3: rat,Z: rat,X2: rat] :
% 5.82/6.08 ( ( Y3 != zero_zero_rat )
% 5.82/6.08 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y3 ) )
% 5.82/6.08 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_num_frac
% 5.82/6.08 thf(fact_2840_add__divide__eq__iff,axiom,
% 5.82/6.08 ! [Z: complex,X2: complex,Y3: complex] :
% 5.82/6.08 ( ( Z != zero_zero_complex )
% 5.82/6.08 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 5.82/6.08 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_divide_eq_iff
% 5.82/6.08 thf(fact_2841_add__divide__eq__iff,axiom,
% 5.82/6.08 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.08 ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y3 @ Z ) )
% 5.82/6.08 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_divide_eq_iff
% 5.82/6.08 thf(fact_2842_add__divide__eq__iff,axiom,
% 5.82/6.08 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.08 ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y3 @ Z ) )
% 5.82/6.08 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_divide_eq_iff
% 5.82/6.08 thf(fact_2843_divide__add__eq__iff,axiom,
% 5.82/6.08 ! [Z: complex,X2: complex,Y3: complex] :
% 5.82/6.08 ( ( Z != zero_zero_complex )
% 5.82/6.08 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y3 )
% 5.82/6.08 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_add_eq_iff
% 5.82/6.08 thf(fact_2844_divide__add__eq__iff,axiom,
% 5.82/6.08 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.08 ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y3 )
% 5.82/6.08 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_add_eq_iff
% 5.82/6.08 thf(fact_2845_divide__add__eq__iff,axiom,
% 5.82/6.08 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.08 ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y3 )
% 5.82/6.08 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_add_eq_iff
% 5.82/6.08 thf(fact_2846_gt__half__sum,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A2 @ B2 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % gt_half_sum
% 5.82/6.08 thf(fact_2847_gt__half__sum,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A2 @ B2 ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % gt_half_sum
% 5.82/6.08 thf(fact_2848_less__half__sum,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_real @ A2 @ ( divide_divide_real @ ( plus_plus_real @ A2 @ B2 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_half_sum
% 5.82/6.08 thf(fact_2849_less__half__sum,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_rat @ A2 @ ( divide_divide_rat @ ( plus_plus_rat @ A2 @ B2 ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_half_sum
% 5.82/6.08 thf(fact_2850_add__divide__eq__if__simps_I4_J,axiom,
% 5.82/6.08 ! [Z: complex,A2: complex,B2: complex] :
% 5.82/6.08 ( ( ( Z = zero_zero_complex )
% 5.82/6.08 => ( ( minus_minus_complex @ A2 @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.82/6.08 = A2 ) )
% 5.82/6.08 & ( ( Z != zero_zero_complex )
% 5.82/6.08 => ( ( minus_minus_complex @ A2 @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.82/6.08 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A2 @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_divide_eq_if_simps(4)
% 5.82/6.08 thf(fact_2851_add__divide__eq__if__simps_I4_J,axiom,
% 5.82/6.08 ! [Z: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ( Z = zero_zero_real )
% 5.82/6.08 => ( ( minus_minus_real @ A2 @ ( divide_divide_real @ B2 @ Z ) )
% 5.82/6.08 = A2 ) )
% 5.82/6.08 & ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( minus_minus_real @ A2 @ ( divide_divide_real @ B2 @ Z ) )
% 5.82/6.08 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A2 @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_divide_eq_if_simps(4)
% 5.82/6.08 thf(fact_2852_add__divide__eq__if__simps_I4_J,axiom,
% 5.82/6.08 ! [Z: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ( Z = zero_zero_rat )
% 5.82/6.08 => ( ( minus_minus_rat @ A2 @ ( divide_divide_rat @ B2 @ Z ) )
% 5.82/6.08 = A2 ) )
% 5.82/6.08 & ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( minus_minus_rat @ A2 @ ( divide_divide_rat @ B2 @ Z ) )
% 5.82/6.08 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A2 @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_divide_eq_if_simps(4)
% 5.82/6.08 thf(fact_2853_diff__frac__eq,axiom,
% 5.82/6.08 ! [Y3: complex,Z: complex,X2: complex,W: complex] :
% 5.82/6.08 ( ( Y3 != zero_zero_complex )
% 5.82/6.08 => ( ( Z != zero_zero_complex )
% 5.82/6.08 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.82/6.08 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_frac_eq
% 5.82/6.08 thf(fact_2854_diff__frac__eq,axiom,
% 5.82/6.08 ! [Y3: real,Z: real,X2: real,W: real] :
% 5.82/6.08 ( ( Y3 != zero_zero_real )
% 5.82/6.08 => ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.82/6.08 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_frac_eq
% 5.82/6.08 thf(fact_2855_diff__frac__eq,axiom,
% 5.82/6.08 ! [Y3: rat,Z: rat,X2: rat,W: rat] :
% 5.82/6.08 ( ( Y3 != zero_zero_rat )
% 5.82/6.08 => ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.82/6.08 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_frac_eq
% 5.82/6.08 thf(fact_2856_diff__divide__eq__iff,axiom,
% 5.82/6.08 ! [Z: complex,X2: complex,Y3: complex] :
% 5.82/6.08 ( ( Z != zero_zero_complex )
% 5.82/6.08 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 5.82/6.08 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_divide_eq_iff
% 5.82/6.08 thf(fact_2857_diff__divide__eq__iff,axiom,
% 5.82/6.08 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.08 ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y3 @ Z ) )
% 5.82/6.08 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_divide_eq_iff
% 5.82/6.08 thf(fact_2858_diff__divide__eq__iff,axiom,
% 5.82/6.08 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.08 ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y3 @ Z ) )
% 5.82/6.08 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_divide_eq_iff
% 5.82/6.08 thf(fact_2859_divide__diff__eq__iff,axiom,
% 5.82/6.08 ! [Z: complex,X2: complex,Y3: complex] :
% 5.82/6.08 ( ( Z != zero_zero_complex )
% 5.82/6.08 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y3 )
% 5.82/6.08 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_diff_eq_iff
% 5.82/6.08 thf(fact_2860_divide__diff__eq__iff,axiom,
% 5.82/6.08 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.08 ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y3 )
% 5.82/6.08 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_diff_eq_iff
% 5.82/6.08 thf(fact_2861_divide__diff__eq__iff,axiom,
% 5.82/6.08 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.08 ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y3 )
% 5.82/6.08 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_diff_eq_iff
% 5.82/6.08 thf(fact_2862_field__le__mult__one__interval,axiom,
% 5.82/6.08 ! [X2: real,Y3: real] :
% 5.82/6.08 ( ! [Z2: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.82/6.08 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.82/6.08 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X2 ) @ Y3 ) ) )
% 5.82/6.08 => ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.08
% 5.82/6.08 % field_le_mult_one_interval
% 5.82/6.08 thf(fact_2863_field__le__mult__one__interval,axiom,
% 5.82/6.08 ! [X2: rat,Y3: rat] :
% 5.82/6.08 ( ! [Z2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.82/6.08 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.82/6.08 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X2 ) @ Y3 ) ) )
% 5.82/6.08 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.08
% 5.82/6.08 % field_le_mult_one_interval
% 5.82/6.08 thf(fact_2864_divide__le__eq__1,axiom,
% 5.82/6.08 ! [B2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A2 ) @ one_one_real )
% 5.82/6.08 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.08 & ( ord_less_eq_real @ B2 @ A2 ) )
% 5.82/6.08 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.08 & ( ord_less_eq_real @ A2 @ B2 ) )
% 5.82/6.08 | ( A2 = zero_zero_real ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_le_eq_1
% 5.82/6.08 thf(fact_2865_divide__le__eq__1,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ A2 ) @ one_one_rat )
% 5.82/6.08 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.08 & ( ord_less_eq_rat @ B2 @ A2 ) )
% 5.82/6.08 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.08 & ( ord_less_eq_rat @ A2 @ B2 ) )
% 5.82/6.08 | ( A2 = zero_zero_rat ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_le_eq_1
% 5.82/6.08 thf(fact_2866_le__divide__eq__1,axiom,
% 5.82/6.08 ! [B2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A2 ) )
% 5.82/6.08 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.08 & ( ord_less_eq_real @ A2 @ B2 ) )
% 5.82/6.08 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.08 & ( ord_less_eq_real @ B2 @ A2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_divide_eq_1
% 5.82/6.08 thf(fact_2867_le__divide__eq__1,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A2 ) )
% 5.82/6.08 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.08 & ( ord_less_eq_rat @ A2 @ B2 ) )
% 5.82/6.08 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.08 & ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_divide_eq_1
% 5.82/6.08 thf(fact_2868_divide__le__eq,axiom,
% 5.82/6.08 ! [B2: real,C2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.08 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ord_less_eq_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) )
% 5.82/6.08 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) )
% 5.82/6.08 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_le_eq
% 5.82/6.08 thf(fact_2869_divide__le__eq,axiom,
% 5.82/6.08 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.08 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) )
% 5.82/6.08 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) )
% 5.82/6.08 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_le_eq
% 5.82/6.08 thf(fact_2870_le__divide__eq,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.08 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) )
% 5.82/6.08 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ord_less_eq_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) )
% 5.82/6.08 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_divide_eq
% 5.82/6.08 thf(fact_2871_le__divide__eq,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.08 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) )
% 5.82/6.08 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) )
% 5.82/6.08 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_divide_eq
% 5.82/6.08 thf(fact_2872_divide__left__mono,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A2 ) @ ( divide_divide_real @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_left_mono
% 5.82/6.08 thf(fact_2873_divide__left__mono,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A2 ) @ ( divide_divide_rat @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_left_mono
% 5.82/6.08 thf(fact_2874_neg__divide__le__eq,axiom,
% 5.82/6.08 ! [C2: real,B2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.08 = ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % neg_divide_le_eq
% 5.82/6.08 thf(fact_2875_neg__divide__le__eq,axiom,
% 5.82/6.08 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.08 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % neg_divide_le_eq
% 5.82/6.08 thf(fact_2876_neg__le__divide__eq,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % neg_le_divide_eq
% 5.82/6.08 thf(fact_2877_neg__le__divide__eq,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % neg_le_divide_eq
% 5.82/6.08 thf(fact_2878_pos__divide__le__eq,axiom,
% 5.82/6.08 ! [C2: real,B2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C2 ) @ A2 )
% 5.82/6.08 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % pos_divide_le_eq
% 5.82/6.08 thf(fact_2879_pos__divide__le__eq,axiom,
% 5.82/6.08 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.08 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % pos_divide_le_eq
% 5.82/6.08 thf(fact_2880_pos__le__divide__eq,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ ( times_times_real @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % pos_le_divide_eq
% 5.82/6.08 thf(fact_2881_pos__le__divide__eq,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % pos_le_divide_eq
% 5.82/6.08 thf(fact_2882_mult__imp__div__pos__le,axiom,
% 5.82/6.08 ! [Y3: real,X2: real,Z: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.08 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y3 ) )
% 5.82/6.08 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult_imp_div_pos_le
% 5.82/6.08 thf(fact_2883_mult__imp__div__pos__le,axiom,
% 5.82/6.08 ! [Y3: rat,X2: rat,Z: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) )
% 5.82/6.08 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult_imp_div_pos_le
% 5.82/6.08 thf(fact_2884_mult__imp__le__div__pos,axiom,
% 5.82/6.08 ! [Y3: real,Z: real,X2: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.08 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y3 ) @ X2 )
% 5.82/6.08 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult_imp_le_div_pos
% 5.82/6.08 thf(fact_2885_mult__imp__le__div__pos,axiom,
% 5.82/6.08 ! [Y3: rat,Z: rat,X2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y3 ) @ X2 )
% 5.82/6.08 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult_imp_le_div_pos
% 5.82/6.08 thf(fact_2886_divide__left__mono__neg,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.08 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A2 ) @ ( divide_divide_real @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_left_mono_neg
% 5.82/6.08 thf(fact_2887_divide__left__mono__neg,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.08 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A2 ) @ ( divide_divide_rat @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % divide_left_mono_neg
% 5.82/6.08 thf(fact_2888_frac__le__eq,axiom,
% 5.82/6.08 ! [Y3: real,Z: real,X2: real,W: real] :
% 5.82/6.08 ( ( Y3 != zero_zero_real )
% 5.82/6.08 => ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.82/6.08 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % frac_le_eq
% 5.82/6.08 thf(fact_2889_frac__le__eq,axiom,
% 5.82/6.08 ! [Y3: rat,Z: rat,X2: rat,W: rat] :
% 5.82/6.08 ( ( Y3 != zero_zero_rat )
% 5.82/6.08 => ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.82/6.08 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % frac_le_eq
% 5.82/6.08 thf(fact_2890_frac__less__eq,axiom,
% 5.82/6.08 ! [Y3: real,Z: real,X2: real,W: real] :
% 5.82/6.08 ( ( Y3 != zero_zero_real )
% 5.82/6.08 => ( ( Z != zero_zero_real )
% 5.82/6.08 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.82/6.08 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % frac_less_eq
% 5.82/6.08 thf(fact_2891_frac__less__eq,axiom,
% 5.82/6.08 ! [Y3: rat,Z: rat,X2: rat,W: rat] :
% 5.82/6.08 ( ( Y3 != zero_zero_rat )
% 5.82/6.08 => ( ( Z != zero_zero_rat )
% 5.82/6.08 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.82/6.08 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % frac_less_eq
% 5.82/6.08 thf(fact_2892_less__log__of__power,axiom,
% 5.82/6.08 ! [B2: real,N: nat,M: real] :
% 5.82/6.08 ( ( ord_less_real @ ( power_power_real @ B2 @ N ) @ M )
% 5.82/6.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.08 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ M ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_log_of_power
% 5.82/6.08 thf(fact_2893_log__of__power__eq,axiom,
% 5.82/6.08 ! [M: nat,B2: real,N: nat] :
% 5.82/6.08 ( ( ( semiri5074537144036343181t_real @ M )
% 5.82/6.08 = ( power_power_real @ B2 @ N ) )
% 5.82/6.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.08 => ( ( semiri5074537144036343181t_real @ N )
% 5.82/6.08 = ( log @ B2 @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % log_of_power_eq
% 5.82/6.08 thf(fact_2894_scaling__mono,axiom,
% 5.82/6.08 ! [U: real,V: real,R2: real,S2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ U @ V )
% 5.82/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % scaling_mono
% 5.82/6.08 thf(fact_2895_scaling__mono,axiom,
% 5.82/6.08 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ U @ V )
% 5.82/6.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % scaling_mono
% 5.82/6.08 thf(fact_2896_le__log__of__power,axiom,
% 5.82/6.08 ! [B2: real,N: nat,M: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( power_power_real @ B2 @ N ) @ M )
% 5.82/6.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ M ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_log_of_power
% 5.82/6.08 thf(fact_2897_log2__of__power__eq,axiom,
% 5.82/6.08 ! [M: nat,N: nat] :
% 5.82/6.08 ( ( M
% 5.82/6.08 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.08 => ( ( semiri5074537144036343181t_real @ N )
% 5.82/6.08 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % log2_of_power_eq
% 5.82/6.08 thf(fact_2898_log__of__power__less,axiom,
% 5.82/6.08 ! [M: nat,B2: real,N: nat] :
% 5.82/6.08 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.82/6.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.08 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.08 => ( ord_less_real @ ( log @ B2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % log_of_power_less
% 5.82/6.08 thf(fact_2899_log__of__power__le,axiom,
% 5.82/6.08 ! [M: nat,B2: real,N: nat] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.82/6.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.08 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.08 => ( ord_less_eq_real @ ( log @ B2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % log_of_power_le
% 5.82/6.08 thf(fact_2900_less__log2__of__power,axiom,
% 5.82/6.08 ! [N: nat,M: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.82/6.08 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_log2_of_power
% 5.82/6.08 thf(fact_2901_le__log2__of__power,axiom,
% 5.82/6.08 ! [N: nat,M: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.82/6.08 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_log2_of_power
% 5.82/6.08 thf(fact_2902_Tb__T__vebt__buildupi_H,axiom,
% 5.82/6.08 ! [N: nat] : ( ord_less_eq_int @ ( vEBT_V9176841429113362141ildupi @ N ) @ ( minus_minus_int @ ( vEBT_VEBT_Tb @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % Tb_T_vebt_buildupi'
% 5.82/6.08 thf(fact_2903_vebt__buildupi__rule,axiom,
% 5.82/6.08 ! [N: nat] : ( time_htt_VEBT_VEBTi @ ( pure_assn @ ( ord_less_nat @ zero_zero_nat @ N ) ) @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_buildupi_rule
% 5.82/6.08 thf(fact_2904_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 5.82/6.08 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.08 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.08 = ( plus_plus_nat @ one_one_nat
% 5.82/6.08 @ ( if_nat @ ( X2 = Mi ) @ zero_zero_nat
% 5.82/6.08 @ ( if_nat @ ( X2 = Ma ) @ zero_zero_nat
% 5.82/6.08 @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ zero_zero_nat
% 5.82/6.08 @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ zero_zero_nat
% 5.82/6.08 @ ( if_nat
% 5.82/6.08 @ ( ( ord_less_nat @ Mi @ X2 )
% 5.82/6.08 & ( ord_less_nat @ X2 @ Ma ) )
% 5.82/6.08 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.82/6.08 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 5.82/6.08 thf(fact_2905_diff__add__zero,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.08 = zero_zero_nat ) ).
% 5.82/6.08
% 5.82/6.08 % diff_add_zero
% 5.82/6.08 thf(fact_2906_diff__gt__0__iff__gt,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_real @ B2 @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_gt_0_iff_gt
% 5.82/6.08 thf(fact_2907_diff__gt__0__iff__gt,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_rat @ B2 @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_gt_0_iff_gt
% 5.82/6.08 thf(fact_2908_diff__gt__0__iff__gt,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_int @ B2 @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_gt_0_iff_gt
% 5.82/6.08 thf(fact_2909_diff__ge__0__iff__ge,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ B2 @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_ge_0_iff_ge
% 5.82/6.08 thf(fact_2910_diff__ge__0__iff__ge,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_ge_0_iff_ge
% 5.82/6.08 thf(fact_2911_diff__ge__0__iff__ge,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_ge_0_iff_ge
% 5.82/6.08 thf(fact_2912_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,
% 5.82/6.08 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.08 ( ( ( vEBT_V1232361888498592333_e_t_e @ X2 @ Xa )
% 5.82/6.08 = Y3 )
% 5.82/6.08 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.08 => ( ( Xa = zero_zero_nat )
% 5.82/6.08 => ( Y3 != one_one_nat ) ) )
% 5.82/6.08 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.08 => ( ( Xa
% 5.82/6.08 = ( suc @ zero_zero_nat ) )
% 5.82/6.08 => ( Y3 != one_one_nat ) ) )
% 5.82/6.08 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.08 => ( ? [N3: nat] :
% 5.82/6.08 ( Xa
% 5.82/6.08 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.08 => ( Y3 != one_one_nat ) ) )
% 5.82/6.08 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.08 => ( Y3 != one_one_nat ) )
% 5.82/6.08 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 5.82/6.08 => ( Y3 != one_one_nat ) )
% 5.82/6.08 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 5.82/6.08 => ( Y3 != one_one_nat ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.08 ( ( X2
% 5.82/6.08 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.08 => ~ ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.08 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.08 => ( Y3 = one_one_nat ) )
% 5.82/6.08 & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.08 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.08 => ( ( ( ( Xa = Mi2 )
% 5.82/6.08 & ( Xa = Ma2 ) )
% 5.82/6.08 => ( Y3 = one_one_nat ) )
% 5.82/6.08 & ( ~ ( ( Xa = Mi2 )
% 5.82/6.08 & ( Xa = Ma2 ) )
% 5.82/6.08 => ( Y3
% 5.82/6.08 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.elims
% 5.82/6.08 thf(fact_2913_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ A2 ) )
% 5.82/6.08 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_less_double_add_iff_zero_less_single_add
% 5.82/6.08 thf(fact_2914_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 5.82/6.08 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_less_double_add_iff_zero_less_single_add
% 5.82/6.08 thf(fact_2915_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 5.82/6.08 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_less_double_add_iff_zero_less_single_add
% 5.82/6.08 thf(fact_2916_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ A2 @ A2 ) @ zero_zero_real )
% 5.82/6.08 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_add_less_zero_iff_single_add_less_zero
% 5.82/6.08 thf(fact_2917_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 5.82/6.08 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_add_less_zero_iff_single_add_less_zero
% 5.82/6.08 thf(fact_2918_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 5.82/6.08 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_add_less_zero_iff_single_add_less_zero
% 5.82/6.08 thf(fact_2919_Leaf__0__not,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A2 @ B2 ) @ zero_zero_nat ) ).
% 5.82/6.08
% 5.82/6.08 % Leaf_0_not
% 5.82/6.08 thf(fact_2920_deg1Leaf,axiom,
% 5.82/6.08 ! [T: vEBT_VEBT] :
% 5.82/6.08 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.82/6.08 = ( ? [A5: $o,B6: $o] :
% 5.82/6.08 ( T
% 5.82/6.08 = ( vEBT_Leaf @ A5 @ B6 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % deg1Leaf
% 5.82/6.08 thf(fact_2921_deg__1__Leaf,axiom,
% 5.82/6.08 ! [T: vEBT_VEBT] :
% 5.82/6.08 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.82/6.08 => ? [A3: $o,B3: $o] :
% 5.82/6.08 ( T
% 5.82/6.08 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % deg_1_Leaf
% 5.82/6.08 thf(fact_2922_deg__1__Leafy,axiom,
% 5.82/6.08 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.08 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.08 => ( ( N = one_one_nat )
% 5.82/6.08 => ? [A3: $o,B3: $o] :
% 5.82/6.08 ( T
% 5.82/6.08 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % deg_1_Leafy
% 5.82/6.08 thf(fact_2923_Tbuildupi__buildupi_H,axiom,
% 5.82/6.08 ! [N: nat] :
% 5.82/6.08 ( ( semiri1314217659103216013at_int @ ( vEBT_V441764108873111860ildupi @ N ) )
% 5.82/6.08 = ( vEBT_V9176841429113362141ildupi @ N ) ) ).
% 5.82/6.08
% 5.82/6.08 % Tbuildupi_buildupi'
% 5.82/6.08 thf(fact_2924_add__left__cancel,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_real @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_cancel
% 5.82/6.08 thf(fact_2925_add__left__cancel,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_rat @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_cancel
% 5.82/6.08 thf(fact_2926_add__left__cancel,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_nat @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_cancel
% 5.82/6.08 thf(fact_2927_add__left__cancel,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_int @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_cancel
% 5.82/6.08 thf(fact_2928_add__right__cancel,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_real @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_cancel
% 5.82/6.08 thf(fact_2929_add__right__cancel,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_rat @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_cancel
% 5.82/6.08 thf(fact_2930_add__right__cancel,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_nat @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_cancel
% 5.82/6.08 thf(fact_2931_add__right__cancel,axiom,
% 5.82/6.08 ! [B2: int,A2: int,C2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_int @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_cancel
% 5.82/6.08 thf(fact_2932_max__enat__simps_I2_J,axiom,
% 5.82/6.08 ! [Q3: extended_enat] :
% 5.82/6.08 ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.82/6.08 = Q3 ) ).
% 5.82/6.08
% 5.82/6.08 % max_enat_simps(2)
% 5.82/6.08 thf(fact_2933_max__enat__simps_I3_J,axiom,
% 5.82/6.08 ! [Q3: extended_enat] :
% 5.82/6.08 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.82/6.08 = Q3 ) ).
% 5.82/6.08
% 5.82/6.08 % max_enat_simps(3)
% 5.82/6.08 thf(fact_2934_le__zero__eq,axiom,
% 5.82/6.08 ! [N: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.82/6.08 = ( N = zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_zero_eq
% 5.82/6.08 thf(fact_2935_not__gr__zero,axiom,
% 5.82/6.08 ! [N: nat] :
% 5.82/6.08 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.82/6.08 = ( N = zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % not_gr_zero
% 5.82/6.08 thf(fact_2936_add_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( plus_plus_complex @ A2 @ zero_zero_complex )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_neutral
% 5.82/6.08 thf(fact_2937_add_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( plus_plus_real @ A2 @ zero_zero_real )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_neutral
% 5.82/6.08 thf(fact_2938_add_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_neutral
% 5.82/6.08 thf(fact_2939_add_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_neutral
% 5.82/6.08 thf(fact_2940_add_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_neutral
% 5.82/6.08 thf(fact_2941_double__zero__sym,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( zero_zero_real
% 5.82/6.08 = ( plus_plus_real @ A2 @ A2 ) )
% 5.82/6.08 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_zero_sym
% 5.82/6.08 thf(fact_2942_double__zero__sym,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( zero_zero_rat
% 5.82/6.08 = ( plus_plus_rat @ A2 @ A2 ) )
% 5.82/6.08 = ( A2 = zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_zero_sym
% 5.82/6.08 thf(fact_2943_double__zero__sym,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( zero_zero_int
% 5.82/6.08 = ( plus_plus_int @ A2 @ A2 ) )
% 5.82/6.08 = ( A2 = zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_zero_sym
% 5.82/6.08 thf(fact_2944_add__cancel__left__left,axiom,
% 5.82/6.08 ! [B2: complex,A2: complex] :
% 5.82/6.08 ( ( ( plus_plus_complex @ B2 @ A2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_complex ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_left
% 5.82/6.08 thf(fact_2945_add__cancel__left__left,axiom,
% 5.82/6.08 ! [B2: real,A2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ B2 @ A2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_left
% 5.82/6.08 thf(fact_2946_add__cancel__left__left,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ B2 @ A2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_left
% 5.82/6.08 thf(fact_2947_add__cancel__left__left,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ B2 @ A2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_left
% 5.82/6.08 thf(fact_2948_add__cancel__left__left,axiom,
% 5.82/6.08 ! [B2: int,A2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ B2 @ A2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_left
% 5.82/6.08 thf(fact_2949_add__cancel__left__right,axiom,
% 5.82/6.08 ! [A2: complex,B2: complex] :
% 5.82/6.08 ( ( ( plus_plus_complex @ A2 @ B2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_complex ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_right
% 5.82/6.08 thf(fact_2950_add__cancel__left__right,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ A2 @ B2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_right
% 5.82/6.08 thf(fact_2951_add__cancel__left__right,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ A2 @ B2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_right
% 5.82/6.08 thf(fact_2952_add__cancel__left__right,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ A2 @ B2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_right
% 5.82/6.08 thf(fact_2953_add__cancel__left__right,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ A2 @ B2 )
% 5.82/6.08 = A2 )
% 5.82/6.08 = ( B2 = zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_left_right
% 5.82/6.08 thf(fact_2954_add__cancel__right__left,axiom,
% 5.82/6.08 ! [A2: complex,B2: complex] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_complex @ B2 @ A2 ) )
% 5.82/6.08 = ( B2 = zero_zero_complex ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_left
% 5.82/6.08 thf(fact_2955_add__cancel__right__left,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_real @ B2 @ A2 ) )
% 5.82/6.08 = ( B2 = zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_left
% 5.82/6.08 thf(fact_2956_add__cancel__right__left,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_rat @ B2 @ A2 ) )
% 5.82/6.08 = ( B2 = zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_left
% 5.82/6.08 thf(fact_2957_add__cancel__right__left,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_nat @ B2 @ A2 ) )
% 5.82/6.08 = ( B2 = zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_left
% 5.82/6.08 thf(fact_2958_add__cancel__right__left,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_int @ B2 @ A2 ) )
% 5.82/6.08 = ( B2 = zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_left
% 5.82/6.08 thf(fact_2959_add__cancel__right__right,axiom,
% 5.82/6.08 ! [A2: complex,B2: complex] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_complex @ A2 @ B2 ) )
% 5.82/6.08 = ( B2 = zero_zero_complex ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_right
% 5.82/6.08 thf(fact_2960_add__cancel__right__right,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.08 = ( B2 = zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_right
% 5.82/6.08 thf(fact_2961_add__cancel__right__right,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.08 = ( B2 = zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_right
% 5.82/6.08 thf(fact_2962_add__cancel__right__right,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.08 = ( B2 = zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_right
% 5.82/6.08 thf(fact_2963_add__cancel__right__right,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( A2
% 5.82/6.08 = ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.08 = ( B2 = zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_cancel_right_right
% 5.82/6.08 thf(fact_2964_add__eq__0__iff__both__eq__0,axiom,
% 5.82/6.08 ! [X2: nat,Y3: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.82/6.08 = zero_zero_nat )
% 5.82/6.08 = ( ( X2 = zero_zero_nat )
% 5.82/6.08 & ( Y3 = zero_zero_nat ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_eq_0_iff_both_eq_0
% 5.82/6.08 thf(fact_2965_zero__eq__add__iff__both__eq__0,axiom,
% 5.82/6.08 ! [X2: nat,Y3: nat] :
% 5.82/6.08 ( ( zero_zero_nat
% 5.82/6.08 = ( plus_plus_nat @ X2 @ Y3 ) )
% 5.82/6.08 = ( ( X2 = zero_zero_nat )
% 5.82/6.08 & ( Y3 = zero_zero_nat ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_eq_add_iff_both_eq_0
% 5.82/6.08 thf(fact_2966_add__0,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( plus_plus_complex @ zero_zero_complex @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_0
% 5.82/6.08 thf(fact_2967_add__0,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( plus_plus_real @ zero_zero_real @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_0
% 5.82/6.08 thf(fact_2968_add__0,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_0
% 5.82/6.08 thf(fact_2969_add__0,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_0
% 5.82/6.08 thf(fact_2970_add__0,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_0
% 5.82/6.08 thf(fact_2971_add__le__cancel__left,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_left
% 5.82/6.08 thf(fact_2972_add__le__cancel__left,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_left
% 5.82/6.08 thf(fact_2973_add__le__cancel__left,axiom,
% 5.82/6.08 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_left
% 5.82/6.08 thf(fact_2974_add__le__cancel__left,axiom,
% 5.82/6.08 ! [C2: int,A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_left
% 5.82/6.08 thf(fact_2975_add__le__cancel__right,axiom,
% 5.82/6.08 ! [A2: real,C2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_right
% 5.82/6.08 thf(fact_2976_add__le__cancel__right,axiom,
% 5.82/6.08 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_right
% 5.82/6.08 thf(fact_2977_add__le__cancel__right,axiom,
% 5.82/6.08 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_right
% 5.82/6.08 thf(fact_2978_add__le__cancel__right,axiom,
% 5.82/6.08 ! [A2: int,C2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_cancel_right
% 5.82/6.08 thf(fact_2979_add__less__cancel__right,axiom,
% 5.82/6.08 ! [A2: real,C2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_right
% 5.82/6.08 thf(fact_2980_add__less__cancel__right,axiom,
% 5.82/6.08 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_right
% 5.82/6.08 thf(fact_2981_add__less__cancel__right,axiom,
% 5.82/6.08 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_right
% 5.82/6.08 thf(fact_2982_add__less__cancel__right,axiom,
% 5.82/6.08 ! [A2: int,C2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.08 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_right
% 5.82/6.08 thf(fact_2983_add__less__cancel__left,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_left
% 5.82/6.08 thf(fact_2984_add__less__cancel__left,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_left
% 5.82/6.08 thf(fact_2985_add__less__cancel__left,axiom,
% 5.82/6.08 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_left
% 5.82/6.08 thf(fact_2986_add__less__cancel__left,axiom,
% 5.82/6.08 ! [C2: int,A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) )
% 5.82/6.08 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_cancel_left
% 5.82/6.08 thf(fact_2987_diff__self,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( minus_minus_complex @ A2 @ A2 )
% 5.82/6.08 = zero_zero_complex ) ).
% 5.82/6.08
% 5.82/6.08 % diff_self
% 5.82/6.08 thf(fact_2988_diff__self,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( minus_minus_real @ A2 @ A2 )
% 5.82/6.08 = zero_zero_real ) ).
% 5.82/6.08
% 5.82/6.08 % diff_self
% 5.82/6.08 thf(fact_2989_diff__self,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ A2 @ A2 )
% 5.82/6.08 = zero_zero_rat ) ).
% 5.82/6.08
% 5.82/6.08 % diff_self
% 5.82/6.08 thf(fact_2990_diff__self,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( minus_minus_int @ A2 @ A2 )
% 5.82/6.08 = zero_zero_int ) ).
% 5.82/6.08
% 5.82/6.08 % diff_self
% 5.82/6.08 thf(fact_2991_diff__0__right,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( minus_minus_complex @ A2 @ zero_zero_complex )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_0_right
% 5.82/6.08 thf(fact_2992_diff__0__right,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( minus_minus_real @ A2 @ zero_zero_real )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_0_right
% 5.82/6.08 thf(fact_2993_diff__0__right,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_0_right
% 5.82/6.08 thf(fact_2994_diff__0__right,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_0_right
% 5.82/6.08 thf(fact_2995_zero__diff,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ zero_zero_nat @ A2 )
% 5.82/6.08 = zero_zero_nat ) ).
% 5.82/6.08
% 5.82/6.08 % zero_diff
% 5.82/6.08 thf(fact_2996_diff__zero,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( minus_minus_complex @ A2 @ zero_zero_complex )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_zero
% 5.82/6.08 thf(fact_2997_diff__zero,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( minus_minus_real @ A2 @ zero_zero_real )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_zero
% 5.82/6.08 thf(fact_2998_diff__zero,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_zero
% 5.82/6.08 thf(fact_2999_diff__zero,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ A2 @ zero_zero_nat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_zero
% 5.82/6.08 thf(fact_3000_diff__zero,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_zero
% 5.82/6.08 thf(fact_3001_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( minus_minus_complex @ A2 @ A2 )
% 5.82/6.08 = zero_zero_complex ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_comm_monoid_add_class.diff_cancel
% 5.82/6.08 thf(fact_3002_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( minus_minus_real @ A2 @ A2 )
% 5.82/6.08 = zero_zero_real ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_comm_monoid_add_class.diff_cancel
% 5.82/6.08 thf(fact_3003_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ A2 @ A2 )
% 5.82/6.08 = zero_zero_rat ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_comm_monoid_add_class.diff_cancel
% 5.82/6.08 thf(fact_3004_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ A2 @ A2 )
% 5.82/6.08 = zero_zero_nat ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_comm_monoid_add_class.diff_cancel
% 5.82/6.08 thf(fact_3005_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( minus_minus_int @ A2 @ A2 )
% 5.82/6.08 = zero_zero_int ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_comm_monoid_add_class.diff_cancel
% 5.82/6.08 thf(fact_3006_mult__1,axiom,
% 5.82/6.08 ! [A2: assn] :
% 5.82/6.08 ( ( times_times_assn @ one_one_assn @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult_1
% 5.82/6.08 thf(fact_3007_mult__1,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( times_times_real @ one_one_real @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult_1
% 5.82/6.08 thf(fact_3008_mult__1,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( times_times_rat @ one_one_rat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult_1
% 5.82/6.08 thf(fact_3009_mult__1,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( times_times_nat @ one_one_nat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult_1
% 5.82/6.08 thf(fact_3010_mult__1,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( times_times_int @ one_one_int @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult_1
% 5.82/6.08 thf(fact_3011_mult_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: assn] :
% 5.82/6.08 ( ( times_times_assn @ A2 @ one_one_assn )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult.right_neutral
% 5.82/6.08 thf(fact_3012_mult_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( times_times_real @ A2 @ one_one_real )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult.right_neutral
% 5.82/6.08 thf(fact_3013_mult_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( times_times_rat @ A2 @ one_one_rat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult.right_neutral
% 5.82/6.08 thf(fact_3014_mult_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( times_times_nat @ A2 @ one_one_nat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult.right_neutral
% 5.82/6.08 thf(fact_3015_mult_Oright__neutral,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( times_times_int @ A2 @ one_one_int )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % mult.right_neutral
% 5.82/6.08 thf(fact_3016_add__diff__cancel,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel
% 5.82/6.08 thf(fact_3017_add__diff__cancel,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel
% 5.82/6.08 thf(fact_3018_add__diff__cancel,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel
% 5.82/6.08 thf(fact_3019_diff__add__cancel,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( plus_plus_real @ ( minus_minus_real @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_add_cancel
% 5.82/6.08 thf(fact_3020_diff__add__cancel,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_add_cancel
% 5.82/6.08 thf(fact_3021_diff__add__cancel,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % diff_add_cancel
% 5.82/6.08 thf(fact_3022_add__diff__cancel__left,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( minus_minus_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) )
% 5.82/6.08 = ( minus_minus_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left
% 5.82/6.08 thf(fact_3023_add__diff__cancel__left,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) )
% 5.82/6.08 = ( minus_minus_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left
% 5.82/6.08 thf(fact_3024_add__diff__cancel__left,axiom,
% 5.82/6.08 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) )
% 5.82/6.08 = ( minus_minus_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left
% 5.82/6.08 thf(fact_3025_add__diff__cancel__left,axiom,
% 5.82/6.08 ! [C2: int,A2: int,B2: int] :
% 5.82/6.08 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) )
% 5.82/6.08 = ( minus_minus_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left
% 5.82/6.08 thf(fact_3026_add__diff__cancel__left_H,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ B2 ) @ A2 )
% 5.82/6.08 = B2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left'
% 5.82/6.08 thf(fact_3027_add__diff__cancel__left_H,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ A2 )
% 5.82/6.08 = B2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left'
% 5.82/6.08 thf(fact_3028_add__diff__cancel__left_H,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B2 ) @ A2 )
% 5.82/6.08 = B2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left'
% 5.82/6.08 thf(fact_3029_add__diff__cancel__left_H,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ A2 )
% 5.82/6.08 = B2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_left'
% 5.82/6.08 thf(fact_3030_add__diff__cancel__right,axiom,
% 5.82/6.08 ! [A2: real,C2: real,B2: real] :
% 5.82/6.08 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.08 = ( minus_minus_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right
% 5.82/6.08 thf(fact_3031_add__diff__cancel__right,axiom,
% 5.82/6.08 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.08 = ( minus_minus_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right
% 5.82/6.08 thf(fact_3032_add__diff__cancel__right,axiom,
% 5.82/6.08 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.08 = ( minus_minus_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right
% 5.82/6.08 thf(fact_3033_add__diff__cancel__right,axiom,
% 5.82/6.08 ! [A2: int,C2: int,B2: int] :
% 5.82/6.08 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.08 = ( minus_minus_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right
% 5.82/6.08 thf(fact_3034_add__diff__cancel__right_H,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right'
% 5.82/6.08 thf(fact_3035_add__diff__cancel__right_H,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right'
% 5.82/6.08 thf(fact_3036_add__diff__cancel__right_H,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right'
% 5.82/6.08 thf(fact_3037_add__diff__cancel__right_H,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add_diff_cancel_right'
% 5.82/6.08 thf(fact_3038_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_le_double_add_iff_zero_le_single_add
% 5.82/6.08 thf(fact_3039_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_le_double_add_iff_zero_le_single_add
% 5.82/6.08 thf(fact_3040_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_le_double_add_iff_zero_le_single_add
% 5.82/6.08 thf(fact_3041_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ A2 ) @ zero_zero_real )
% 5.82/6.08 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_add_le_zero_iff_single_add_le_zero
% 5.82/6.08 thf(fact_3042_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 5.82/6.08 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_add_le_zero_iff_single_add_le_zero
% 5.82/6.08 thf(fact_3043_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 5.82/6.08 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % double_add_le_zero_iff_single_add_le_zero
% 5.82/6.08 thf(fact_3044_le__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ ( plus_plus_real @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel2
% 5.82/6.08 thf(fact_3045_le__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel2
% 5.82/6.08 thf(fact_3046_le__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel2
% 5.82/6.08 thf(fact_3047_le__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel2
% 5.82/6.08 thf(fact_3048_le__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel1
% 5.82/6.08 thf(fact_3049_le__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel1
% 5.82/6.08 thf(fact_3050_le__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel1
% 5.82/6.08 thf(fact_3051_le__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_add_same_cancel1
% 5.82/6.08 thf(fact_3052_add__le__same__cancel2,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel2
% 5.82/6.08 thf(fact_3053_add__le__same__cancel2,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel2
% 5.82/6.08 thf(fact_3054_add__le__same__cancel2,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel2
% 5.82/6.08 thf(fact_3055_add__le__same__cancel2,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel2
% 5.82/6.08 thf(fact_3056_add__le__same__cancel1,axiom,
% 5.82/6.08 ! [B2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel1
% 5.82/6.08 thf(fact_3057_add__le__same__cancel1,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel1
% 5.82/6.08 thf(fact_3058_add__le__same__cancel1,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel1
% 5.82/6.08 thf(fact_3059_add__le__same__cancel1,axiom,
% 5.82/6.08 ! [B2: int,A2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_same_cancel1
% 5.82/6.08 thf(fact_3060_add__less__same__cancel1,axiom,
% 5.82/6.08 ! [B2: real,A2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel1
% 5.82/6.08 thf(fact_3061_add__less__same__cancel1,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel1
% 5.82/6.08 thf(fact_3062_add__less__same__cancel1,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel1
% 5.82/6.08 thf(fact_3063_add__less__same__cancel1,axiom,
% 5.82/6.08 ! [B2: int,A2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A2 ) @ B2 )
% 5.82/6.08 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel1
% 5.82/6.08 thf(fact_3064_add__less__same__cancel2,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel2
% 5.82/6.08 thf(fact_3065_add__less__same__cancel2,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel2
% 5.82/6.08 thf(fact_3066_add__less__same__cancel2,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel2
% 5.82/6.08 thf(fact_3067_add__less__same__cancel2,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.08 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_same_cancel2
% 5.82/6.08 thf(fact_3068_less__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_real @ zero_zero_real @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel1
% 5.82/6.08 thf(fact_3069_less__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_rat @ zero_zero_rat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel1
% 5.82/6.08 thf(fact_3070_less__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel1
% 5.82/6.08 thf(fact_3071_less__add__same__cancel1,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.08 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel1
% 5.82/6.08 thf(fact_3072_less__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ ( plus_plus_real @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_real @ zero_zero_real @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel2
% 5.82/6.08 thf(fact_3073_less__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_rat @ zero_zero_rat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel2
% 5.82/6.08 thf(fact_3074_less__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel2
% 5.82/6.08 thf(fact_3075_less__add__same__cancel2,axiom,
% 5.82/6.08 ! [A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ A2 @ ( plus_plus_int @ B2 @ A2 ) )
% 5.82/6.08 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_add_same_cancel2
% 5.82/6.08 thf(fact_3076_imult__is__0,axiom,
% 5.82/6.08 ! [M: extended_enat,N: extended_enat] :
% 5.82/6.08 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.82/6.08 = zero_z5237406670263579293d_enat )
% 5.82/6.08 = ( ( M = zero_z5237406670263579293d_enat )
% 5.82/6.08 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % imult_is_0
% 5.82/6.08 thf(fact_3077_zero__one__enat__neq_I1_J,axiom,
% 5.82/6.08 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.82/6.08
% 5.82/6.08 % zero_one_enat_neq(1)
% 5.82/6.08 thf(fact_3078_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o,X2: nat] :
% 5.82/6.08 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 5.82/6.08 thf(fact_3079_vebt__assn__raw_Osimps_I1_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o,Ai: $o,Bi: $o] :
% 5.82/6.08 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ A2 @ B2 ) @ ( vEBT_Leafi @ Ai @ Bi ) )
% 5.82/6.08 = ( pure_assn
% 5.82/6.08 @ ( ( Ai = A2 )
% 5.82/6.08 & ( Bi = B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_assn_raw.simps(1)
% 5.82/6.08 thf(fact_3080_VEBT_Oexhaust,axiom,
% 5.82/6.08 ! [Y3: vEBT_VEBT] :
% 5.82/6.08 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.82/6.08 ( Y3
% 5.82/6.08 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.82/6.08 => ~ ! [X212: $o,X223: $o] :
% 5.82/6.08 ( Y3
% 5.82/6.08 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT.exhaust
% 5.82/6.08 thf(fact_3081_VEBT_Odistinct_I1_J,axiom,
% 5.82/6.08 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.82/6.08 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.82/6.08 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT.distinct(1)
% 5.82/6.08 thf(fact_3082_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [Uu2: $o,Uv2: $o,D4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D4 ) )
% 5.82/6.08 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.valid'.cases
% 5.82/6.08 thf(fact_3083_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.82/6.08 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.minNull.simps(1)
% 5.82/6.08 thf(fact_3084_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.82/6.08 ! [Uv: $o] :
% 5.82/6.08 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.minNull.simps(2)
% 5.82/6.08 thf(fact_3085_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.82/6.08 ! [Uu: $o] :
% 5.82/6.08 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.minNull.simps(3)
% 5.82/6.08 thf(fact_3086_vebt__delete_Osimps_I3_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o,N: nat] :
% 5.82/6.08 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ N ) ) )
% 5.82/6.08 = ( vEBT_Leaf @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_delete.simps(3)
% 5.82/6.08 thf(fact_3087_vebt__delete_Osimps_I1_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A2 @ B2 ) @ zero_zero_nat )
% 5.82/6.08 = ( vEBT_Leaf @ $false @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_delete.simps(1)
% 5.82/6.08 thf(fact_3088_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o,X2: nat] :
% 5.82/6.08 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 5.82/6.08 thf(fact_3089_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [A3: $o,B3: $o,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X4 ) )
% 5.82/6.08 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.82/6.08 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ X4 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.naive_member.cases
% 5.82/6.08 thf(fact_3090_invar__vebt_Ointros_I1_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % invar_vebt.intros(1)
% 5.82/6.08 thf(fact_3091_VEBT__internal_OT__vebt__buildupi_H_Osimps_I1_J,axiom,
% 5.82/6.08 ( ( vEBT_V9176841429113362141ildupi @ zero_zero_nat )
% 5.82/6.08 = one_one_int ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T_vebt_buildupi'.simps(1)
% 5.82/6.08 thf(fact_3092_vebt__delete_Osimps_I2_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.08 = ( vEBT_Leaf @ A2 @ $false ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_delete.simps(2)
% 5.82/6.08 thf(fact_3093_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 5.82/6.08 ! [X2: vEBT_VEBT] :
% 5.82/6.08 ( ( X2
% 5.82/6.08 != ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.08 => ( ! [Uv2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.08 => ( ! [Uu2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.08 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.08 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 5.82/6.08 thf(fact_3094_vebt__member_Osimps_I1_J,axiom,
% 5.82/6.08 ! [A2: $o,B2: $o,X2: nat] :
% 5.82/6.08 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.08 = ( ( ( X2 = zero_zero_nat )
% 5.82/6.08 => A2 )
% 5.82/6.08 & ( ( X2 != zero_zero_nat )
% 5.82/6.08 => ( ( ( X2 = one_one_nat )
% 5.82/6.08 => B2 )
% 5.82/6.08 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_member.simps(1)
% 5.82/6.08 thf(fact_3095_vebt__buildup_Osimps_I2_J,axiom,
% 5.82/6.08 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.82/6.08 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_buildup.simps(2)
% 5.82/6.08 thf(fact_3096_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.82/6.08 ! [X2: vEBT_VEBT] :
% 5.82/6.08 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.82/6.08 => ( ! [Uv2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.08 => ( ! [Uu2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.08 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.minNull.elims(3)
% 5.82/6.08 thf(fact_3097_vebt__assn__raw_Ocases,axiom,
% 5.82/6.08 ! [X2: produc3625547720036274456_VEBTi] :
% 5.82/6.08 ( ! [A3: $o,B3: $o,Ai2: $o,Bi2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A3 @ B3 ) @ ( vEBT_Leafi @ Ai2 @ Bi2 ) ) )
% 5.82/6.08 => ( ! [Mmo: option4927543243414619207at_nat,Deg2: nat,Tree_list: list_VEBT_VEBT,Summary2: vEBT_VEBT,Mmoi: option4927543243414619207at_nat,Degi: nat,Tree_array: array_VEBT_VEBTi,Summaryi: vEBT_VEBTi] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo @ Deg2 @ Tree_list @ Summary2 ) @ ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) ) )
% 5.82/6.08 => ( ! [V2: option4927543243414619207at_nat,Va3: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT,Vd: $o,Ve: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V2 @ Va3 @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd @ Ve ) ) )
% 5.82/6.08 => ~ ! [Vd: $o,Ve: $o,V2: option4927543243414619207at_nat,Va3: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd @ Ve ) @ ( vEBT_Nodei @ V2 @ Va3 @ Vb3 @ Vc3 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_assn_raw.cases
% 5.82/6.08 thf(fact_3098_vebt__insert_Osimps_I1_J,axiom,
% 5.82/6.08 ! [X2: nat,A2: $o,B2: $o] :
% 5.82/6.08 ( ( ( X2 = zero_zero_nat )
% 5.82/6.08 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.08 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.82/6.08 & ( ( X2 != zero_zero_nat )
% 5.82/6.08 => ( ( ( X2 = one_one_nat )
% 5.82/6.08 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.08 = ( vEBT_Leaf @ A2 @ $true ) ) )
% 5.82/6.08 & ( ( X2 != one_one_nat )
% 5.82/6.08 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.08 = ( vEBT_Leaf @ A2 @ B2 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % vebt_insert.simps(1)
% 5.82/6.08 thf(fact_3099_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ( plus_plus_real @ I @ K )
% 5.82/6.08 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(4)
% 5.82/6.08 thf(fact_3100_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ( plus_plus_rat @ I @ K )
% 5.82/6.08 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(4)
% 5.82/6.08 thf(fact_3101_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ( plus_plus_nat @ I @ K )
% 5.82/6.08 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(4)
% 5.82/6.08 thf(fact_3102_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ( plus_plus_int @ I @ K )
% 5.82/6.08 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(4)
% 5.82/6.08 thf(fact_3103_group__cancel_Oadd1,axiom,
% 5.82/6.08 ! [A: real,K: real,A2: real,B2: real] :
% 5.82/6.08 ( ( A
% 5.82/6.08 = ( plus_plus_real @ K @ A2 ) )
% 5.82/6.08 => ( ( plus_plus_real @ A @ B2 )
% 5.82/6.08 = ( plus_plus_real @ K @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add1
% 5.82/6.08 thf(fact_3104_group__cancel_Oadd1,axiom,
% 5.82/6.08 ! [A: rat,K: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( A
% 5.82/6.08 = ( plus_plus_rat @ K @ A2 ) )
% 5.82/6.08 => ( ( plus_plus_rat @ A @ B2 )
% 5.82/6.08 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add1
% 5.82/6.08 thf(fact_3105_group__cancel_Oadd1,axiom,
% 5.82/6.08 ! [A: nat,K: nat,A2: nat,B2: nat] :
% 5.82/6.08 ( ( A
% 5.82/6.08 = ( plus_plus_nat @ K @ A2 ) )
% 5.82/6.08 => ( ( plus_plus_nat @ A @ B2 )
% 5.82/6.08 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add1
% 5.82/6.08 thf(fact_3106_group__cancel_Oadd1,axiom,
% 5.82/6.08 ! [A: int,K: int,A2: int,B2: int] :
% 5.82/6.08 ( ( A
% 5.82/6.08 = ( plus_plus_int @ K @ A2 ) )
% 5.82/6.08 => ( ( plus_plus_int @ A @ B2 )
% 5.82/6.08 = ( plus_plus_int @ K @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add1
% 5.82/6.08 thf(fact_3107_group__cancel_Oadd2,axiom,
% 5.82/6.08 ! [B: real,K: real,B2: real,A2: real] :
% 5.82/6.08 ( ( B
% 5.82/6.08 = ( plus_plus_real @ K @ B2 ) )
% 5.82/6.08 => ( ( plus_plus_real @ A2 @ B )
% 5.82/6.08 = ( plus_plus_real @ K @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add2
% 5.82/6.08 thf(fact_3108_group__cancel_Oadd2,axiom,
% 5.82/6.08 ! [B: rat,K: rat,B2: rat,A2: rat] :
% 5.82/6.08 ( ( B
% 5.82/6.08 = ( plus_plus_rat @ K @ B2 ) )
% 5.82/6.08 => ( ( plus_plus_rat @ A2 @ B )
% 5.82/6.08 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add2
% 5.82/6.08 thf(fact_3109_group__cancel_Oadd2,axiom,
% 5.82/6.08 ! [B: nat,K: nat,B2: nat,A2: nat] :
% 5.82/6.08 ( ( B
% 5.82/6.08 = ( plus_plus_nat @ K @ B2 ) )
% 5.82/6.08 => ( ( plus_plus_nat @ A2 @ B )
% 5.82/6.08 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add2
% 5.82/6.08 thf(fact_3110_group__cancel_Oadd2,axiom,
% 5.82/6.08 ! [B: int,K: int,B2: int,A2: int] :
% 5.82/6.08 ( ( B
% 5.82/6.08 = ( plus_plus_int @ K @ B2 ) )
% 5.82/6.08 => ( ( plus_plus_int @ A2 @ B )
% 5.82/6.08 = ( plus_plus_int @ K @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % group_cancel.add2
% 5.82/6.08 thf(fact_3111_add_Oassoc,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( plus_plus_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( plus_plus_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.assoc
% 5.82/6.08 thf(fact_3112_add_Oassoc,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.assoc
% 5.82/6.08 thf(fact_3113_add_Oassoc,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.assoc
% 5.82/6.08 thf(fact_3114_add_Oassoc,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( plus_plus_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.assoc
% 5.82/6.08 thf(fact_3115_add_Oleft__cancel,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_real @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.left_cancel
% 5.82/6.08 thf(fact_3116_add_Oleft__cancel,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_rat @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.left_cancel
% 5.82/6.08 thf(fact_3117_add_Oleft__cancel,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_int @ A2 @ C2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.left_cancel
% 5.82/6.08 thf(fact_3118_add_Oright__cancel,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_real @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_cancel
% 5.82/6.08 thf(fact_3119_add_Oright__cancel,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_rat @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_cancel
% 5.82/6.08 thf(fact_3120_add_Oright__cancel,axiom,
% 5.82/6.08 ! [B2: int,A2: int,C2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_int @ C2 @ A2 ) )
% 5.82/6.08 = ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add.right_cancel
% 5.82/6.08 thf(fact_3121_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 5.82/6.08 ( plus_plus_real
% 5.82/6.08 = ( ^ [A5: real,B6: real] : ( plus_plus_real @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.commute
% 5.82/6.08 thf(fact_3122_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 5.82/6.08 ( plus_plus_rat
% 5.82/6.08 = ( ^ [A5: rat,B6: rat] : ( plus_plus_rat @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.commute
% 5.82/6.08 thf(fact_3123_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 5.82/6.08 ( plus_plus_nat
% 5.82/6.08 = ( ^ [A5: nat,B6: nat] : ( plus_plus_nat @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.commute
% 5.82/6.08 thf(fact_3124_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 5.82/6.08 ( plus_plus_int
% 5.82/6.08 = ( ^ [A5: int,B6: int] : ( plus_plus_int @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.commute
% 5.82/6.08 thf(fact_3125_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( plus_plus_real @ B2 @ ( plus_plus_real @ A2 @ C2 ) )
% 5.82/6.08 = ( plus_plus_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.left_commute
% 5.82/6.08 thf(fact_3126_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ B2 @ ( plus_plus_rat @ A2 @ C2 ) )
% 5.82/6.08 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.left_commute
% 5.82/6.08 thf(fact_3127_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.08 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A2 @ C2 ) )
% 5.82/6.08 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.left_commute
% 5.82/6.08 thf(fact_3128_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: int,A2: int,C2: int] :
% 5.82/6.08 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A2 @ C2 ) )
% 5.82/6.08 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_add_class.add.left_commute
% 5.82/6.08 thf(fact_3129_add__left__imp__eq,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_real @ A2 @ C2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_imp_eq
% 5.82/6.08 thf(fact_3130_add__left__imp__eq,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_rat @ A2 @ C2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_imp_eq
% 5.82/6.08 thf(fact_3131_add__left__imp__eq,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_nat @ A2 @ C2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_imp_eq
% 5.82/6.08 thf(fact_3132_add__left__imp__eq,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ A2 @ B2 )
% 5.82/6.08 = ( plus_plus_int @ A2 @ C2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_imp_eq
% 5.82/6.08 thf(fact_3133_add__right__imp__eq,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( ( plus_plus_real @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_real @ C2 @ A2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_imp_eq
% 5.82/6.08 thf(fact_3134_add__right__imp__eq,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.08 ( ( ( plus_plus_rat @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_rat @ C2 @ A2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_imp_eq
% 5.82/6.08 thf(fact_3135_add__right__imp__eq,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.08 ( ( ( plus_plus_nat @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_nat @ C2 @ A2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_imp_eq
% 5.82/6.08 thf(fact_3136_add__right__imp__eq,axiom,
% 5.82/6.08 ! [B2: int,A2: int,C2: int] :
% 5.82/6.08 ( ( ( plus_plus_int @ B2 @ A2 )
% 5.82/6.08 = ( plus_plus_int @ C2 @ A2 ) )
% 5.82/6.08 => ( B2 = C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_imp_eq
% 5.82/6.08 thf(fact_3137_one__reorient,axiom,
% 5.82/6.08 ! [X2: assn] :
% 5.82/6.08 ( ( one_one_assn = X2 )
% 5.82/6.08 = ( X2 = one_one_assn ) ) ).
% 5.82/6.08
% 5.82/6.08 % one_reorient
% 5.82/6.08 thf(fact_3138_one__reorient,axiom,
% 5.82/6.08 ! [X2: real] :
% 5.82/6.08 ( ( one_one_real = X2 )
% 5.82/6.08 = ( X2 = one_one_real ) ) ).
% 5.82/6.08
% 5.82/6.08 % one_reorient
% 5.82/6.08 thf(fact_3139_one__reorient,axiom,
% 5.82/6.08 ! [X2: rat] :
% 5.82/6.08 ( ( one_one_rat = X2 )
% 5.82/6.08 = ( X2 = one_one_rat ) ) ).
% 5.82/6.08
% 5.82/6.08 % one_reorient
% 5.82/6.08 thf(fact_3140_one__reorient,axiom,
% 5.82/6.08 ! [X2: nat] :
% 5.82/6.08 ( ( one_one_nat = X2 )
% 5.82/6.08 = ( X2 = one_one_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % one_reorient
% 5.82/6.08 thf(fact_3141_one__reorient,axiom,
% 5.82/6.08 ! [X2: int] :
% 5.82/6.08 ( ( one_one_int = X2 )
% 5.82/6.08 = ( X2 = one_one_int ) ) ).
% 5.82/6.08
% 5.82/6.08 % one_reorient
% 5.82/6.08 thf(fact_3142_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( times_times_real @ B2 @ ( times_times_real @ A2 @ C2 ) )
% 5.82/6.08 = ( times_times_real @ A2 @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.left_commute
% 5.82/6.08 thf(fact_3143_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.08 ( ( times_times_rat @ B2 @ ( times_times_rat @ A2 @ C2 ) )
% 5.82/6.08 = ( times_times_rat @ A2 @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.left_commute
% 5.82/6.08 thf(fact_3144_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.08 ( ( times_times_nat @ B2 @ ( times_times_nat @ A2 @ C2 ) )
% 5.82/6.08 = ( times_times_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.left_commute
% 5.82/6.08 thf(fact_3145_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.82/6.08 ! [B2: int,A2: int,C2: int] :
% 5.82/6.08 ( ( times_times_int @ B2 @ ( times_times_int @ A2 @ C2 ) )
% 5.82/6.08 = ( times_times_int @ A2 @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.left_commute
% 5.82/6.08 thf(fact_3146_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.82/6.08 ( times_times_real
% 5.82/6.08 = ( ^ [A5: real,B6: real] : ( times_times_real @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.commute
% 5.82/6.08 thf(fact_3147_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.82/6.08 ( times_times_rat
% 5.82/6.08 = ( ^ [A5: rat,B6: rat] : ( times_times_rat @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.commute
% 5.82/6.08 thf(fact_3148_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.82/6.08 ( times_times_nat
% 5.82/6.08 = ( ^ [A5: nat,B6: nat] : ( times_times_nat @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.commute
% 5.82/6.08 thf(fact_3149_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.82/6.08 ( times_times_int
% 5.82/6.08 = ( ^ [A5: int,B6: int] : ( times_times_int @ B6 @ A5 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % ab_semigroup_mult_class.mult.commute
% 5.82/6.08 thf(fact_3150_mult_Oassoc,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( times_times_real @ ( times_times_real @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( times_times_real @ A2 @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult.assoc
% 5.82/6.08 thf(fact_3151_mult_Oassoc,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( times_times_rat @ ( times_times_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( times_times_rat @ A2 @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult.assoc
% 5.82/6.08 thf(fact_3152_mult_Oassoc,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( times_times_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( times_times_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult.assoc
% 5.82/6.08 thf(fact_3153_mult_Oassoc,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( times_times_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.08 = ( times_times_int @ A2 @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % mult.assoc
% 5.82/6.08 thf(fact_3154_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.82/6.08 ! [X2: vEBT_VEBT] :
% 5.82/6.08 ( ( vEBT_VEBT_minNull @ X2 )
% 5.82/6.08 => ( ( X2
% 5.82/6.08 != ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.08 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.minNull.elims(2)
% 5.82/6.08 thf(fact_3155_diff__eq__diff__eq,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.08 ( ( ( minus_minus_real @ A2 @ B2 )
% 5.82/6.08 = ( minus_minus_real @ C2 @ D2 ) )
% 5.82/6.08 => ( ( A2 = B2 )
% 5.82/6.08 = ( C2 = D2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_eq_diff_eq
% 5.82/6.08 thf(fact_3156_diff__eq__diff__eq,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.08 ( ( ( minus_minus_rat @ A2 @ B2 )
% 5.82/6.08 = ( minus_minus_rat @ C2 @ D2 ) )
% 5.82/6.08 => ( ( A2 = B2 )
% 5.82/6.08 = ( C2 = D2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_eq_diff_eq
% 5.82/6.08 thf(fact_3157_diff__eq__diff__eq,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.08 ( ( ( minus_minus_int @ A2 @ B2 )
% 5.82/6.08 = ( minus_minus_int @ C2 @ D2 ) )
% 5.82/6.08 => ( ( A2 = B2 )
% 5.82/6.08 = ( C2 = D2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_eq_diff_eq
% 5.82/6.08 thf(fact_3158_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 5.82/6.08 ! [A2: real,C2: real,B2: real] :
% 5.82/6.08 ( ( minus_minus_real @ ( minus_minus_real @ A2 @ C2 ) @ B2 )
% 5.82/6.08 = ( minus_minus_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_ab_semigroup_add_class.diff_right_commute
% 5.82/6.08 thf(fact_3159_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 5.82/6.08 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C2 ) @ B2 )
% 5.82/6.08 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_ab_semigroup_add_class.diff_right_commute
% 5.82/6.08 thf(fact_3160_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 5.82/6.08 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.08 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ C2 ) @ B2 )
% 5.82/6.08 = ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_ab_semigroup_add_class.diff_right_commute
% 5.82/6.08 thf(fact_3161_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 5.82/6.08 ! [A2: int,C2: int,B2: int] :
% 5.82/6.08 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ C2 ) @ B2 )
% 5.82/6.08 = ( minus_minus_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % cancel_ab_semigroup_add_class.diff_right_commute
% 5.82/6.08 thf(fact_3162_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,
% 5.82/6.08 ! [A2: $o,B2: $o,N: nat] :
% 5.82/6.08 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ N ) ) )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(3)
% 5.82/6.08 thf(fact_3163_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,
% 5.82/6.08 ! [A2: $o,B2: $o,N: nat] :
% 5.82/6.08 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ N ) ) )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(3)
% 5.82/6.08 thf(fact_3164_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,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A2 @ B2 ) @ zero_zero_nat )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(1)
% 5.82/6.08 thf(fact_3165_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,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A2 @ B2 ) @ zero_zero_nat )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(1)
% 5.82/6.08 thf(fact_3166_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 5.82/6.08 ! [X2: vEBT_VEBT] :
% 5.82/6.08 ( ! [A3: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.08 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 5.82/6.08 thf(fact_3167_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,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(2)
% 5.82/6.08 thf(fact_3168_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,
% 5.82/6.08 ! [A2: $o,B2: $o] :
% 5.82/6.08 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(2)
% 5.82/6.08 thf(fact_3169_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.82/6.08 ! [X2: vEBT_VEBT,Y3: $o] :
% 5.82/6.08 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.82/6.08 = Y3 )
% 5.82/6.08 => ( ( ( X2
% 5.82/6.08 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.08 => ~ Y3 )
% 5.82/6.08 => ( ( ? [Uv2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.08 => Y3 )
% 5.82/6.08 => ( ( ? [Uu2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.08 => Y3 )
% 5.82/6.08 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.08 => ~ Y3 )
% 5.82/6.08 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.08 ( X2
% 5.82/6.08 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.08 => Y3 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.minNull.elims(1)
% 5.82/6.08 thf(fact_3170_VEBT__internal_OT__vebt__buildupi_H_Osimps_I2_J,axiom,
% 5.82/6.08 ( ( vEBT_V9176841429113362141ildupi @ ( suc @ zero_zero_nat ) )
% 5.82/6.08 = one_one_int ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T_vebt_buildupi'.simps(2)
% 5.82/6.08 thf(fact_3171_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 5.82/6.08 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.82/6.08 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 )
% 5.82/6.08 = one_one_nat ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 5.82/6.08 thf(fact_3172_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,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [A3: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 5.82/6.08 => ( ! [A3: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 5.82/6.08 => ( ! [A3: $o,B3: $o,N3: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 5.82/6.08 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu2 ) )
% 5.82/6.08 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ X4 ) )
% 5.82/6.08 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ X4 ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.cases
% 5.82/6.08 thf(fact_3173_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [A3: $o,B3: $o,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X4 ) )
% 5.82/6.08 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X4 ) )
% 5.82/6.08 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 5.82/6.08 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X4 ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 5.82/6.08 thf(fact_3174_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [A3: $o,B3: $o,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X4 ) )
% 5.82/6.08 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X4 ) )
% 5.82/6.08 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X4 ) )
% 5.82/6.08 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 5.82/6.08 thf(fact_3175_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [Uu2: $o,B3: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 5.82/6.08 => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 5.82/6.08 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va2 ) )
% 5.82/6.08 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 5.82/6.08 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.cases
% 5.82/6.08 thf(fact_3176_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.82/6.08 => ( ! [A3: $o,Uw2: $o] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.82/6.08 => ( ! [A3: $o,B3: $o,Va3: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va3 ) ) ) )
% 5.82/6.08 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.82/6.08 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf ) )
% 5.82/6.08 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.82/6.08 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.cases
% 5.82/6.08 thf(fact_3177_VEBT__internal_Omembermima_Ocases,axiom,
% 5.82/6.08 ! [X2: produc9072475918466114483BT_nat] :
% 5.82/6.08 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.82/6.08 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.82/6.08 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X4 ) )
% 5.82/6.08 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X4 ) )
% 5.82/6.08 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 5.82/6.08 ( X2
% 5.82/6.08 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X4 ) ) ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % VEBT_internal.membermima.cases
% 5.82/6.08 thf(fact_3178_zero__le,axiom,
% 5.82/6.08 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 5.82/6.08
% 5.82/6.08 % zero_le
% 5.82/6.08 thf(fact_3179_zero__less__iff__neq__zero,axiom,
% 5.82/6.08 ! [N: nat] :
% 5.82/6.08 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.08 = ( N != zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % zero_less_iff_neq_zero
% 5.82/6.08 thf(fact_3180_gr__implies__not__zero,axiom,
% 5.82/6.08 ! [M: nat,N: nat] :
% 5.82/6.08 ( ( ord_less_nat @ M @ N )
% 5.82/6.08 => ( N != zero_zero_nat ) ) ).
% 5.82/6.08
% 5.82/6.08 % gr_implies_not_zero
% 5.82/6.08 thf(fact_3181_not__less__zero,axiom,
% 5.82/6.08 ! [N: nat] :
% 5.82/6.08 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.82/6.08
% 5.82/6.08 % not_less_zero
% 5.82/6.08 thf(fact_3182_gr__zeroI,axiom,
% 5.82/6.08 ! [N: nat] :
% 5.82/6.08 ( ( N != zero_zero_nat )
% 5.82/6.08 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.08
% 5.82/6.08 % gr_zeroI
% 5.82/6.08 thf(fact_3183_comm__monoid__add__class_Oadd__0,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( plus_plus_complex @ zero_zero_complex @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % comm_monoid_add_class.add_0
% 5.82/6.08 thf(fact_3184_comm__monoid__add__class_Oadd__0,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( plus_plus_real @ zero_zero_real @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % comm_monoid_add_class.add_0
% 5.82/6.08 thf(fact_3185_comm__monoid__add__class_Oadd__0,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % comm_monoid_add_class.add_0
% 5.82/6.08 thf(fact_3186_comm__monoid__add__class_Oadd__0,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % comm_monoid_add_class.add_0
% 5.82/6.08 thf(fact_3187_comm__monoid__add__class_Oadd__0,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % comm_monoid_add_class.add_0
% 5.82/6.08 thf(fact_3188_add_Ocomm__neutral,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( plus_plus_complex @ A2 @ zero_zero_complex )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.comm_neutral
% 5.82/6.08 thf(fact_3189_add_Ocomm__neutral,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( plus_plus_real @ A2 @ zero_zero_real )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.comm_neutral
% 5.82/6.08 thf(fact_3190_add_Ocomm__neutral,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.comm_neutral
% 5.82/6.08 thf(fact_3191_add_Ocomm__neutral,axiom,
% 5.82/6.08 ! [A2: nat] :
% 5.82/6.08 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.comm_neutral
% 5.82/6.08 thf(fact_3192_add_Ocomm__neutral,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.comm_neutral
% 5.82/6.08 thf(fact_3193_add_Ogroup__left__neutral,axiom,
% 5.82/6.08 ! [A2: complex] :
% 5.82/6.08 ( ( plus_plus_complex @ zero_zero_complex @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.group_left_neutral
% 5.82/6.08 thf(fact_3194_add_Ogroup__left__neutral,axiom,
% 5.82/6.08 ! [A2: real] :
% 5.82/6.08 ( ( plus_plus_real @ zero_zero_real @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.group_left_neutral
% 5.82/6.08 thf(fact_3195_add_Ogroup__left__neutral,axiom,
% 5.82/6.08 ! [A2: rat] :
% 5.82/6.08 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.group_left_neutral
% 5.82/6.08 thf(fact_3196_add_Ogroup__left__neutral,axiom,
% 5.82/6.08 ! [A2: int] :
% 5.82/6.08 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 5.82/6.08 = A2 ) ).
% 5.82/6.08
% 5.82/6.08 % add.group_left_neutral
% 5.82/6.08 thf(fact_3197_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( ord_less_eq_real @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(3)
% 5.82/6.08 thf(fact_3198_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( ord_less_eq_rat @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(3)
% 5.82/6.08 thf(fact_3199_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(3)
% 5.82/6.08 thf(fact_3200_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( ord_less_eq_int @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(3)
% 5.82/6.08 thf(fact_3201_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_eq_real @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(2)
% 5.82/6.08 thf(fact_3202_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_eq_rat @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(2)
% 5.82/6.08 thf(fact_3203_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_eq_nat @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(2)
% 5.82/6.08 thf(fact_3204_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_eq_int @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(2)
% 5.82/6.08 thf(fact_3205_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( ord_less_eq_real @ I @ J )
% 5.82/6.08 & ( ord_less_eq_real @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(1)
% 5.82/6.08 thf(fact_3206_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( ord_less_eq_rat @ I @ J )
% 5.82/6.08 & ( ord_less_eq_rat @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(1)
% 5.82/6.08 thf(fact_3207_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.08 & ( ord_less_eq_nat @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(1)
% 5.82/6.08 thf(fact_3208_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( ord_less_eq_int @ I @ J )
% 5.82/6.08 & ( ord_less_eq_int @ K @ L ) )
% 5.82/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_semiring(1)
% 5.82/6.08 thf(fact_3209_add__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono
% 5.82/6.08 thf(fact_3210_add__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono
% 5.82/6.08 thf(fact_3211_add__mono,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono
% 5.82/6.08 thf(fact_3212_add__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_int @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono
% 5.82/6.08 thf(fact_3213_add__left__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_mono
% 5.82/6.08 thf(fact_3214_add__left__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_mono
% 5.82/6.08 thf(fact_3215_add__left__mono,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_mono
% 5.82/6.08 thf(fact_3216_add__left__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_left_mono
% 5.82/6.08 thf(fact_3217_less__eqE,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.08 => ~ ! [C3: nat] :
% 5.82/6.08 ( B2
% 5.82/6.08 != ( plus_plus_nat @ A2 @ C3 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % less_eqE
% 5.82/6.08 thf(fact_3218_add__right__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_mono
% 5.82/6.08 thf(fact_3219_add__right__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_mono
% 5.82/6.08 thf(fact_3220_add__right__mono,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_mono
% 5.82/6.08 thf(fact_3221_add__right__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_right_mono
% 5.82/6.08 thf(fact_3222_le__iff__add,axiom,
% 5.82/6.08 ( ord_less_eq_nat
% 5.82/6.08 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.08 ? [C4: nat] :
% 5.82/6.08 ( B6
% 5.82/6.08 = ( plus_plus_nat @ A5 @ C4 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % le_iff_add
% 5.82/6.08 thf(fact_3223_add__le__imp__le__left,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_left
% 5.82/6.08 thf(fact_3224_add__le__imp__le__left,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_left
% 5.82/6.08 thf(fact_3225_add__le__imp__le__left,axiom,
% 5.82/6.08 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_left
% 5.82/6.08 thf(fact_3226_add__le__imp__le__left,axiom,
% 5.82/6.08 ! [C2: int,A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_left
% 5.82/6.08 thf(fact_3227_add__le__imp__le__right,axiom,
% 5.82/6.08 ! [A2: real,C2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_eq_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_right
% 5.82/6.08 thf(fact_3228_add__le__imp__le__right,axiom,
% 5.82/6.08 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_right
% 5.82/6.08 thf(fact_3229_add__le__imp__le__right,axiom,
% 5.82/6.08 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_right
% 5.82/6.08 thf(fact_3230_add__le__imp__le__right,axiom,
% 5.82/6.08 ! [A2: int,C2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_le_imp_le_right
% 5.82/6.08 thf(fact_3231_add__less__imp__less__right,axiom,
% 5.82/6.08 ! [A2: real,C2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_right
% 5.82/6.08 thf(fact_3232_add__less__imp__less__right,axiom,
% 5.82/6.08 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_right
% 5.82/6.08 thf(fact_3233_add__less__imp__less__right,axiom,
% 5.82/6.08 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_right
% 5.82/6.08 thf(fact_3234_add__less__imp__less__right,axiom,
% 5.82/6.08 ! [A2: int,C2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.08 => ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_right
% 5.82/6.08 thf(fact_3235_add__less__imp__less__left,axiom,
% 5.82/6.08 ! [C2: real,A2: real,B2: real] :
% 5.82/6.08 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_left
% 5.82/6.08 thf(fact_3236_add__less__imp__less__left,axiom,
% 5.82/6.08 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_left
% 5.82/6.08 thf(fact_3237_add__less__imp__less__left,axiom,
% 5.82/6.08 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_left
% 5.82/6.08 thf(fact_3238_add__less__imp__less__left,axiom,
% 5.82/6.08 ! [C2: int,A2: int,B2: int] :
% 5.82/6.08 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) )
% 5.82/6.08 => ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_less_imp_less_left
% 5.82/6.08 thf(fact_3239_add__strict__right__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_right_mono
% 5.82/6.08 thf(fact_3240_add__strict__right__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_right_mono
% 5.82/6.08 thf(fact_3241_add__strict__right__mono,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_right_mono
% 5.82/6.08 thf(fact_3242_add__strict__right__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_right_mono
% 5.82/6.08 thf(fact_3243_add__strict__left__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_real @ ( plus_plus_real @ C2 @ A2 ) @ ( plus_plus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_left_mono
% 5.82/6.08 thf(fact_3244_add__strict__left__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A2 ) @ ( plus_plus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_left_mono
% 5.82/6.08 thf(fact_3245_add__strict__left__mono,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A2 ) @ ( plus_plus_nat @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_left_mono
% 5.82/6.08 thf(fact_3246_add__strict__left__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int] :
% 5.82/6.08 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.08 => ( ord_less_int @ ( plus_plus_int @ C2 @ A2 ) @ ( plus_plus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_left_mono
% 5.82/6.08 thf(fact_3247_add__strict__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.08 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_mono
% 5.82/6.08 thf(fact_3248_add__strict__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.08 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_mono
% 5.82/6.08 thf(fact_3249_add__strict__mono,axiom,
% 5.82/6.08 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.08 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_mono
% 5.82/6.08 thf(fact_3250_add__strict__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.08 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.08 => ( ord_less_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_strict_mono
% 5.82/6.08 thf(fact_3251_add__mono__thms__linordered__field_I1_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( ord_less_real @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(1)
% 5.82/6.08 thf(fact_3252_add__mono__thms__linordered__field_I1_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( ord_less_rat @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(1)
% 5.82/6.08 thf(fact_3253_add__mono__thms__linordered__field_I1_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( ord_less_nat @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(1)
% 5.82/6.08 thf(fact_3254_add__mono__thms__linordered__field_I1_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( ord_less_int @ I @ J )
% 5.82/6.08 & ( K = L ) )
% 5.82/6.08 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(1)
% 5.82/6.08 thf(fact_3255_add__mono__thms__linordered__field_I2_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_real @ K @ L ) )
% 5.82/6.08 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(2)
% 5.82/6.08 thf(fact_3256_add__mono__thms__linordered__field_I2_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_rat @ K @ L ) )
% 5.82/6.08 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(2)
% 5.82/6.08 thf(fact_3257_add__mono__thms__linordered__field_I2_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_nat @ K @ L ) )
% 5.82/6.08 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(2)
% 5.82/6.08 thf(fact_3258_add__mono__thms__linordered__field_I2_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( I = J )
% 5.82/6.08 & ( ord_less_int @ K @ L ) )
% 5.82/6.08 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(2)
% 5.82/6.08 thf(fact_3259_add__mono__thms__linordered__field_I5_J,axiom,
% 5.82/6.08 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.08 ( ( ( ord_less_real @ I @ J )
% 5.82/6.08 & ( ord_less_real @ K @ L ) )
% 5.82/6.08 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(5)
% 5.82/6.08 thf(fact_3260_add__mono__thms__linordered__field_I5_J,axiom,
% 5.82/6.08 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.08 ( ( ( ord_less_rat @ I @ J )
% 5.82/6.08 & ( ord_less_rat @ K @ L ) )
% 5.82/6.08 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(5)
% 5.82/6.08 thf(fact_3261_add__mono__thms__linordered__field_I5_J,axiom,
% 5.82/6.08 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.08 ( ( ( ord_less_nat @ I @ J )
% 5.82/6.08 & ( ord_less_nat @ K @ L ) )
% 5.82/6.08 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(5)
% 5.82/6.08 thf(fact_3262_add__mono__thms__linordered__field_I5_J,axiom,
% 5.82/6.08 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.08 ( ( ( ord_less_int @ I @ J )
% 5.82/6.08 & ( ord_less_int @ K @ L ) )
% 5.82/6.08 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % add_mono_thms_linordered_field(5)
% 5.82/6.08 thf(fact_3263_eq__iff__diff__eq__0,axiom,
% 5.82/6.08 ( ( ^ [Y6: complex,Z3: complex] : ( Y6 = Z3 ) )
% 5.82/6.08 = ( ^ [A5: complex,B6: complex] :
% 5.82/6.08 ( ( minus_minus_complex @ A5 @ B6 )
% 5.82/6.08 = zero_zero_complex ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % eq_iff_diff_eq_0
% 5.82/6.08 thf(fact_3264_eq__iff__diff__eq__0,axiom,
% 5.82/6.08 ( ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 ) )
% 5.82/6.08 = ( ^ [A5: real,B6: real] :
% 5.82/6.08 ( ( minus_minus_real @ A5 @ B6 )
% 5.82/6.08 = zero_zero_real ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % eq_iff_diff_eq_0
% 5.82/6.08 thf(fact_3265_eq__iff__diff__eq__0,axiom,
% 5.82/6.08 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.82/6.08 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.08 ( ( minus_minus_rat @ A5 @ B6 )
% 5.82/6.08 = zero_zero_rat ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % eq_iff_diff_eq_0
% 5.82/6.08 thf(fact_3266_eq__iff__diff__eq__0,axiom,
% 5.82/6.08 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.82/6.08 = ( ^ [A5: int,B6: int] :
% 5.82/6.08 ( ( minus_minus_int @ A5 @ B6 )
% 5.82/6.08 = zero_zero_int ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % eq_iff_diff_eq_0
% 5.82/6.08 thf(fact_3267_diff__mono,axiom,
% 5.82/6.08 ! [A2: real,B2: real,D2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_real @ D2 @ C2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( minus_minus_real @ A2 @ C2 ) @ ( minus_minus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_mono
% 5.82/6.08 thf(fact_3268_diff__mono,axiom,
% 5.82/6.08 ! [A2: rat,B2: rat,D2: rat,C2: rat] :
% 5.82/6.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_rat @ D2 @ C2 )
% 5.82/6.08 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C2 ) @ ( minus_minus_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_mono
% 5.82/6.08 thf(fact_3269_diff__mono,axiom,
% 5.82/6.08 ! [A2: int,B2: int,D2: int,C2: int] :
% 5.82/6.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.08 => ( ( ord_less_eq_int @ D2 @ C2 )
% 5.82/6.08 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C2 ) @ ( minus_minus_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_mono
% 5.82/6.08 thf(fact_3270_diff__left__mono,axiom,
% 5.82/6.08 ! [B2: real,A2: real,C2: real] :
% 5.82/6.08 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.08 => ( ord_less_eq_real @ ( minus_minus_real @ C2 @ A2 ) @ ( minus_minus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.08
% 5.82/6.08 % diff_left_mono
% 5.82/6.08 thf(fact_3271_diff__left__mono,axiom,
% 5.82/6.09 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A2 ) @ ( minus_minus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_left_mono
% 5.82/6.09 thf(fact_3272_diff__left__mono,axiom,
% 5.82/6.09 ! [B2: int,A2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A2 ) @ ( minus_minus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_left_mono
% 5.82/6.09 thf(fact_3273_diff__right__mono,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_real @ ( minus_minus_real @ A2 @ C2 ) @ ( minus_minus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_right_mono
% 5.82/6.09 thf(fact_3274_diff__right__mono,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C2 ) @ ( minus_minus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_right_mono
% 5.82/6.09 thf(fact_3275_diff__right__mono,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C2 ) @ ( minus_minus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_right_mono
% 5.82/6.09 thf(fact_3276_diff__eq__diff__less__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.09 ( ( ( minus_minus_real @ A2 @ B2 )
% 5.82/6.09 = ( minus_minus_real @ C2 @ D2 ) )
% 5.82/6.09 => ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.09 = ( ord_less_eq_real @ C2 @ D2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_diff_less_eq
% 5.82/6.09 thf(fact_3277_diff__eq__diff__less__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.09 ( ( ( minus_minus_rat @ A2 @ B2 )
% 5.82/6.09 = ( minus_minus_rat @ C2 @ D2 ) )
% 5.82/6.09 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.09 = ( ord_less_eq_rat @ C2 @ D2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_diff_less_eq
% 5.82/6.09 thf(fact_3278_diff__eq__diff__less__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.09 ( ( ( minus_minus_int @ A2 @ B2 )
% 5.82/6.09 = ( minus_minus_int @ C2 @ D2 ) )
% 5.82/6.09 => ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.09 = ( ord_less_eq_int @ C2 @ D2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_diff_less_eq
% 5.82/6.09 thf(fact_3279_diff__strict__right__mono,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_real @ ( minus_minus_real @ A2 @ C2 ) @ ( minus_minus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_right_mono
% 5.82/6.09 thf(fact_3280_diff__strict__right__mono,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C2 ) @ ( minus_minus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_right_mono
% 5.82/6.09 thf(fact_3281_diff__strict__right__mono,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_int @ ( minus_minus_int @ A2 @ C2 ) @ ( minus_minus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_right_mono
% 5.82/6.09 thf(fact_3282_diff__strict__left__mono,axiom,
% 5.82/6.09 ! [B2: real,A2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_real @ ( minus_minus_real @ C2 @ A2 ) @ ( minus_minus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_left_mono
% 5.82/6.09 thf(fact_3283_diff__strict__left__mono,axiom,
% 5.82/6.09 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A2 ) @ ( minus_minus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_left_mono
% 5.82/6.09 thf(fact_3284_diff__strict__left__mono,axiom,
% 5.82/6.09 ! [B2: int,A2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_int @ ( minus_minus_int @ C2 @ A2 ) @ ( minus_minus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_left_mono
% 5.82/6.09 thf(fact_3285_diff__eq__diff__less,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.09 ( ( ( minus_minus_real @ A2 @ B2 )
% 5.82/6.09 = ( minus_minus_real @ C2 @ D2 ) )
% 5.82/6.09 => ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.09 = ( ord_less_real @ C2 @ D2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_diff_less
% 5.82/6.09 thf(fact_3286_diff__eq__diff__less,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.09 ( ( ( minus_minus_rat @ A2 @ B2 )
% 5.82/6.09 = ( minus_minus_rat @ C2 @ D2 ) )
% 5.82/6.09 => ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.09 = ( ord_less_rat @ C2 @ D2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_diff_less
% 5.82/6.09 thf(fact_3287_diff__eq__diff__less,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.09 ( ( ( minus_minus_int @ A2 @ B2 )
% 5.82/6.09 = ( minus_minus_int @ C2 @ D2 ) )
% 5.82/6.09 => ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.09 = ( ord_less_int @ C2 @ D2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_diff_less
% 5.82/6.09 thf(fact_3288_diff__strict__mono,axiom,
% 5.82/6.09 ! [A2: real,B2: real,D2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_real @ D2 @ C2 )
% 5.82/6.09 => ( ord_less_real @ ( minus_minus_real @ A2 @ C2 ) @ ( minus_minus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_mono
% 5.82/6.09 thf(fact_3289_diff__strict__mono,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,D2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_rat @ D2 @ C2 )
% 5.82/6.09 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C2 ) @ ( minus_minus_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_mono
% 5.82/6.09 thf(fact_3290_diff__strict__mono,axiom,
% 5.82/6.09 ! [A2: int,B2: int,D2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_int @ D2 @ C2 )
% 5.82/6.09 => ( ord_less_int @ ( minus_minus_int @ A2 @ C2 ) @ ( minus_minus_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_strict_mono
% 5.82/6.09 thf(fact_3291_mult_Ocomm__neutral,axiom,
% 5.82/6.09 ! [A2: assn] :
% 5.82/6.09 ( ( times_times_assn @ A2 @ one_one_assn )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % mult.comm_neutral
% 5.82/6.09 thf(fact_3292_mult_Ocomm__neutral,axiom,
% 5.82/6.09 ! [A2: real] :
% 5.82/6.09 ( ( times_times_real @ A2 @ one_one_real )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % mult.comm_neutral
% 5.82/6.09 thf(fact_3293_mult_Ocomm__neutral,axiom,
% 5.82/6.09 ! [A2: rat] :
% 5.82/6.09 ( ( times_times_rat @ A2 @ one_one_rat )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % mult.comm_neutral
% 5.82/6.09 thf(fact_3294_mult_Ocomm__neutral,axiom,
% 5.82/6.09 ! [A2: nat] :
% 5.82/6.09 ( ( times_times_nat @ A2 @ one_one_nat )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % mult.comm_neutral
% 5.82/6.09 thf(fact_3295_mult_Ocomm__neutral,axiom,
% 5.82/6.09 ! [A2: int] :
% 5.82/6.09 ( ( times_times_int @ A2 @ one_one_int )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % mult.comm_neutral
% 5.82/6.09 thf(fact_3296_comm__monoid__mult__class_Omult__1,axiom,
% 5.82/6.09 ! [A2: assn] :
% 5.82/6.09 ( ( times_times_assn @ one_one_assn @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % comm_monoid_mult_class.mult_1
% 5.82/6.09 thf(fact_3297_comm__monoid__mult__class_Omult__1,axiom,
% 5.82/6.09 ! [A2: real] :
% 5.82/6.09 ( ( times_times_real @ one_one_real @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % comm_monoid_mult_class.mult_1
% 5.82/6.09 thf(fact_3298_comm__monoid__mult__class_Omult__1,axiom,
% 5.82/6.09 ! [A2: rat] :
% 5.82/6.09 ( ( times_times_rat @ one_one_rat @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % comm_monoid_mult_class.mult_1
% 5.82/6.09 thf(fact_3299_comm__monoid__mult__class_Omult__1,axiom,
% 5.82/6.09 ! [A2: nat] :
% 5.82/6.09 ( ( times_times_nat @ one_one_nat @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % comm_monoid_mult_class.mult_1
% 5.82/6.09 thf(fact_3300_comm__monoid__mult__class_Omult__1,axiom,
% 5.82/6.09 ! [A2: int] :
% 5.82/6.09 ( ( times_times_int @ one_one_int @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % comm_monoid_mult_class.mult_1
% 5.82/6.09 thf(fact_3301_group__cancel_Osub1,axiom,
% 5.82/6.09 ! [A: real,K: real,A2: real,B2: real] :
% 5.82/6.09 ( ( A
% 5.82/6.09 = ( plus_plus_real @ K @ A2 ) )
% 5.82/6.09 => ( ( minus_minus_real @ A @ B2 )
% 5.82/6.09 = ( plus_plus_real @ K @ ( minus_minus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % group_cancel.sub1
% 5.82/6.09 thf(fact_3302_group__cancel_Osub1,axiom,
% 5.82/6.09 ! [A: rat,K: rat,A2: rat,B2: rat] :
% 5.82/6.09 ( ( A
% 5.82/6.09 = ( plus_plus_rat @ K @ A2 ) )
% 5.82/6.09 => ( ( minus_minus_rat @ A @ B2 )
% 5.82/6.09 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % group_cancel.sub1
% 5.82/6.09 thf(fact_3303_group__cancel_Osub1,axiom,
% 5.82/6.09 ! [A: int,K: int,A2: int,B2: int] :
% 5.82/6.09 ( ( A
% 5.82/6.09 = ( plus_plus_int @ K @ A2 ) )
% 5.82/6.09 => ( ( minus_minus_int @ A @ B2 )
% 5.82/6.09 = ( plus_plus_int @ K @ ( minus_minus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % group_cancel.sub1
% 5.82/6.09 thf(fact_3304_diff__eq__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ( minus_minus_real @ A2 @ B2 )
% 5.82/6.09 = C2 )
% 5.82/6.09 = ( A2
% 5.82/6.09 = ( plus_plus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_eq
% 5.82/6.09 thf(fact_3305_diff__eq__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ( minus_minus_rat @ A2 @ B2 )
% 5.82/6.09 = C2 )
% 5.82/6.09 = ( A2
% 5.82/6.09 = ( plus_plus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_eq
% 5.82/6.09 thf(fact_3306_diff__eq__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ( minus_minus_int @ A2 @ B2 )
% 5.82/6.09 = C2 )
% 5.82/6.09 = ( A2
% 5.82/6.09 = ( plus_plus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_eq_eq
% 5.82/6.09 thf(fact_3307_eq__diff__eq,axiom,
% 5.82/6.09 ! [A2: real,C2: real,B2: real] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( minus_minus_real @ C2 @ B2 ) )
% 5.82/6.09 = ( ( plus_plus_real @ A2 @ B2 )
% 5.82/6.09 = C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % eq_diff_eq
% 5.82/6.09 thf(fact_3308_eq__diff__eq,axiom,
% 5.82/6.09 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( minus_minus_rat @ C2 @ B2 ) )
% 5.82/6.09 = ( ( plus_plus_rat @ A2 @ B2 )
% 5.82/6.09 = C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % eq_diff_eq
% 5.82/6.09 thf(fact_3309_eq__diff__eq,axiom,
% 5.82/6.09 ! [A2: int,C2: int,B2: int] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( minus_minus_int @ C2 @ B2 ) )
% 5.82/6.09 = ( ( plus_plus_int @ A2 @ B2 )
% 5.82/6.09 = C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % eq_diff_eq
% 5.82/6.09 thf(fact_3310_add__diff__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( plus_plus_real @ A2 @ ( minus_minus_real @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_diff_eq
% 5.82/6.09 thf(fact_3311_add__diff__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( plus_plus_rat @ A2 @ ( minus_minus_rat @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_diff_eq
% 5.82/6.09 thf(fact_3312_add__diff__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( plus_plus_int @ A2 @ ( minus_minus_int @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_diff_eq
% 5.82/6.09 thf(fact_3313_diff__diff__eq2,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( minus_minus_real @ A2 @ ( minus_minus_real @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_real @ ( plus_plus_real @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq2
% 5.82/6.09 thf(fact_3314_diff__diff__eq2,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( minus_minus_rat @ A2 @ ( minus_minus_rat @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq2
% 5.82/6.09 thf(fact_3315_diff__diff__eq2,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( minus_minus_int @ A2 @ ( minus_minus_int @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq2
% 5.82/6.09 thf(fact_3316_diff__add__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( plus_plus_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_real @ ( plus_plus_real @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_add_eq
% 5.82/6.09 thf(fact_3317_diff__add__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_add_eq
% 5.82/6.09 thf(fact_3318_diff__add__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_add_eq
% 5.82/6.09 thf(fact_3319_diff__add__eq__diff__diff__swap,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( minus_minus_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_real @ ( minus_minus_real @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_add_eq_diff_diff_swap
% 5.82/6.09 thf(fact_3320_diff__add__eq__diff__diff__swap,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_add_eq_diff_diff_swap
% 5.82/6.09 thf(fact_3321_diff__add__eq__diff__diff__swap,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( minus_minus_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.09 = ( minus_minus_int @ ( minus_minus_int @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_add_eq_diff_diff_swap
% 5.82/6.09 thf(fact_3322_add__implies__diff,axiom,
% 5.82/6.09 ! [C2: real,B2: real,A2: real] :
% 5.82/6.09 ( ( ( plus_plus_real @ C2 @ B2 )
% 5.82/6.09 = A2 )
% 5.82/6.09 => ( C2
% 5.82/6.09 = ( minus_minus_real @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_implies_diff
% 5.82/6.09 thf(fact_3323_add__implies__diff,axiom,
% 5.82/6.09 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.09 ( ( ( plus_plus_rat @ C2 @ B2 )
% 5.82/6.09 = A2 )
% 5.82/6.09 => ( C2
% 5.82/6.09 = ( minus_minus_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_implies_diff
% 5.82/6.09 thf(fact_3324_add__implies__diff,axiom,
% 5.82/6.09 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.09 ( ( ( plus_plus_nat @ C2 @ B2 )
% 5.82/6.09 = A2 )
% 5.82/6.09 => ( C2
% 5.82/6.09 = ( minus_minus_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_implies_diff
% 5.82/6.09 thf(fact_3325_add__implies__diff,axiom,
% 5.82/6.09 ! [C2: int,B2: int,A2: int] :
% 5.82/6.09 ( ( ( plus_plus_int @ C2 @ B2 )
% 5.82/6.09 = A2 )
% 5.82/6.09 => ( C2
% 5.82/6.09 = ( minus_minus_int @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_implies_diff
% 5.82/6.09 thf(fact_3326_diff__diff__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( minus_minus_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq
% 5.82/6.09 thf(fact_3327_diff__diff__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq
% 5.82/6.09 thf(fact_3328_diff__diff__eq,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq
% 5.82/6.09 thf(fact_3329_diff__diff__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_diff_eq
% 5.82/6.09 thf(fact_3330_max__add__distrib__left,axiom,
% 5.82/6.09 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.09 ( ( plus_plus_real @ ( ord_max_real @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_real @ ( plus_plus_real @ X2 @ Z ) @ ( plus_plus_real @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_left
% 5.82/6.09 thf(fact_3331_max__add__distrib__left,axiom,
% 5.82/6.09 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.09 ( ( plus_plus_rat @ ( ord_max_rat @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Z ) @ ( plus_plus_rat @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_left
% 5.82/6.09 thf(fact_3332_max__add__distrib__left,axiom,
% 5.82/6.09 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.09 ( ( plus_plus_nat @ ( ord_max_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Z ) @ ( plus_plus_nat @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_left
% 5.82/6.09 thf(fact_3333_max__add__distrib__left,axiom,
% 5.82/6.09 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.09 ( ( plus_plus_int @ ( ord_max_int @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_int @ ( plus_plus_int @ X2 @ Z ) @ ( plus_plus_int @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_left
% 5.82/6.09 thf(fact_3334_max__add__distrib__right,axiom,
% 5.82/6.09 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.09 ( ( plus_plus_real @ X2 @ ( ord_max_real @ Y3 @ Z ) )
% 5.82/6.09 = ( ord_max_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_right
% 5.82/6.09 thf(fact_3335_max__add__distrib__right,axiom,
% 5.82/6.09 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.09 ( ( plus_plus_rat @ X2 @ ( ord_max_rat @ Y3 @ Z ) )
% 5.82/6.09 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( plus_plus_rat @ X2 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_right
% 5.82/6.09 thf(fact_3336_max__add__distrib__right,axiom,
% 5.82/6.09 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.09 ( ( plus_plus_nat @ X2 @ ( ord_max_nat @ Y3 @ Z ) )
% 5.82/6.09 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ ( plus_plus_nat @ X2 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_right
% 5.82/6.09 thf(fact_3337_max__add__distrib__right,axiom,
% 5.82/6.09 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.09 ( ( plus_plus_int @ X2 @ ( ord_max_int @ Y3 @ Z ) )
% 5.82/6.09 = ( ord_max_int @ ( plus_plus_int @ X2 @ Y3 ) @ ( plus_plus_int @ X2 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_add_distrib_right
% 5.82/6.09 thf(fact_3338_max__diff__distrib__left,axiom,
% 5.82/6.09 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.09 ( ( minus_minus_real @ ( ord_max_real @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_real @ ( minus_minus_real @ X2 @ Z ) @ ( minus_minus_real @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_diff_distrib_left
% 5.82/6.09 thf(fact_3339_max__diff__distrib__left,axiom,
% 5.82/6.09 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.09 ( ( minus_minus_rat @ ( ord_max_rat @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_rat @ ( minus_minus_rat @ X2 @ Z ) @ ( minus_minus_rat @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_diff_distrib_left
% 5.82/6.09 thf(fact_3340_max__diff__distrib__left,axiom,
% 5.82/6.09 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.09 ( ( minus_minus_int @ ( ord_max_int @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ord_max_int @ ( minus_minus_int @ X2 @ Z ) @ ( minus_minus_int @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_diff_distrib_left
% 5.82/6.09 thf(fact_3341_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 5.82/6.09 ! [A2: $o,B2: $o,X2: nat] :
% 5.82/6.09 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.09 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 5.82/6.09 thf(fact_3342_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 5.82/6.09 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.82/6.09 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.82/6.09 = one_one_nat ) ).
% 5.82/6.09
% 5.82/6.09 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 5.82/6.09 thf(fact_3343_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 5.82/6.09 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.82/6.09 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.82/6.09 = one_one_nat ) ).
% 5.82/6.09
% 5.82/6.09 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 5.82/6.09 thf(fact_3344_member__bound__height_H,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.09 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.09 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % member_bound_height'
% 5.82/6.09 thf(fact_3345_add__nonpos__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: real,Y3: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.82/6.09 => ( ( ( plus_plus_real @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_real )
% 5.82/6.09 = ( ( X2 = zero_zero_real )
% 5.82/6.09 & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_eq_0_iff
% 5.82/6.09 thf(fact_3346_add__nonpos__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: rat,Y3: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.82/6.09 => ( ( ( plus_plus_rat @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_rat )
% 5.82/6.09 = ( ( X2 = zero_zero_rat )
% 5.82/6.09 & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_eq_0_iff
% 5.82/6.09 thf(fact_3347_add__nonpos__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: nat,Y3: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_eq_nat @ Y3 @ zero_zero_nat )
% 5.82/6.09 => ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_nat )
% 5.82/6.09 = ( ( X2 = zero_zero_nat )
% 5.82/6.09 & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_eq_0_iff
% 5.82/6.09 thf(fact_3348_add__nonpos__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: int,Y3: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.82/6.09 => ( ( ( plus_plus_int @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_int )
% 5.82/6.09 = ( ( X2 = zero_zero_int )
% 5.82/6.09 & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_eq_0_iff
% 5.82/6.09 thf(fact_3349_add__nonneg__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: real,Y3: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.09 => ( ( ( plus_plus_real @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_real )
% 5.82/6.09 = ( ( X2 = zero_zero_real )
% 5.82/6.09 & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_eq_0_iff
% 5.82/6.09 thf(fact_3350_add__nonneg__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: rat,Y3: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.82/6.09 => ( ( ( plus_plus_rat @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_rat )
% 5.82/6.09 = ( ( X2 = zero_zero_rat )
% 5.82/6.09 & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_eq_0_iff
% 5.82/6.09 thf(fact_3351_add__nonneg__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: nat,Y3: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.82/6.09 => ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_nat )
% 5.82/6.09 = ( ( X2 = zero_zero_nat )
% 5.82/6.09 & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_eq_0_iff
% 5.82/6.09 thf(fact_3352_add__nonneg__eq__0__iff,axiom,
% 5.82/6.09 ! [X2: int,Y3: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.09 => ( ( ( plus_plus_int @ X2 @ Y3 )
% 5.82/6.09 = zero_zero_int )
% 5.82/6.09 = ( ( X2 = zero_zero_int )
% 5.82/6.09 & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_eq_0_iff
% 5.82/6.09 thf(fact_3353_add__nonpos__nonpos,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.82/6.09 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_nonpos
% 5.82/6.09 thf(fact_3354_add__nonpos__nonpos,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.82/6.09 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_nonpos
% 5.82/6.09 thf(fact_3355_add__nonpos__nonpos,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.82/6.09 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_nonpos
% 5.82/6.09 thf(fact_3356_add__nonpos__nonpos,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.82/6.09 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_nonpos
% 5.82/6.09 thf(fact_3357_add__nonneg__nonneg,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.09 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_nonneg
% 5.82/6.09 thf(fact_3358_add__nonneg__nonneg,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.09 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_nonneg
% 5.82/6.09 thf(fact_3359_add__nonneg__nonneg,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.09 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_nonneg
% 5.82/6.09 thf(fact_3360_add__nonneg__nonneg,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.09 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_nonneg
% 5.82/6.09 thf(fact_3361_add__increasing2,axiom,
% 5.82/6.09 ! [C2: real,B2: real,A2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_eq_real @ B2 @ ( plus_plus_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing2
% 5.82/6.09 thf(fact_3362_add__increasing2,axiom,
% 5.82/6.09 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_eq_rat @ B2 @ ( plus_plus_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing2
% 5.82/6.09 thf(fact_3363_add__increasing2,axiom,
% 5.82/6.09 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing2
% 5.82/6.09 thf(fact_3364_add__increasing2,axiom,
% 5.82/6.09 ! [C2: int,B2: int,A2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.09 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing2
% 5.82/6.09 thf(fact_3365_add__decreasing2,axiom,
% 5.82/6.09 ! [C2: real,A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing2
% 5.82/6.09 thf(fact_3366_add__decreasing2,axiom,
% 5.82/6.09 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing2
% 5.82/6.09 thf(fact_3367_add__decreasing2,axiom,
% 5.82/6.09 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing2
% 5.82/6.09 thf(fact_3368_add__decreasing2,axiom,
% 5.82/6.09 ! [C2: int,A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing2
% 5.82/6.09 thf(fact_3369_add__increasing,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_eq_real @ B2 @ ( plus_plus_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing
% 5.82/6.09 thf(fact_3370_add__increasing,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_eq_rat @ B2 @ ( plus_plus_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing
% 5.82/6.09 thf(fact_3371_add__increasing,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing
% 5.82/6.09 thf(fact_3372_add__increasing,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_increasing
% 5.82/6.09 thf(fact_3373_add__decreasing,axiom,
% 5.82/6.09 ! [A2: real,C2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_eq_real @ C2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing
% 5.82/6.09 thf(fact_3374_add__decreasing,axiom,
% 5.82/6.09 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_eq_rat @ C2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing
% 5.82/6.09 thf(fact_3375_add__decreasing,axiom,
% 5.82/6.09 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_eq_nat @ C2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing
% 5.82/6.09 thf(fact_3376_add__decreasing,axiom,
% 5.82/6.09 ! [A2: int,C2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_eq_int @ C2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_decreasing
% 5.82/6.09 thf(fact_3377_add__neg__neg,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_neg
% 5.82/6.09 thf(fact_3378_add__neg__neg,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_neg
% 5.82/6.09 thf(fact_3379_add__neg__neg,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_neg
% 5.82/6.09 thf(fact_3380_add__neg__neg,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_neg
% 5.82/6.09 thf(fact_3381_add__pos__pos,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.09 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_pos
% 5.82/6.09 thf(fact_3382_add__pos__pos,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.09 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_pos
% 5.82/6.09 thf(fact_3383_add__pos__pos,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.09 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_pos
% 5.82/6.09 thf(fact_3384_add__pos__pos,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.09 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_pos
% 5.82/6.09 thf(fact_3385_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.09 => ~ ! [C3: nat] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 = ( plus_plus_nat @ A2 @ C3 ) )
% 5.82/6.09 => ( C3 = zero_zero_nat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % canonically_ordered_monoid_add_class.lessE
% 5.82/6.09 thf(fact_3386_pos__add__strict,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_real @ B2 @ ( plus_plus_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % pos_add_strict
% 5.82/6.09 thf(fact_3387_pos__add__strict,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % pos_add_strict
% 5.82/6.09 thf(fact_3388_pos__add__strict,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % pos_add_strict
% 5.82/6.09 thf(fact_3389_pos__add__strict,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_int @ B2 @ ( plus_plus_int @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % pos_add_strict
% 5.82/6.09 thf(fact_3390_add__mono__thms__linordered__field_I4_J,axiom,
% 5.82/6.09 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.09 ( ( ( ord_less_eq_real @ I @ J )
% 5.82/6.09 & ( ord_less_real @ K @ L ) )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(4)
% 5.82/6.09 thf(fact_3391_add__mono__thms__linordered__field_I4_J,axiom,
% 5.82/6.09 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.09 ( ( ( ord_less_eq_rat @ I @ J )
% 5.82/6.09 & ( ord_less_rat @ K @ L ) )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(4)
% 5.82/6.09 thf(fact_3392_add__mono__thms__linordered__field_I4_J,axiom,
% 5.82/6.09 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.09 ( ( ( ord_less_eq_nat @ I @ J )
% 5.82/6.09 & ( ord_less_nat @ K @ L ) )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(4)
% 5.82/6.09 thf(fact_3393_add__mono__thms__linordered__field_I4_J,axiom,
% 5.82/6.09 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.09 ( ( ( ord_less_eq_int @ I @ J )
% 5.82/6.09 & ( ord_less_int @ K @ L ) )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(4)
% 5.82/6.09 thf(fact_3394_add__mono__thms__linordered__field_I3_J,axiom,
% 5.82/6.09 ! [I: real,J: real,K: real,L: real] :
% 5.82/6.09 ( ( ( ord_less_real @ I @ J )
% 5.82/6.09 & ( ord_less_eq_real @ K @ L ) )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(3)
% 5.82/6.09 thf(fact_3395_add__mono__thms__linordered__field_I3_J,axiom,
% 5.82/6.09 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.82/6.09 ( ( ( ord_less_rat @ I @ J )
% 5.82/6.09 & ( ord_less_eq_rat @ K @ L ) )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(3)
% 5.82/6.09 thf(fact_3396_add__mono__thms__linordered__field_I3_J,axiom,
% 5.82/6.09 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.82/6.09 ( ( ( ord_less_nat @ I @ J )
% 5.82/6.09 & ( ord_less_eq_nat @ K @ L ) )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(3)
% 5.82/6.09 thf(fact_3397_add__mono__thms__linordered__field_I3_J,axiom,
% 5.82/6.09 ! [I: int,J: int,K: int,L: int] :
% 5.82/6.09 ( ( ( ord_less_int @ I @ J )
% 5.82/6.09 & ( ord_less_eq_int @ K @ L ) )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_mono_thms_linordered_field(3)
% 5.82/6.09 thf(fact_3398_add__le__less__mono,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_le_less_mono
% 5.82/6.09 thf(fact_3399_add__le__less__mono,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_le_less_mono
% 5.82/6.09 thf(fact_3400_add__le__less__mono,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_le_less_mono
% 5.82/6.09 thf(fact_3401_add__le__less__mono,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_le_less_mono
% 5.82/6.09 thf(fact_3402_add__less__le__mono,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_less_le_mono
% 5.82/6.09 thf(fact_3403_add__less__le__mono,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C2 ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_less_le_mono
% 5.82/6.09 thf(fact_3404_add__less__le__mono,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C2 ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_less_le_mono
% 5.82/6.09 thf(fact_3405_add__less__le__mono,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ C2 @ D2 )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ A2 @ C2 ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_less_le_mono
% 5.82/6.09 thf(fact_3406_le__iff__diff__le__0,axiom,
% 5.82/6.09 ( ord_less_eq_real
% 5.82/6.09 = ( ^ [A5: real,B6: real] : ( ord_less_eq_real @ ( minus_minus_real @ A5 @ B6 ) @ zero_zero_real ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_iff_diff_le_0
% 5.82/6.09 thf(fact_3407_le__iff__diff__le__0,axiom,
% 5.82/6.09 ( ord_less_eq_rat
% 5.82/6.09 = ( ^ [A5: rat,B6: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B6 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_iff_diff_le_0
% 5.82/6.09 thf(fact_3408_le__iff__diff__le__0,axiom,
% 5.82/6.09 ( ord_less_eq_int
% 5.82/6.09 = ( ^ [A5: int,B6: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B6 ) @ zero_zero_int ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_iff_diff_le_0
% 5.82/6.09 thf(fact_3409_less__iff__diff__less__0,axiom,
% 5.82/6.09 ( ord_less_real
% 5.82/6.09 = ( ^ [A5: real,B6: real] : ( ord_less_real @ ( minus_minus_real @ A5 @ B6 ) @ zero_zero_real ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_iff_diff_less_0
% 5.82/6.09 thf(fact_3410_less__iff__diff__less__0,axiom,
% 5.82/6.09 ( ord_less_rat
% 5.82/6.09 = ( ^ [A5: rat,B6: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B6 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_iff_diff_less_0
% 5.82/6.09 thf(fact_3411_less__iff__diff__less__0,axiom,
% 5.82/6.09 ( ord_less_int
% 5.82/6.09 = ( ^ [A5: int,B6: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B6 ) @ zero_zero_int ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_iff_diff_less_0
% 5.82/6.09 thf(fact_3412_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ( minus_minus_nat @ B2 @ A2 )
% 5.82/6.09 = C2 )
% 5.82/6.09 = ( B2
% 5.82/6.09 = ( plus_plus_nat @ C2 @ A2 ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.82/6.09 thf(fact_3413_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( plus_plus_nat @ A2 @ ( minus_minus_nat @ B2 @ A2 ) )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.82/6.09 thf(fact_3414_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B2 @ A2 ) )
% 5.82/6.09 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.82/6.09 thf(fact_3415_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.09 = ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A2 ) @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.82/6.09 thf(fact_3416_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A2 ) @ C2 )
% 5.82/6.09 = ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.82/6.09 thf(fact_3417_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B2 ) @ A2 )
% 5.82/6.09 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B2 @ A2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.82/6.09 thf(fact_3418_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B2 @ A2 ) )
% 5.82/6.09 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B2 ) @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.82/6.09 thf(fact_3419_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B2 @ A2 ) )
% 5.82/6.09 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A2 ) @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.82/6.09 thf(fact_3420_le__add__diff,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_add_diff
% 5.82/6.09 thf(fact_3421_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A2 ) @ A2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % ordered_cancel_comm_monoid_diff_class.diff_add
% 5.82/6.09 thf(fact_3422_le__diff__eq,axiom,
% 5.82/6.09 ! [A2: real,C2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ A2 @ ( minus_minus_real @ C2 @ B2 ) )
% 5.82/6.09 = ( ord_less_eq_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_diff_eq
% 5.82/6.09 thf(fact_3423_le__diff__eq,axiom,
% 5.82/6.09 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ ( minus_minus_rat @ C2 @ B2 ) )
% 5.82/6.09 = ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_diff_eq
% 5.82/6.09 thf(fact_3424_le__diff__eq,axiom,
% 5.82/6.09 ! [A2: int,C2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ ( minus_minus_int @ C2 @ B2 ) )
% 5.82/6.09 = ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % le_diff_eq
% 5.82/6.09 thf(fact_3425_diff__le__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_less_eq_real @ A2 @ ( plus_plus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_le_eq
% 5.82/6.09 thf(fact_3426_diff__le__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_le_eq
% 5.82/6.09 thf(fact_3427_diff__le__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_less_eq_int @ A2 @ ( plus_plus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_le_eq
% 5.82/6.09 thf(fact_3428_diff__less__eq,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_real @ ( minus_minus_real @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_less_real @ A2 @ ( plus_plus_real @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_less_eq
% 5.82/6.09 thf(fact_3429_diff__less__eq,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_less_rat @ A2 @ ( plus_plus_rat @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_less_eq
% 5.82/6.09 thf(fact_3430_diff__less__eq,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_less_int @ A2 @ ( plus_plus_int @ C2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % diff_less_eq
% 5.82/6.09 thf(fact_3431_less__diff__eq,axiom,
% 5.82/6.09 ! [A2: real,C2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ ( minus_minus_real @ C2 @ B2 ) )
% 5.82/6.09 = ( ord_less_real @ ( plus_plus_real @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_diff_eq
% 5.82/6.09 thf(fact_3432_less__diff__eq,axiom,
% 5.82/6.09 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ ( minus_minus_rat @ C2 @ B2 ) )
% 5.82/6.09 = ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_diff_eq
% 5.82/6.09 thf(fact_3433_less__diff__eq,axiom,
% 5.82/6.09 ! [A2: int,C2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ ( minus_minus_int @ C2 @ B2 ) )
% 5.82/6.09 = ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_diff_eq
% 5.82/6.09 thf(fact_3434_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.09 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.09 ( ? [Summary2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( plus_plus_nat @ one_one_nat
% 5.82/6.09 @ ( if_nat @ ( Xa = Mi2 ) @ zero_zero_nat
% 5.82/6.09 @ ( if_nat @ ( Xa = Ma2 ) @ zero_zero_nat
% 5.82/6.09 @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ zero_zero_nat
% 5.82/6.09 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ zero_zero_nat
% 5.82/6.09 @ ( if_nat
% 5.82/6.09 @ ( ( ord_less_nat @ Mi2 @ Xa )
% 5.82/6.09 & ( ord_less_nat @ Xa @ Ma2 ) )
% 5.82/6.09 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.82/6.09 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 5.82/6.09 thf(fact_3435_add__neg__nonpos,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_nonpos
% 5.82/6.09 thf(fact_3436_add__neg__nonpos,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_nonpos
% 5.82/6.09 thf(fact_3437_add__neg__nonpos,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_nonpos
% 5.82/6.09 thf(fact_3438_add__neg__nonpos,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_neg_nonpos
% 5.82/6.09 thf(fact_3439_add__nonneg__pos,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.09 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_pos
% 5.82/6.09 thf(fact_3440_add__nonneg__pos,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.82/6.09 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_pos
% 5.82/6.09 thf(fact_3441_add__nonneg__pos,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.09 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_pos
% 5.82/6.09 thf(fact_3442_add__nonneg__pos,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.09 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonneg_pos
% 5.82/6.09 thf(fact_3443_add__nonpos__neg,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.09 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.82/6.09 => ( ord_less_real @ ( plus_plus_real @ A2 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_neg
% 5.82/6.09 thf(fact_3444_add__nonpos__neg,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.82/6.09 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.82/6.09 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_neg
% 5.82/6.09 thf(fact_3445_add__nonpos__neg,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.82/6.09 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.82/6.09 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_neg
% 5.82/6.09 thf(fact_3446_add__nonpos__neg,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.09 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.09 => ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_nonpos_neg
% 5.82/6.09 thf(fact_3447_add__pos__nonneg,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.09 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_nonneg
% 5.82/6.09 thf(fact_3448_add__pos__nonneg,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.09 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_nonneg
% 5.82/6.09 thf(fact_3449_add__pos__nonneg,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.82/6.09 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_nonneg
% 5.82/6.09 thf(fact_3450_add__pos__nonneg,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.09 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_pos_nonneg
% 5.82/6.09 thf(fact_3451_add__strict__increasing,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_real @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_real @ B2 @ ( plus_plus_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing
% 5.82/6.09 thf(fact_3452_add__strict__increasing,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing
% 5.82/6.09 thf(fact_3453_add__strict__increasing,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing
% 5.82/6.09 thf(fact_3454_add__strict__increasing,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_int @ B2 @ ( plus_plus_int @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing
% 5.82/6.09 thf(fact_3455_add__strict__increasing2,axiom,
% 5.82/6.09 ! [A2: real,B2: real,C2: real] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.09 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_real @ B2 @ ( plus_plus_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing2
% 5.82/6.09 thf(fact_3456_add__strict__increasing2,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.09 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing2
% 5.82/6.09 thf(fact_3457_add__strict__increasing2,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.09 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing2
% 5.82/6.09 thf(fact_3458_add__strict__increasing2,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.09 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.09 => ( ord_less_int @ B2 @ ( plus_plus_int @ A2 @ C2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % add_strict_increasing2
% 5.82/6.09 thf(fact_3459_vebt__member_Oelims_I2_J,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.09 ( ( vEBT_vebt_member @ X2 @ Xa )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.09 => A3 )
% 5.82/6.09 & ( ( Xa != zero_zero_nat )
% 5.82/6.09 => ( ( ( Xa = one_one_nat )
% 5.82/6.09 => B3 )
% 5.82/6.09 & ( Xa = one_one_nat ) ) ) ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.09 ( ? [Summary2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ~ ( ( Xa != Mi2 )
% 5.82/6.09 => ( ( Xa != Ma2 )
% 5.82/6.09 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.09 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.09 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_member.elims(2)
% 5.82/6.09 thf(fact_3460_vebt__member_Oelims_I1_J,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.82/6.09 ( ( ( vEBT_vebt_member @ X2 @ Xa )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.09 => A3 )
% 5.82/6.09 & ( ( Xa != zero_zero_nat )
% 5.82/6.09 => ( ( ( Xa = one_one_nat )
% 5.82/6.09 => B3 )
% 5.82/6.09 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.82/6.09 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.09 => Y3 )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.09 => Y3 )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.09 => Y3 )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.09 ( ? [Summary2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( ~ ( ( Xa != Mi2 )
% 5.82/6.09 => ( ( Xa != Ma2 )
% 5.82/6.09 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.09 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.09 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_member.elims(1)
% 5.82/6.09 thf(fact_3461_vebt__member_Oelims_I3_J,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.09 ( ~ ( vEBT_vebt_member @ X2 @ Xa )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( ( ( Xa = zero_zero_nat )
% 5.82/6.09 => A3 )
% 5.82/6.09 & ( ( Xa != zero_zero_nat )
% 5.82/6.09 => ( ( ( Xa = one_one_nat )
% 5.82/6.09 => B3 )
% 5.82/6.09 & ( Xa = one_one_nat ) ) ) ) )
% 5.82/6.09 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.09 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.09 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.09 ( ? [Summary2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( ( Xa != Mi2 )
% 5.82/6.09 => ( ( Xa != Ma2 )
% 5.82/6.09 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.09 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.09 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_member.elims(3)
% 5.82/6.09 thf(fact_3462_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.09 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.82/6.09 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.09 ( ? [Summary2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 5.82/6.09 thf(fact_3463_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.09 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X2 @ Xa )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3 != one_one_nat ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( if_nat
% 5.82/6.09 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.09 & ~ ( ( Xa = Mi2 )
% 5.82/6.09 | ( Xa = Ma2 ) ) )
% 5.82/6.09 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.09 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 5.82/6.09 thf(fact_3464_invar__vebt_Osimps,axiom,
% 5.82/6.09 ( vEBT_invar_vebt
% 5.82/6.09 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.82/6.09 ( ( ? [A5: $o,B6: $o] :
% 5.82/6.09 ( A1
% 5.82/6.09 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.82/6.09 & ( A22
% 5.82/6.09 = ( suc @ zero_zero_nat ) ) )
% 5.82/6.09 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 5.82/6.09 ( ( A1
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 5.82/6.09 & ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.82/6.09 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 5.82/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.82/6.09 & ( A22
% 5.82/6.09 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.82/6.09 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 5.82/6.09 & ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X7 ) ) )
% 5.82/6.09 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 5.82/6.09 ( ( A1
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 5.82/6.09 & ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.82/6.09 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 5.82/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.82/6.09 & ( A22
% 5.82/6.09 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.82/6.09 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 5.82/6.09 & ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X7 ) ) )
% 5.82/6.09 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.82/6.09 ( ( A1
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 5.82/6.09 & ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.82/6.09 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 5.82/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.82/6.09 & ( A22
% 5.82/6.09 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.82/6.09 & ! [I4: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.82/6.09 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X7 ) )
% 5.82/6.09 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.82/6.09 & ( ( Mi3 = Ma3 )
% 5.82/6.09 => ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X7 ) ) )
% 5.82/6.09 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.82/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.82/6.09 & ( ( Mi3 != Ma3 )
% 5.82/6.09 => ! [I4: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.82/6.09 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.82/6.09 = I4 )
% 5.82/6.09 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.82/6.09 & ! [X3: nat] :
% 5.82/6.09 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 5.82/6.09 = I4 )
% 5.82/6.09 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 5.82/6.09 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.82/6.09 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) )
% 5.82/6.09 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.82/6.09 ( ( A1
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 5.82/6.09 & ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.82/6.09 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 5.82/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.82/6.09 & ( A22
% 5.82/6.09 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.82/6.09 & ! [I4: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.82/6.09 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X7 ) )
% 5.82/6.09 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.82/6.09 & ( ( Mi3 = Ma3 )
% 5.82/6.09 => ! [X3: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.82/6.09 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X7 ) ) )
% 5.82/6.09 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.82/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.82/6.09 & ( ( Mi3 != Ma3 )
% 5.82/6.09 => ! [I4: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.82/6.09 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.82/6.09 = I4 )
% 5.82/6.09 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.82/6.09 & ! [X3: nat] :
% 5.82/6.09 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 5.82/6.09 = I4 )
% 5.82/6.09 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 5.82/6.09 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.82/6.09 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % invar_vebt.simps
% 5.82/6.09 thf(fact_3465_invar__vebt_Ocases,axiom,
% 5.82/6.09 ! [A12: vEBT_VEBT,A23: nat] :
% 5.82/6.09 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.82/6.09 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.09 ( A12
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( A23
% 5.82/6.09 != ( suc @ zero_zero_nat ) ) )
% 5.82/6.09 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.82/6.09 ( ( A12
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( ( A23 = Deg2 )
% 5.82/6.09 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X8 @ N3 ) )
% 5.82/6.09 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.82/6.09 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( M5 = N3 )
% 5.82/6.09 => ( ( Deg2
% 5.82/6.09 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.82/6.09 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.82/6.09 => ~ ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X8 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.82/6.09 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.82/6.09 ( ( A12
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( ( A23 = Deg2 )
% 5.82/6.09 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X8 @ N3 ) )
% 5.82/6.09 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.82/6.09 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( M5
% 5.82/6.09 = ( suc @ N3 ) )
% 5.82/6.09 => ( ( Deg2
% 5.82/6.09 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.82/6.09 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.82/6.09 => ~ ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X8 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.82/6.09 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.82/6.09 ( ( A12
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( ( A23 = Deg2 )
% 5.82/6.09 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X8 @ N3 ) )
% 5.82/6.09 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.82/6.09 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( M5 = N3 )
% 5.82/6.09 => ( ( Deg2
% 5.82/6.09 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.82/6.09 => ( ! [I5: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X7 ) )
% 5.82/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.82/6.09 => ( ( ( Mi2 = Ma2 )
% 5.82/6.09 => ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X8 @ X_12 ) ) )
% 5.82/6.09 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.82/6.09 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.82/6.09 => ~ ( ( Mi2 != Ma2 )
% 5.82/6.09 => ! [I5: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.82/6.09 = I5 )
% 5.82/6.09 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.82/6.09 & ! [X8: nat] :
% 5.82/6.09 ( ( ( ( vEBT_VEBT_high @ X8 @ N3 )
% 5.82/6.09 = I5 )
% 5.82/6.09 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ X8 @ N3 ) ) )
% 5.82/6.09 => ( ( ord_less_nat @ Mi2 @ X8 )
% 5.82/6.09 & ( ord_less_eq_nat @ X8 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.09 => ~ ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.82/6.09 ( ( A12
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( ( A23 = Deg2 )
% 5.82/6.09 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ( vEBT_invar_vebt @ X8 @ N3 ) )
% 5.82/6.09 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.82/6.09 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.82/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( M5
% 5.82/6.09 = ( suc @ N3 ) )
% 5.82/6.09 => ( ( Deg2
% 5.82/6.09 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.82/6.09 => ( ! [I5: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X7 ) )
% 5.82/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.82/6.09 => ( ( ( Mi2 = Ma2 )
% 5.82/6.09 => ! [X8: vEBT_VEBT] :
% 5.82/6.09 ( ( member_VEBT_VEBT @ X8 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.82/6.09 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X8 @ X_12 ) ) )
% 5.82/6.09 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.82/6.09 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.82/6.09 => ~ ( ( Mi2 != Ma2 )
% 5.82/6.09 => ! [I5: nat] :
% 5.82/6.09 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.82/6.09 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.82/6.09 = I5 )
% 5.82/6.09 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.82/6.09 & ! [X8: nat] :
% 5.82/6.09 ( ( ( ( vEBT_VEBT_high @ X8 @ N3 )
% 5.82/6.09 = I5 )
% 5.82/6.09 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ X8 @ N3 ) ) )
% 5.82/6.09 => ( ( ord_less_nat @ Mi2 @ X8 )
% 5.82/6.09 & ( ord_less_eq_nat @ X8 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % invar_vebt.cases
% 5.82/6.09 thf(fact_3466_vebt__insert_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 5.82/6.09 ( ( ( vEBT_vebt_insert @ X2 @ Xa )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.82/6.09 & ( ( Xa != zero_zero_nat )
% 5.82/6.09 => ( ( ( Xa = one_one_nat )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.82/6.09 & ( ( Xa != one_one_nat )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 5.82/6.09 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 5.82/6.09 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 5.82/6.09 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( if_VEBT_VEBT
% 5.82/6.09 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.09 & ~ ( ( Xa = Mi2 )
% 5.82/6.09 | ( Xa = Ma2 ) ) )
% 5.82/6.09 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.82/6.09 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_insert.elims
% 5.82/6.09 thf(fact_3467_vebt__delete_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 5.82/6.09 ( ( ( vEBT_vebt_delete @ X2 @ Xa )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( ( Xa = zero_zero_nat )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 5.82/6.09 => ( ! [A3: $o] :
% 5.82/6.09 ( ? [B3: $o] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( ( Xa
% 5.82/6.09 = ( suc @ zero_zero_nat ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ( ? [N3: nat] :
% 5.82/6.09 ( Xa
% 5.82/6.09 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.09 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 5.82/6.09 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 5.82/6.09 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.09 => ~ ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.82/6.09 & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.09 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.09 => ( ( ( ( Xa = Mi2 )
% 5.82/6.09 & ( Xa = Ma2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.82/6.09 & ( ~ ( ( Xa = Mi2 )
% 5.82/6.09 & ( Xa = Ma2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.09 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 @ ( vEBT_Node
% 5.82/6.09 @ ( some_P7363390416028606310at_nat
% 5.82/6.09 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 5.82/6.09 @ ( if_nat
% 5.82/6.09 @ ( ( ( Xa = Mi2 )
% 5.82/6.09 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.09 = Ma2 ) )
% 5.82/6.09 & ( ( Xa != Mi2 )
% 5.82/6.09 => ( Xa = Ma2 ) ) )
% 5.82/6.09 @ ( if_nat
% 5.82/6.09 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 = none_nat )
% 5.82/6.09 @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 5.82/6.09 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.09 @ Ma2 ) ) )
% 5.82/6.09 @ ( suc @ ( suc @ Va3 ) )
% 5.82/6.09 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 @ ( vEBT_Node
% 5.82/6.09 @ ( some_P7363390416028606310at_nat
% 5.82/6.09 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 5.82/6.09 @ ( if_nat
% 5.82/6.09 @ ( ( ( Xa = Mi2 )
% 5.82/6.09 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.09 = Ma2 ) )
% 5.82/6.09 & ( ( Xa != Mi2 )
% 5.82/6.09 => ( Xa = Ma2 ) ) )
% 5.82/6.09 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.09 @ Ma2 ) ) )
% 5.82/6.09 @ ( suc @ ( suc @ Va3 ) )
% 5.82/6.09 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.09 @ Summary2 ) )
% 5.82/6.09 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_delete.elims
% 5.82/6.09 thf(fact_3468_minNrulli__ruleT,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 5.82/6.09 ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_minNulli @ Ti )
% 5.82/6.09 @ ^ [R5: $o] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_VEBT_minNull @ T ) ) ) )
% 5.82/6.09 @ one_one_nat ) ).
% 5.82/6.09
% 5.82/6.09 % minNrulli_ruleT
% 5.82/6.09 thf(fact_3469_vebt__maxt_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.82/6.09 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ~ ( ( B3
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.09 & ( ~ B3
% 5.82/6.09 => ( ( A3
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.09 & ( ~ A3
% 5.82/6.09 => ( Y3 = none_nat ) ) ) ) ) )
% 5.82/6.09 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.09 => ( Y3 != none_nat ) )
% 5.82/6.09 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.82/6.09 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_maxt.elims
% 5.82/6.09 thf(fact_3470_vebt__mint_Oelims,axiom,
% 5.82/6.09 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.82/6.09 ( ( ( vEBT_vebt_mint @ X2 )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ! [A3: $o,B3: $o] :
% 5.82/6.09 ( ( X2
% 5.82/6.09 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.09 => ~ ( ( A3
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.09 & ( ~ A3
% 5.82/6.09 => ( ( B3
% 5.82/6.09 => ( Y3
% 5.82/6.09 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.09 & ( ~ B3
% 5.82/6.09 => ( Y3 = none_nat ) ) ) ) ) )
% 5.82/6.09 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.09 => ( Y3 != none_nat ) )
% 5.82/6.09 => ~ ! [Mi2: nat] :
% 5.82/6.09 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.09 ( X2
% 5.82/6.09 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_mint.elims
% 5.82/6.09 thf(fact_3471_norm__pre__pure__iff__sng,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.09 ( ( hoare_1429296392585015714_VEBTi @ ( pure_assn @ B2 ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff_sng
% 5.82/6.09 thf(fact_3472_norm__pre__pure__iff__sng,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.09 ( ( hoare_hoare_triple_o @ ( pure_assn @ B2 ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_hoare_triple_o @ one_one_assn @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff_sng
% 5.82/6.09 thf(fact_3473_norm__pre__pure__iff__sng,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.09 ( ( hoare_7629718768684598413on_nat @ ( pure_assn @ B2 ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ one_one_assn @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff_sng
% 5.82/6.09 thf(fact_3474_norm__pre__pure__iff__sng,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.09 ( ( hoare_3067605981109127869le_nat @ ( pure_assn @ B2 ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ one_one_assn @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff_sng
% 5.82/6.09 thf(fact_3475_ent__pure__pre__iff__sng,axiom,
% 5.82/6.09 ! [B2: $o,Q: assn] :
% 5.82/6.09 ( ( entails @ ( pure_assn @ B2 ) @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( entails @ one_one_assn @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ent_pure_pre_iff_sng
% 5.82/6.09 thf(fact_3476_norm__pre__pure__iff,axiom,
% 5.82/6.09 ! [P: assn,B2: $o,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.09 ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ P @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff
% 5.82/6.09 thf(fact_3477_norm__pre__pure__iff,axiom,
% 5.82/6.09 ! [P: assn,B2: $o,F: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.09 ( ( hoare_hoare_triple_o @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_hoare_triple_o @ P @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff
% 5.82/6.09 thf(fact_3478_norm__pre__pure__iff,axiom,
% 5.82/6.09 ! [P: assn,B2: $o,F: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.09 ( ( hoare_7629718768684598413on_nat @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ P @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff
% 5.82/6.09 thf(fact_3479_norm__pre__pure__iff,axiom,
% 5.82/6.09 ! [P: assn,B2: $o,F: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.09 ( ( hoare_3067605981109127869le_nat @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ P @ F @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_iff
% 5.82/6.09 thf(fact_3480_ent__pure__pre__iff,axiom,
% 5.82/6.09 ! [P: assn,B2: $o,Q: assn] :
% 5.82/6.09 ( ( entails @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ Q )
% 5.82/6.09 = ( B2
% 5.82/6.09 => ( entails @ P @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ent_pure_pre_iff
% 5.82/6.09 thf(fact_3481_vebt__pred_Osimps_I3_J,axiom,
% 5.82/6.09 ! [B2: $o,A2: $o,Va: nat] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.09 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.09 & ( ~ B2
% 5.82/6.09 => ( ( A2
% 5.82/6.09 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.09 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.09 & ( ~ A2
% 5.82/6.09 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.09 = none_nat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred.simps(3)
% 5.82/6.09 thf(fact_3482_minNulli__rule,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 5.82/6.09 ( hoare_hoare_triple_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_minNulli @ Ti )
% 5.82/6.09 @ ^ [R5: $o] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_VEBT_minNull @ T ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % minNulli_rule
% 5.82/6.09 thf(fact_3483_vebt__memberi_H__rf__abstr,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.09 ( hoare_hoare_triple_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X2 )
% 5.82/6.09 @ ^ [R5: $o] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_member @ T @ X2 ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_memberi'_rf_abstr
% 5.82/6.09 thf(fact_3484_vebt__pred_H__rf__abstr,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.09 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X2 )
% 5.82/6.09 @ ^ [R5: option_nat] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_pred @ T @ X2 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred'_rf_abstr
% 5.82/6.09 thf(fact_3485_vebt__succi_H__rf__abstr,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.09 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X2 )
% 5.82/6.09 @ ^ [R5: option_nat] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_succ @ T @ X2 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_succi'_rf_abstr
% 5.82/6.09 thf(fact_3486_merge__pure__star,axiom,
% 5.82/6.09 ! [A2: $o,B2: $o] :
% 5.82/6.09 ( ( times_times_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B2 ) )
% 5.82/6.09 = ( pure_assn
% 5.82/6.09 @ ( A2
% 5.82/6.09 & B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % merge_pure_star
% 5.82/6.09 thf(fact_3487_pure__true,axiom,
% 5.82/6.09 ( ( pure_assn @ $true )
% 5.82/6.09 = one_one_assn ) ).
% 5.82/6.09
% 5.82/6.09 % pure_true
% 5.82/6.09 thf(fact_3488_pure__assn__eq__emp__iff,axiom,
% 5.82/6.09 ! [P: $o] :
% 5.82/6.09 ( ( ( pure_assn @ P )
% 5.82/6.09 = one_one_assn )
% 5.82/6.09 = P ) ).
% 5.82/6.09
% 5.82/6.09 % pure_assn_eq_emp_iff
% 5.82/6.09 thf(fact_3489_htt__vebt__memberi,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.09 ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X2 )
% 5.82/6.09 @ ^ [R5: $o] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_member @ T @ X2 ) ) ) )
% 5.82/6.09 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % htt_vebt_memberi
% 5.82/6.09 thf(fact_3490_assn__times__comm,axiom,
% 5.82/6.09 ( times_times_assn
% 5.82/6.09 = ( ^ [P3: assn,Q7: assn] : ( times_times_assn @ Q7 @ P3 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % assn_times_comm
% 5.82/6.09 thf(fact_3491_assn__times__assoc,axiom,
% 5.82/6.09 ! [P: assn,Q: assn,R: assn] :
% 5.82/6.09 ( ( times_times_assn @ ( times_times_assn @ P @ Q ) @ R )
% 5.82/6.09 = ( times_times_assn @ P @ ( times_times_assn @ Q @ R ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % assn_times_assoc
% 5.82/6.09 thf(fact_3492_ent__iffI,axiom,
% 5.82/6.09 ! [A: assn,B: assn] :
% 5.82/6.09 ( ( entails @ A @ B )
% 5.82/6.09 => ( ( entails @ B @ A )
% 5.82/6.09 => ( A = B ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ent_iffI
% 5.82/6.09 thf(fact_3493_ent__refl,axiom,
% 5.82/6.09 ! [P: assn] : ( entails @ P @ P ) ).
% 5.82/6.09
% 5.82/6.09 % ent_refl
% 5.82/6.09 thf(fact_3494_ent__trans,axiom,
% 5.82/6.09 ! [P: assn,Q: assn,R: assn] :
% 5.82/6.09 ( ( entails @ P @ Q )
% 5.82/6.09 => ( ( entails @ Q @ R )
% 5.82/6.09 => ( entails @ P @ R ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ent_trans
% 5.82/6.09 thf(fact_3495_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.82/6.09 ! [X2: produc5542196010084753463at_nat] :
% 5.82/6.09 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.82/6.09 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.82/6.09 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.cases
% 5.82/6.09 thf(fact_3496_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.82/6.09 ! [X2: produc8306885398267862888on_nat] :
% 5.82/6.09 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.82/6.09 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.82/6.09 => ~ ! [F2: nat > nat > nat,A3: nat,B3: nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.cases
% 5.82/6.09 thf(fact_3497_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.82/6.09 ! [X2: produc5491161045314408544at_nat] :
% 5.82/6.09 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.82/6.09 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.82/6.09 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X4 ) @ ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_comp_shift.cases
% 5.82/6.09 thf(fact_3498_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.82/6.09 ! [X2: produc2233624965454879586on_nat] :
% 5.82/6.09 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.82/6.09 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.82/6.09 => ~ ! [F2: nat > nat > $o,X4: nat,Y4: nat] :
% 5.82/6.09 ( X2
% 5.82/6.09 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_comp_shift.cases
% 5.82/6.09 thf(fact_3499_ent__star__mono,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,Q: assn,Q2: assn] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ( entails @ Q @ Q2 )
% 5.82/6.09 => ( entails @ ( times_times_assn @ P @ Q ) @ ( times_times_assn @ P5 @ Q2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % ent_star_mono
% 5.82/6.09 thf(fact_3500_cons__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,Q: vEBT_VEBTi > assn,Q2: vEBT_VEBTi > assn,C2: heap_T8145700208782473153_VEBTi] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ! [X4: vEBT_VEBTi] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( ( hoare_1429296392585015714_VEBTi @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_rule
% 5.82/6.09 thf(fact_3501_cons__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,Q: $o > assn,Q2: $o > assn,C2: heap_Time_Heap_o] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ! [X4: $o] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( ( hoare_hoare_triple_o @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_hoare_triple_o @ P @ C2 @ Q2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_rule
% 5.82/6.09 thf(fact_3502_cons__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,Q: option_nat > assn,Q2: option_nat > assn,C2: heap_T2636463487746394924on_nat] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ! [X4: option_nat] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( ( hoare_7629718768684598413on_nat @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ P @ C2 @ Q2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_rule
% 5.82/6.09 thf(fact_3503_cons__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,Q: nat > assn,Q2: nat > assn,C2: heap_Time_Heap_nat] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ! [X4: nat] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( ( hoare_3067605981109127869le_nat @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ P @ C2 @ Q2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_rule
% 5.82/6.09 thf(fact_3504_cons__post__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,Q2: vEBT_VEBTi > assn] :
% 5.82/6.09 ( ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q )
% 5.82/6.09 => ( ! [X4: vEBT_VEBTi] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_post_rule
% 5.82/6.09 thf(fact_3505_cons__post__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_Time_Heap_o,Q: $o > assn,Q2: $o > assn] :
% 5.82/6.09 ( ( hoare_hoare_triple_o @ P @ C2 @ Q )
% 5.82/6.09 => ( ! [X4: $o] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( hoare_hoare_triple_o @ P @ C2 @ Q2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_post_rule
% 5.82/6.09 thf(fact_3506_cons__post__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn,Q2: option_nat > assn] :
% 5.82/6.09 ( ( hoare_7629718768684598413on_nat @ P @ C2 @ Q )
% 5.82/6.09 => ( ! [X4: option_nat] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ P @ C2 @ Q2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_post_rule
% 5.82/6.09 thf(fact_3507_cons__post__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_Time_Heap_nat,Q: nat > assn,Q2: nat > assn] :
% 5.82/6.09 ( ( hoare_3067605981109127869le_nat @ P @ C2 @ Q )
% 5.82/6.09 => ( ! [X4: nat] : ( entails @ ( Q @ X4 ) @ ( Q2 @ X4 ) )
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ P @ C2 @ Q2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_post_rule
% 5.82/6.09 thf(fact_3508_assn__one__left,axiom,
% 5.82/6.09 ! [P: assn] :
% 5.82/6.09 ( ( times_times_assn @ one_one_assn @ P )
% 5.82/6.09 = P ) ).
% 5.82/6.09
% 5.82/6.09 % assn_one_left
% 5.82/6.09 thf(fact_3509_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.82/6.09 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.82/6.09 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A2 ) @ ( some_P7363390416028606310at_nat @ B2 ) )
% 5.82/6.09 = ( some_P7363390416028606310at_nat @ ( F @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.simps(3)
% 5.82/6.09 thf(fact_3510_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.82/6.09 ! [F: nat > nat > nat,A2: nat,B2: nat] :
% 5.82/6.09 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A2 ) @ ( some_nat @ B2 ) )
% 5.82/6.09 = ( some_nat @ ( F @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.simps(3)
% 5.82/6.09 thf(fact_3511_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.82/6.09 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.82/6.09 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.82/6.09 = none_P5556105721700978146at_nat ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.simps(1)
% 5.82/6.09 thf(fact_3512_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.82/6.09 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.82/6.09 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.simps(1)
% 5.82/6.09 thf(fact_3513_frame__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,R: assn] :
% 5.82/6.09 ( ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q )
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ P @ R ) @ C2
% 5.82/6.09 @ ^ [X3: vEBT_VEBTi] : ( times_times_assn @ ( Q @ X3 ) @ R ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % frame_rule
% 5.82/6.09 thf(fact_3514_frame__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_Time_Heap_o,Q: $o > assn,R: assn] :
% 5.82/6.09 ( ( hoare_hoare_triple_o @ P @ C2 @ Q )
% 5.82/6.09 => ( hoare_hoare_triple_o @ ( times_times_assn @ P @ R ) @ C2
% 5.82/6.09 @ ^ [X3: $o] : ( times_times_assn @ ( Q @ X3 ) @ R ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % frame_rule
% 5.82/6.09 thf(fact_3515_frame__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn,R: assn] :
% 5.82/6.09 ( ( hoare_7629718768684598413on_nat @ P @ C2 @ Q )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( times_times_assn @ P @ R ) @ C2
% 5.82/6.09 @ ^ [X3: option_nat] : ( times_times_assn @ ( Q @ X3 ) @ R ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % frame_rule
% 5.82/6.09 thf(fact_3516_frame__rule,axiom,
% 5.82/6.09 ! [P: assn,C2: heap_Time_Heap_nat,Q: nat > assn,R: assn] :
% 5.82/6.09 ( ( hoare_3067605981109127869le_nat @ P @ C2 @ Q )
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ ( times_times_assn @ P @ R ) @ C2
% 5.82/6.09 @ ^ [X3: nat] : ( times_times_assn @ ( Q @ X3 ) @ R ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % frame_rule
% 5.82/6.09 thf(fact_3517_cons__pre__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ( hoare_1429296392585015714_VEBTi @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_pre_rule
% 5.82/6.09 thf(fact_3518_cons__pre__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,C2: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ( hoare_hoare_triple_o @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_hoare_triple_o @ P @ C2 @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_pre_rule
% 5.82/6.09 thf(fact_3519_cons__pre__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ( hoare_7629718768684598413on_nat @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ P @ C2 @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_pre_rule
% 5.82/6.09 thf(fact_3520_cons__pre__rule,axiom,
% 5.82/6.09 ! [P: assn,P5: assn,C2: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.09 ( ( entails @ P @ P5 )
% 5.82/6.09 => ( ( hoare_3067605981109127869le_nat @ P5 @ C2 @ Q )
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ P @ C2 @ Q ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % cons_pre_rule
% 5.82/6.09 thf(fact_3521_norm__pre__pure__rule1,axiom,
% 5.82/6.09 ! [B2: $o,P: assn,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ P @ F @ Q ) )
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule1
% 5.82/6.09 thf(fact_3522_norm__pre__pure__rule1,axiom,
% 5.82/6.09 ! [B2: $o,P: assn,F: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_hoare_triple_o @ P @ F @ Q ) )
% 5.82/6.09 => ( hoare_hoare_triple_o @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule1
% 5.82/6.09 thf(fact_3523_norm__pre__pure__rule1,axiom,
% 5.82/6.09 ! [B2: $o,P: assn,F: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ P @ F @ Q ) )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule1
% 5.82/6.09 thf(fact_3524_norm__pre__pure__rule1,axiom,
% 5.82/6.09 ! [B2: $o,P: assn,F: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ P @ F @ Q ) )
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule1
% 5.82/6.09 thf(fact_3525_norm__pre__pure__rule2,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ F @ Q ) )
% 5.82/6.09 => ( hoare_1429296392585015714_VEBTi @ ( pure_assn @ B2 ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule2
% 5.82/6.09 thf(fact_3526_norm__pre__pure__rule2,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_hoare_triple_o @ one_one_assn @ F @ Q ) )
% 5.82/6.09 => ( hoare_hoare_triple_o @ ( pure_assn @ B2 ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule2
% 5.82/6.09 thf(fact_3527_norm__pre__pure__rule2,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ one_one_assn @ F @ Q ) )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( pure_assn @ B2 ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule2
% 5.82/6.09 thf(fact_3528_norm__pre__pure__rule2,axiom,
% 5.82/6.09 ! [B2: $o,F: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ one_one_assn @ F @ Q ) )
% 5.82/6.09 => ( hoare_3067605981109127869le_nat @ ( pure_assn @ B2 ) @ F @ Q ) ) ).
% 5.82/6.09
% 5.82/6.09 % norm_pre_pure_rule2
% 5.82/6.09 thf(fact_3529_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.82/6.09 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.82/6.09 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.82/6.09 = none_P5556105721700978146at_nat ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.simps(2)
% 5.82/6.09 thf(fact_3530_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.82/6.09 ! [Uw: nat > nat > nat,V: nat] :
% 5.82/6.09 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.simps(2)
% 5.82/6.09 thf(fact_3531_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.82/6.09 ! [X2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y3: option4927543243414619207at_nat] :
% 5.82/6.09 ( ( ( vEBT_V1502963449132264192at_nat @ X2 @ Xa @ Xb )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ( ( Xa = none_P5556105721700978146at_nat )
% 5.82/6.09 => ( Y3 != none_P5556105721700978146at_nat ) )
% 5.82/6.09 => ( ( ? [V2: product_prod_nat_nat] :
% 5.82/6.09 ( Xa
% 5.82/6.09 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.82/6.09 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.82/6.09 => ( Y3 != none_P5556105721700978146at_nat ) ) )
% 5.82/6.09 => ~ ! [A3: product_prod_nat_nat] :
% 5.82/6.09 ( ( Xa
% 5.82/6.09 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.82/6.09 => ! [B3: product_prod_nat_nat] :
% 5.82/6.09 ( ( Xb
% 5.82/6.09 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( some_P7363390416028606310at_nat @ ( X2 @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.elims
% 5.82/6.09 thf(fact_3532_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.82/6.09 ! [X2: nat > nat > nat,Xa: option_nat,Xb: option_nat,Y3: option_nat] :
% 5.82/6.09 ( ( ( vEBT_V4262088993061758097ft_nat @ X2 @ Xa @ Xb )
% 5.82/6.09 = Y3 )
% 5.82/6.09 => ( ( ( Xa = none_nat )
% 5.82/6.09 => ( Y3 != none_nat ) )
% 5.82/6.09 => ( ( ? [V2: nat] :
% 5.82/6.09 ( Xa
% 5.82/6.09 = ( some_nat @ V2 ) )
% 5.82/6.09 => ( ( Xb = none_nat )
% 5.82/6.09 => ( Y3 != none_nat ) ) )
% 5.82/6.09 => ~ ! [A3: nat] :
% 5.82/6.09 ( ( Xa
% 5.82/6.09 = ( some_nat @ A3 ) )
% 5.82/6.09 => ! [B3: nat] :
% 5.82/6.09 ( ( Xb
% 5.82/6.09 = ( some_nat @ B3 ) )
% 5.82/6.09 => ( Y3
% 5.82/6.09 != ( some_nat @ ( X2 @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % VEBT_internal.option_shift.elims
% 5.82/6.09 thf(fact_3533_is__pred__in__set__def,axiom,
% 5.82/6.09 ( vEBT_is_pred_in_set
% 5.82/6.09 = ( ^ [Xs2: set_nat,X3: nat,Y: nat] :
% 5.82/6.09 ( ( member_nat @ Y @ Xs2 )
% 5.82/6.09 & ( ord_less_nat @ Y @ X3 )
% 5.82/6.09 & ! [Z4: nat] :
% 5.82/6.09 ( ( member_nat @ Z4 @ Xs2 )
% 5.82/6.09 => ( ( ord_less_nat @ Z4 @ X3 )
% 5.82/6.09 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % is_pred_in_set_def
% 5.82/6.09 thf(fact_3534_vebt__mint_Osimps_I2_J,axiom,
% 5.82/6.09 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.82/6.09 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_mint.simps(2)
% 5.82/6.09 thf(fact_3535_vebt__maxt_Osimps_I2_J,axiom,
% 5.82/6.09 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.82/6.09 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_maxt.simps(2)
% 5.82/6.09 thf(fact_3536_vebt__pred_Osimps_I1_J,axiom,
% 5.82/6.09 ! [Uu: $o,Uv: $o] :
% 5.82/6.09 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred.simps(1)
% 5.82/6.09 thf(fact_3537_vebt__pred_Osimps_I4_J,axiom,
% 5.82/6.09 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.82/6.09 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred.simps(4)
% 5.82/6.09 thf(fact_3538_vebt__mint_Osimps_I3_J,axiom,
% 5.82/6.09 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.82/6.09 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.82/6.09 = ( some_nat @ Mi ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_mint.simps(3)
% 5.82/6.09 thf(fact_3539_vebt__maxt_Osimps_I3_J,axiom,
% 5.82/6.09 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.82/6.09 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.82/6.09 = ( some_nat @ Ma ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_maxt.simps(3)
% 5.82/6.09 thf(fact_3540_vebt__pred_Osimps_I5_J,axiom,
% 5.82/6.09 ! [V: product_prod_nat_nat,Vd3: list_VEBT_VEBT,Ve3: vEBT_VEBT,Vf2: nat] :
% 5.82/6.09 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd3 @ Ve3 ) @ Vf2 )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred.simps(5)
% 5.82/6.09 thf(fact_3541_vebt__mint_Osimps_I1_J,axiom,
% 5.82/6.09 ! [A2: $o,B2: $o] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.09 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.09 & ( ~ A2
% 5.82/6.09 => ( ( B2
% 5.82/6.09 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.09 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.09 & ( ~ B2
% 5.82/6.09 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.09 = none_nat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_mint.simps(1)
% 5.82/6.09 thf(fact_3542_vebt__maxt_Osimps_I1_J,axiom,
% 5.82/6.09 ! [B2: $o,A2: $o] :
% 5.82/6.09 ( ( B2
% 5.82/6.09 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.09 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.09 & ( ~ B2
% 5.82/6.09 => ( ( A2
% 5.82/6.09 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.09 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.09 & ( ~ A2
% 5.82/6.09 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.09 = none_nat ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_maxt.simps(1)
% 5.82/6.09 thf(fact_3543_vebt__pred_Osimps_I6_J,axiom,
% 5.82/6.09 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.82/6.09 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.82/6.09 = none_nat ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred.simps(6)
% 5.82/6.09 thf(fact_3544_vebt__pred_Osimps_I2_J,axiom,
% 5.82/6.09 ! [A2: $o,Uw: $o] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.09 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.09 & ( ~ A2
% 5.82/6.09 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.09 = none_nat ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_pred.simps(2)
% 5.82/6.09 thf(fact_3545_linear__plus__1__le__power,axiom,
% 5.82/6.09 ! [X2: real,N: nat] :
% 5.82/6.09 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.09 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X2 @ one_one_real ) @ N ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % linear_plus_1_le_power
% 5.82/6.09 thf(fact_3546_vebt__maxtilist,axiom,
% 5.82/6.09 ! [I: nat,Ts: list_VEBT_VEBT,Tsi: list_VEBT_VEBTi] :
% 5.82/6.09 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ts ) )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts @ Tsi ) @ ( vEBT_vebt_maxti @ ( nth_VEBT_VEBTi @ Tsi @ I ) )
% 5.82/6.09 @ ^ [R5: option_nat] :
% 5.82/6.09 ( times_times_assn
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Ts @ I ) ) ) )
% 5.82/6.09 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts @ Tsi ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_maxtilist
% 5.82/6.09 thf(fact_3547_vebt__mintilist,axiom,
% 5.82/6.09 ! [I: nat,Ts: list_VEBT_VEBT,Tsi: list_VEBT_VEBTi] :
% 5.82/6.09 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ts ) )
% 5.82/6.09 => ( hoare_7629718768684598413on_nat @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts @ Tsi ) @ ( vEBT_vebt_minti @ ( nth_VEBT_VEBTi @ Tsi @ I ) )
% 5.82/6.09 @ ^ [R5: option_nat] :
% 5.82/6.09 ( times_times_assn
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ Ts @ I ) ) ) )
% 5.82/6.09 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts @ Tsi ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_mintilist
% 5.82/6.09 thf(fact_3548_arcosh__1,axiom,
% 5.82/6.09 ( ( arcosh_real @ one_one_real )
% 5.82/6.09 = zero_zero_real ) ).
% 5.82/6.09
% 5.82/6.09 % arcosh_1
% 5.82/6.09 thf(fact_3549_less__shift,axiom,
% 5.82/6.09 ( ord_less_nat
% 5.82/6.09 = ( ^ [X3: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X3 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % less_shift
% 5.82/6.09 thf(fact_3550_greater__shift,axiom,
% 5.82/6.09 ( ord_less_nat
% 5.82/6.09 = ( ^ [Y: nat,X3: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X3 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % greater_shift
% 5.82/6.09 thf(fact_3551_TBOUND__vebt__maxti,axiom,
% 5.82/6.09 ! [T: vEBT_VEBTi] : ( time_T8353473612707095248on_nat @ ( vEBT_vebt_maxti @ T ) @ one_one_nat ) ).
% 5.82/6.09
% 5.82/6.09 % TBOUND_vebt_maxti
% 5.82/6.09 thf(fact_3552_TBOUND__vebt__minti,axiom,
% 5.82/6.09 ! [T: vEBT_VEBTi] : ( time_T8353473612707095248on_nat @ ( vEBT_vebt_minti @ T ) @ one_one_nat ) ).
% 5.82/6.09
% 5.82/6.09 % TBOUND_vebt_minti
% 5.82/6.09 thf(fact_3553_max_Oidem,axiom,
% 5.82/6.09 ! [A2: nat] :
% 5.82/6.09 ( ( ord_max_nat @ A2 @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % max.idem
% 5.82/6.09 thf(fact_3554_max_Oidem,axiom,
% 5.82/6.09 ! [A2: extended_enat] :
% 5.82/6.09 ( ( ord_ma741700101516333627d_enat @ A2 @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % max.idem
% 5.82/6.09 thf(fact_3555_max_Oidem,axiom,
% 5.82/6.09 ! [A2: int] :
% 5.82/6.09 ( ( ord_max_int @ A2 @ A2 )
% 5.82/6.09 = A2 ) ).
% 5.82/6.09
% 5.82/6.09 % max.idem
% 5.82/6.09 thf(fact_3556_max_Oleft__idem,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_max_nat @ A2 @ ( ord_max_nat @ A2 @ B2 ) )
% 5.82/6.09 = ( ord_max_nat @ A2 @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.left_idem
% 5.82/6.09 thf(fact_3557_max_Oleft__idem,axiom,
% 5.82/6.09 ! [A2: extended_enat,B2: extended_enat] :
% 5.82/6.09 ( ( ord_ma741700101516333627d_enat @ A2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) )
% 5.82/6.09 = ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.left_idem
% 5.82/6.09 thf(fact_3558_max_Oleft__idem,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_max_int @ A2 @ ( ord_max_int @ A2 @ B2 ) )
% 5.82/6.09 = ( ord_max_int @ A2 @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.left_idem
% 5.82/6.09 thf(fact_3559_max_Oright__idem,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_max_nat @ ( ord_max_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.09 = ( ord_max_nat @ A2 @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.right_idem
% 5.82/6.09 thf(fact_3560_max_Oright__idem,axiom,
% 5.82/6.09 ! [A2: extended_enat,B2: extended_enat] :
% 5.82/6.09 ( ( ord_ma741700101516333627d_enat @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) @ B2 )
% 5.82/6.09 = ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.right_idem
% 5.82/6.09 thf(fact_3561_max_Oright__idem,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_max_int @ ( ord_max_int @ A2 @ B2 ) @ B2 )
% 5.82/6.09 = ( ord_max_int @ A2 @ B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.right_idem
% 5.82/6.09 thf(fact_3562_vebt__minti__h,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 5.82/6.09 ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 5.82/6.09 @ ^ [R5: option_nat] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_mint @ T ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_minti_h
% 5.82/6.09 thf(fact_3563_vebt__maxti__h,axiom,
% 5.82/6.09 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 5.82/6.09 ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 5.82/6.09 @ ^ [R5: option_nat] :
% 5.82/6.09 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.09 @ ( pure_assn
% 5.82/6.09 @ ( R5
% 5.82/6.09 = ( vEBT_vebt_maxt @ T ) ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % vebt_maxti_h
% 5.82/6.09 thf(fact_3564_max_Oabsorb1,axiom,
% 5.82/6.09 ! [B2: extended_enat,A2: extended_enat] :
% 5.82/6.09 ( ( ord_le2932123472753598470d_enat @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_ma741700101516333627d_enat @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb1
% 5.82/6.09 thf(fact_3565_max_Oabsorb1,axiom,
% 5.82/6.09 ! [B2: rat,A2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_rat @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb1
% 5.82/6.09 thf(fact_3566_max_Oabsorb1,axiom,
% 5.82/6.09 ! [B2: num,A2: num] :
% 5.82/6.09 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_num @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb1
% 5.82/6.09 thf(fact_3567_max_Oabsorb1,axiom,
% 5.82/6.09 ! [B2: nat,A2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_nat @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb1
% 5.82/6.09 thf(fact_3568_max_Oabsorb1,axiom,
% 5.82/6.09 ! [B2: int,A2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_int @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb1
% 5.82/6.09 thf(fact_3569_max_Oabsorb2,axiom,
% 5.82/6.09 ! [A2: extended_enat,B2: extended_enat] :
% 5.82/6.09 ( ( ord_le2932123472753598470d_enat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_ma741700101516333627d_enat @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb2
% 5.82/6.09 thf(fact_3570_max_Oabsorb2,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_rat @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb2
% 5.82/6.09 thf(fact_3571_max_Oabsorb2,axiom,
% 5.82/6.09 ! [A2: num,B2: num] :
% 5.82/6.09 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_num @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb2
% 5.82/6.09 thf(fact_3572_max_Oabsorb2,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_nat @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb2
% 5.82/6.09 thf(fact_3573_max_Oabsorb2,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_int @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb2
% 5.82/6.09 thf(fact_3574_max_Obounded__iff,axiom,
% 5.82/6.09 ! [B2: extended_enat,C2: extended_enat,A2: extended_enat] :
% 5.82/6.09 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B2 @ C2 ) @ A2 )
% 5.82/6.09 = ( ( ord_le2932123472753598470d_enat @ B2 @ A2 )
% 5.82/6.09 & ( ord_le2932123472753598470d_enat @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.bounded_iff
% 5.82/6.09 thf(fact_3575_max_Obounded__iff,axiom,
% 5.82/6.09 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ ( ord_max_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.09 = ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.09 & ( ord_less_eq_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.bounded_iff
% 5.82/6.09 thf(fact_3576_max_Obounded__iff,axiom,
% 5.82/6.09 ! [B2: num,C2: num,A2: num] :
% 5.82/6.09 ( ( ord_less_eq_num @ ( ord_max_num @ B2 @ C2 ) @ A2 )
% 5.82/6.09 = ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.09 & ( ord_less_eq_num @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.bounded_iff
% 5.82/6.09 thf(fact_3577_max_Obounded__iff,axiom,
% 5.82/6.09 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ ( ord_max_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.09 = ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.09 & ( ord_less_eq_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.bounded_iff
% 5.82/6.09 thf(fact_3578_max_Obounded__iff,axiom,
% 5.82/6.09 ! [B2: int,C2: int,A2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ ( ord_max_int @ B2 @ C2 ) @ A2 )
% 5.82/6.09 = ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.09 & ( ord_less_eq_int @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.bounded_iff
% 5.82/6.09 thf(fact_3579_max__less__iff__conj,axiom,
% 5.82/6.09 ! [X2: extended_enat,Y3: extended_enat,Z: extended_enat] :
% 5.82/6.09 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 5.82/6.09 & ( ord_le72135733267957522d_enat @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_less_iff_conj
% 5.82/6.09 thf(fact_3580_max__less__iff__conj,axiom,
% 5.82/6.09 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.09 ( ( ord_less_real @ ( ord_max_real @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ( ord_less_real @ X2 @ Z )
% 5.82/6.09 & ( ord_less_real @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_less_iff_conj
% 5.82/6.09 thf(fact_3581_max__less__iff__conj,axiom,
% 5.82/6.09 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.09 ( ( ord_less_rat @ ( ord_max_rat @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ( ord_less_rat @ X2 @ Z )
% 5.82/6.09 & ( ord_less_rat @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_less_iff_conj
% 5.82/6.09 thf(fact_3582_max__less__iff__conj,axiom,
% 5.82/6.09 ! [X2: num,Y3: num,Z: num] :
% 5.82/6.09 ( ( ord_less_num @ ( ord_max_num @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ( ord_less_num @ X2 @ Z )
% 5.82/6.09 & ( ord_less_num @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_less_iff_conj
% 5.82/6.09 thf(fact_3583_max__less__iff__conj,axiom,
% 5.82/6.09 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.09 ( ( ord_less_nat @ ( ord_max_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ( ord_less_nat @ X2 @ Z )
% 5.82/6.09 & ( ord_less_nat @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_less_iff_conj
% 5.82/6.09 thf(fact_3584_max__less__iff__conj,axiom,
% 5.82/6.09 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.09 ( ( ord_less_int @ ( ord_max_int @ X2 @ Y3 ) @ Z )
% 5.82/6.09 = ( ( ord_less_int @ X2 @ Z )
% 5.82/6.09 & ( ord_less_int @ Y3 @ Z ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max_less_iff_conj
% 5.82/6.09 thf(fact_3585_max_Oabsorb4,axiom,
% 5.82/6.09 ! [A2: extended_enat,B2: extended_enat] :
% 5.82/6.09 ( ( ord_le72135733267957522d_enat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_ma741700101516333627d_enat @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb4
% 5.82/6.09 thf(fact_3586_max_Oabsorb4,axiom,
% 5.82/6.09 ! [A2: real,B2: real] :
% 5.82/6.09 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_real @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb4
% 5.82/6.09 thf(fact_3587_max_Oabsorb4,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_rat @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb4
% 5.82/6.09 thf(fact_3588_max_Oabsorb4,axiom,
% 5.82/6.09 ! [A2: num,B2: num] :
% 5.82/6.09 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_num @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb4
% 5.82/6.09 thf(fact_3589_max_Oabsorb4,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_nat @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb4
% 5.82/6.09 thf(fact_3590_max_Oabsorb4,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.09 => ( ( ord_max_int @ A2 @ B2 )
% 5.82/6.09 = B2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb4
% 5.82/6.09 thf(fact_3591_max_Oabsorb3,axiom,
% 5.82/6.09 ! [B2: extended_enat,A2: extended_enat] :
% 5.82/6.09 ( ( ord_le72135733267957522d_enat @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_ma741700101516333627d_enat @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb3
% 5.82/6.09 thf(fact_3592_max_Oabsorb3,axiom,
% 5.82/6.09 ! [B2: real,A2: real] :
% 5.82/6.09 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_real @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb3
% 5.82/6.09 thf(fact_3593_max_Oabsorb3,axiom,
% 5.82/6.09 ! [B2: rat,A2: rat] :
% 5.82/6.09 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_rat @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb3
% 5.82/6.09 thf(fact_3594_max_Oabsorb3,axiom,
% 5.82/6.09 ! [B2: num,A2: num] :
% 5.82/6.09 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_num @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb3
% 5.82/6.09 thf(fact_3595_max_Oabsorb3,axiom,
% 5.82/6.09 ! [B2: nat,A2: nat] :
% 5.82/6.09 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_nat @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb3
% 5.82/6.09 thf(fact_3596_max_Oabsorb3,axiom,
% 5.82/6.09 ! [B2: int,A2: int] :
% 5.82/6.09 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.09 => ( ( ord_max_int @ A2 @ B2 )
% 5.82/6.09 = A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.absorb3
% 5.82/6.09 thf(fact_3597_max_Oassoc,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_max_nat @ ( ord_max_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_max_nat @ A2 @ ( ord_max_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.assoc
% 5.82/6.09 thf(fact_3598_max_Oassoc,axiom,
% 5.82/6.09 ! [A2: extended_enat,B2: extended_enat,C2: extended_enat] :
% 5.82/6.09 ( ( ord_ma741700101516333627d_enat @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_ma741700101516333627d_enat @ A2 @ ( ord_ma741700101516333627d_enat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.assoc
% 5.82/6.09 thf(fact_3599_max_Oassoc,axiom,
% 5.82/6.09 ! [A2: int,B2: int,C2: int] :
% 5.82/6.09 ( ( ord_max_int @ ( ord_max_int @ A2 @ B2 ) @ C2 )
% 5.82/6.09 = ( ord_max_int @ A2 @ ( ord_max_int @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.assoc
% 5.82/6.09 thf(fact_3600_max_Ocommute,axiom,
% 5.82/6.09 ( ord_max_nat
% 5.82/6.09 = ( ^ [A5: nat,B6: nat] : ( ord_max_nat @ B6 @ A5 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.commute
% 5.82/6.09 thf(fact_3601_max_Ocommute,axiom,
% 5.82/6.09 ( ord_ma741700101516333627d_enat
% 5.82/6.09 = ( ^ [A5: extended_enat,B6: extended_enat] : ( ord_ma741700101516333627d_enat @ B6 @ A5 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.commute
% 5.82/6.09 thf(fact_3602_max_Ocommute,axiom,
% 5.82/6.09 ( ord_max_int
% 5.82/6.09 = ( ^ [A5: int,B6: int] : ( ord_max_int @ B6 @ A5 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.commute
% 5.82/6.09 thf(fact_3603_max_Oleft__commute,axiom,
% 5.82/6.09 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.09 ( ( ord_max_nat @ B2 @ ( ord_max_nat @ A2 @ C2 ) )
% 5.82/6.09 = ( ord_max_nat @ A2 @ ( ord_max_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.left_commute
% 5.82/6.09 thf(fact_3604_max_Oleft__commute,axiom,
% 5.82/6.09 ! [B2: extended_enat,A2: extended_enat,C2: extended_enat] :
% 5.82/6.09 ( ( ord_ma741700101516333627d_enat @ B2 @ ( ord_ma741700101516333627d_enat @ A2 @ C2 ) )
% 5.82/6.09 = ( ord_ma741700101516333627d_enat @ A2 @ ( ord_ma741700101516333627d_enat @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.left_commute
% 5.82/6.09 thf(fact_3605_max_Oleft__commute,axiom,
% 5.82/6.09 ! [B2: int,A2: int,C2: int] :
% 5.82/6.09 ( ( ord_max_int @ B2 @ ( ord_max_int @ A2 @ C2 ) )
% 5.82/6.09 = ( ord_max_int @ A2 @ ( ord_max_int @ B2 @ C2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.left_commute
% 5.82/6.09 thf(fact_3606_max_Omono,axiom,
% 5.82/6.09 ! [C2: extended_enat,A2: extended_enat,D2: extended_enat,B2: extended_enat] :
% 5.82/6.09 ( ( ord_le2932123472753598470d_enat @ C2 @ A2 )
% 5.82/6.09 => ( ( ord_le2932123472753598470d_enat @ D2 @ B2 )
% 5.82/6.09 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C2 @ D2 ) @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.mono
% 5.82/6.09 thf(fact_3607_max_Omono,axiom,
% 5.82/6.09 ! [C2: rat,A2: rat,D2: rat,B2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_rat @ D2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D2 ) @ ( ord_max_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.mono
% 5.82/6.09 thf(fact_3608_max_Omono,axiom,
% 5.82/6.09 ! [C2: num,A2: num,D2: num,B2: num] :
% 5.82/6.09 ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_num @ D2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D2 ) @ ( ord_max_num @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.mono
% 5.82/6.09 thf(fact_3609_max_Omono,axiom,
% 5.82/6.09 ! [C2: nat,A2: nat,D2: nat,B2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_nat @ D2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D2 ) @ ( ord_max_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.mono
% 5.82/6.09 thf(fact_3610_max_Omono,axiom,
% 5.82/6.09 ! [C2: int,A2: int,D2: int,B2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.09 => ( ( ord_less_eq_int @ D2 @ B2 )
% 5.82/6.09 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D2 ) @ ( ord_max_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.mono
% 5.82/6.09 thf(fact_3611_max_OorderE,axiom,
% 5.82/6.09 ! [B2: extended_enat,A2: extended_enat] :
% 5.82/6.09 ( ( ord_le2932123472753598470d_enat @ B2 @ A2 )
% 5.82/6.09 => ( A2
% 5.82/6.09 = ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderE
% 5.82/6.09 thf(fact_3612_max_OorderE,axiom,
% 5.82/6.09 ! [B2: rat,A2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.09 => ( A2
% 5.82/6.09 = ( ord_max_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderE
% 5.82/6.09 thf(fact_3613_max_OorderE,axiom,
% 5.82/6.09 ! [B2: num,A2: num] :
% 5.82/6.09 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.09 => ( A2
% 5.82/6.09 = ( ord_max_num @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderE
% 5.82/6.09 thf(fact_3614_max_OorderE,axiom,
% 5.82/6.09 ! [B2: nat,A2: nat] :
% 5.82/6.09 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.09 => ( A2
% 5.82/6.09 = ( ord_max_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderE
% 5.82/6.09 thf(fact_3615_max_OorderE,axiom,
% 5.82/6.09 ! [B2: int,A2: int] :
% 5.82/6.09 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.09 => ( A2
% 5.82/6.09 = ( ord_max_int @ A2 @ B2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderE
% 5.82/6.09 thf(fact_3616_max_OorderI,axiom,
% 5.82/6.09 ! [A2: extended_enat,B2: extended_enat] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( ord_ma741700101516333627d_enat @ A2 @ B2 ) )
% 5.82/6.09 => ( ord_le2932123472753598470d_enat @ B2 @ A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderI
% 5.82/6.09 thf(fact_3617_max_OorderI,axiom,
% 5.82/6.09 ! [A2: rat,B2: rat] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( ord_max_rat @ A2 @ B2 ) )
% 5.82/6.09 => ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderI
% 5.82/6.09 thf(fact_3618_max_OorderI,axiom,
% 5.82/6.09 ! [A2: num,B2: num] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( ord_max_num @ A2 @ B2 ) )
% 5.82/6.09 => ( ord_less_eq_num @ B2 @ A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderI
% 5.82/6.09 thf(fact_3619_max_OorderI,axiom,
% 5.82/6.09 ! [A2: nat,B2: nat] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( ord_max_nat @ A2 @ B2 ) )
% 5.82/6.09 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderI
% 5.82/6.09 thf(fact_3620_max_OorderI,axiom,
% 5.82/6.09 ! [A2: int,B2: int] :
% 5.82/6.09 ( ( A2
% 5.82/6.09 = ( ord_max_int @ A2 @ B2 ) )
% 5.82/6.09 => ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.orderI
% 5.82/6.09 thf(fact_3621_max_OboundedE,axiom,
% 5.82/6.09 ! [B2: extended_enat,C2: extended_enat,A2: extended_enat] :
% 5.82/6.09 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B2 @ C2 ) @ A2 )
% 5.82/6.09 => ~ ( ( ord_le2932123472753598470d_enat @ B2 @ A2 )
% 5.82/6.09 => ~ ( ord_le2932123472753598470d_enat @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.boundedE
% 5.82/6.09 thf(fact_3622_max_OboundedE,axiom,
% 5.82/6.09 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.09 ( ( ord_less_eq_rat @ ( ord_max_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.09 => ~ ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.09 => ~ ( ord_less_eq_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.09
% 5.82/6.09 % max.boundedE
% 5.82/6.09 thf(fact_3623_max_OboundedE,axiom,
% 5.82/6.10 ! [B2: num,C2: num,A2: num] :
% 5.82/6.10 ( ( ord_less_eq_num @ ( ord_max_num @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_eq_num @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedE
% 5.82/6.10 thf(fact_3624_max_OboundedE,axiom,
% 5.82/6.10 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ ( ord_max_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_eq_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedE
% 5.82/6.10 thf(fact_3625_max_OboundedE,axiom,
% 5.82/6.10 ! [B2: int,C2: int,A2: int] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( ord_max_int @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_eq_int @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedE
% 5.82/6.10 thf(fact_3626_max_OboundedI,axiom,
% 5.82/6.10 ! [B2: extended_enat,A2: extended_enat,C2: extended_enat] :
% 5.82/6.10 ( ( ord_le2932123472753598470d_enat @ B2 @ A2 )
% 5.82/6.10 => ( ( ord_le2932123472753598470d_enat @ C2 @ A2 )
% 5.82/6.10 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedI
% 5.82/6.10 thf(fact_3627_max_OboundedI,axiom,
% 5.82/6.10 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.10 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.10 => ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_rat @ ( ord_max_rat @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedI
% 5.82/6.10 thf(fact_3628_max_OboundedI,axiom,
% 5.82/6.10 ! [B2: num,A2: num,C2: num] :
% 5.82/6.10 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.10 => ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_num @ ( ord_max_num @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedI
% 5.82/6.10 thf(fact_3629_max_OboundedI,axiom,
% 5.82/6.10 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.10 => ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_nat @ ( ord_max_nat @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedI
% 5.82/6.10 thf(fact_3630_max_OboundedI,axiom,
% 5.82/6.10 ! [B2: int,A2: int,C2: int] :
% 5.82/6.10 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.10 => ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_int @ ( ord_max_int @ B2 @ C2 ) @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.boundedI
% 5.82/6.10 thf(fact_3631_max_Oorder__iff,axiom,
% 5.82/6.10 ( ord_le2932123472753598470d_enat
% 5.82/6.10 = ( ^ [B6: extended_enat,A5: extended_enat] :
% 5.82/6.10 ( A5
% 5.82/6.10 = ( ord_ma741700101516333627d_enat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.order_iff
% 5.82/6.10 thf(fact_3632_max_Oorder__iff,axiom,
% 5.82/6.10 ( ord_less_eq_rat
% 5.82/6.10 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.10 ( A5
% 5.82/6.10 = ( ord_max_rat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.order_iff
% 5.82/6.10 thf(fact_3633_max_Oorder__iff,axiom,
% 5.82/6.10 ( ord_less_eq_num
% 5.82/6.10 = ( ^ [B6: num,A5: num] :
% 5.82/6.10 ( A5
% 5.82/6.10 = ( ord_max_num @ A5 @ B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.order_iff
% 5.82/6.10 thf(fact_3634_max_Oorder__iff,axiom,
% 5.82/6.10 ( ord_less_eq_nat
% 5.82/6.10 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.10 ( A5
% 5.82/6.10 = ( ord_max_nat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.order_iff
% 5.82/6.10 thf(fact_3635_max_Oorder__iff,axiom,
% 5.82/6.10 ( ord_less_eq_int
% 5.82/6.10 = ( ^ [B6: int,A5: int] :
% 5.82/6.10 ( A5
% 5.82/6.10 = ( ord_max_int @ A5 @ B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.order_iff
% 5.82/6.10 thf(fact_3636_max_Ocobounded1,axiom,
% 5.82/6.10 ! [A2: extended_enat,B2: extended_enat] : ( ord_le2932123472753598470d_enat @ A2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded1
% 5.82/6.10 thf(fact_3637_max_Ocobounded1,axiom,
% 5.82/6.10 ! [A2: rat,B2: rat] : ( ord_less_eq_rat @ A2 @ ( ord_max_rat @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded1
% 5.82/6.10 thf(fact_3638_max_Ocobounded1,axiom,
% 5.82/6.10 ! [A2: num,B2: num] : ( ord_less_eq_num @ A2 @ ( ord_max_num @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded1
% 5.82/6.10 thf(fact_3639_max_Ocobounded1,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ A2 @ ( ord_max_nat @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded1
% 5.82/6.10 thf(fact_3640_max_Ocobounded1,axiom,
% 5.82/6.10 ! [A2: int,B2: int] : ( ord_less_eq_int @ A2 @ ( ord_max_int @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded1
% 5.82/6.10 thf(fact_3641_max_Ocobounded2,axiom,
% 5.82/6.10 ! [B2: extended_enat,A2: extended_enat] : ( ord_le2932123472753598470d_enat @ B2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded2
% 5.82/6.10 thf(fact_3642_max_Ocobounded2,axiom,
% 5.82/6.10 ! [B2: rat,A2: rat] : ( ord_less_eq_rat @ B2 @ ( ord_max_rat @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded2
% 5.82/6.10 thf(fact_3643_max_Ocobounded2,axiom,
% 5.82/6.10 ! [B2: num,A2: num] : ( ord_less_eq_num @ B2 @ ( ord_max_num @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded2
% 5.82/6.10 thf(fact_3644_max_Ocobounded2,axiom,
% 5.82/6.10 ! [B2: nat,A2: nat] : ( ord_less_eq_nat @ B2 @ ( ord_max_nat @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded2
% 5.82/6.10 thf(fact_3645_max_Ocobounded2,axiom,
% 5.82/6.10 ! [B2: int,A2: int] : ( ord_less_eq_int @ B2 @ ( ord_max_int @ A2 @ B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.cobounded2
% 5.82/6.10 thf(fact_3646_le__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: extended_enat,X2: extended_enat,Y3: extended_enat] :
% 5.82/6.10 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_le2932123472753598470d_enat @ Z @ X2 )
% 5.82/6.10 | ( ord_le2932123472753598470d_enat @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % le_max_iff_disj
% 5.82/6.10 thf(fact_3647_le__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.10 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_eq_rat @ Z @ X2 )
% 5.82/6.10 | ( ord_less_eq_rat @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % le_max_iff_disj
% 5.82/6.10 thf(fact_3648_le__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: num,X2: num,Y3: num] :
% 5.82/6.10 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_eq_num @ Z @ X2 )
% 5.82/6.10 | ( ord_less_eq_num @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % le_max_iff_disj
% 5.82/6.10 thf(fact_3649_le__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: nat,X2: nat,Y3: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_eq_nat @ Z @ X2 )
% 5.82/6.10 | ( ord_less_eq_nat @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % le_max_iff_disj
% 5.82/6.10 thf(fact_3650_le__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: int,X2: int,Y3: int] :
% 5.82/6.10 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_eq_int @ Z @ X2 )
% 5.82/6.10 | ( ord_less_eq_int @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % le_max_iff_disj
% 5.82/6.10 thf(fact_3651_max_Oabsorb__iff1,axiom,
% 5.82/6.10 ( ord_le2932123472753598470d_enat
% 5.82/6.10 = ( ^ [B6: extended_enat,A5: extended_enat] :
% 5.82/6.10 ( ( ord_ma741700101516333627d_enat @ A5 @ B6 )
% 5.82/6.10 = A5 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff1
% 5.82/6.10 thf(fact_3652_max_Oabsorb__iff1,axiom,
% 5.82/6.10 ( ord_less_eq_rat
% 5.82/6.10 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.10 ( ( ord_max_rat @ A5 @ B6 )
% 5.82/6.10 = A5 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff1
% 5.82/6.10 thf(fact_3653_max_Oabsorb__iff1,axiom,
% 5.82/6.10 ( ord_less_eq_num
% 5.82/6.10 = ( ^ [B6: num,A5: num] :
% 5.82/6.10 ( ( ord_max_num @ A5 @ B6 )
% 5.82/6.10 = A5 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff1
% 5.82/6.10 thf(fact_3654_max_Oabsorb__iff1,axiom,
% 5.82/6.10 ( ord_less_eq_nat
% 5.82/6.10 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.10 ( ( ord_max_nat @ A5 @ B6 )
% 5.82/6.10 = A5 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff1
% 5.82/6.10 thf(fact_3655_max_Oabsorb__iff1,axiom,
% 5.82/6.10 ( ord_less_eq_int
% 5.82/6.10 = ( ^ [B6: int,A5: int] :
% 5.82/6.10 ( ( ord_max_int @ A5 @ B6 )
% 5.82/6.10 = A5 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff1
% 5.82/6.10 thf(fact_3656_max_Oabsorb__iff2,axiom,
% 5.82/6.10 ( ord_le2932123472753598470d_enat
% 5.82/6.10 = ( ^ [A5: extended_enat,B6: extended_enat] :
% 5.82/6.10 ( ( ord_ma741700101516333627d_enat @ A5 @ B6 )
% 5.82/6.10 = B6 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff2
% 5.82/6.10 thf(fact_3657_max_Oabsorb__iff2,axiom,
% 5.82/6.10 ( ord_less_eq_rat
% 5.82/6.10 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.10 ( ( ord_max_rat @ A5 @ B6 )
% 5.82/6.10 = B6 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff2
% 5.82/6.10 thf(fact_3658_max_Oabsorb__iff2,axiom,
% 5.82/6.10 ( ord_less_eq_num
% 5.82/6.10 = ( ^ [A5: num,B6: num] :
% 5.82/6.10 ( ( ord_max_num @ A5 @ B6 )
% 5.82/6.10 = B6 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff2
% 5.82/6.10 thf(fact_3659_max_Oabsorb__iff2,axiom,
% 5.82/6.10 ( ord_less_eq_nat
% 5.82/6.10 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.10 ( ( ord_max_nat @ A5 @ B6 )
% 5.82/6.10 = B6 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff2
% 5.82/6.10 thf(fact_3660_max_Oabsorb__iff2,axiom,
% 5.82/6.10 ( ord_less_eq_int
% 5.82/6.10 = ( ^ [A5: int,B6: int] :
% 5.82/6.10 ( ( ord_max_int @ A5 @ B6 )
% 5.82/6.10 = B6 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.absorb_iff2
% 5.82/6.10 thf(fact_3661_max_OcoboundedI1,axiom,
% 5.82/6.10 ! [C2: extended_enat,A2: extended_enat,B2: extended_enat] :
% 5.82/6.10 ( ( ord_le2932123472753598470d_enat @ C2 @ A2 )
% 5.82/6.10 => ( ord_le2932123472753598470d_enat @ C2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI1
% 5.82/6.10 thf(fact_3662_max_OcoboundedI1,axiom,
% 5.82/6.10 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.10 ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI1
% 5.82/6.10 thf(fact_3663_max_OcoboundedI1,axiom,
% 5.82/6.10 ! [C2: num,A2: num,B2: num] :
% 5.82/6.10 ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI1
% 5.82/6.10 thf(fact_3664_max_OcoboundedI1,axiom,
% 5.82/6.10 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI1
% 5.82/6.10 thf(fact_3665_max_OcoboundedI1,axiom,
% 5.82/6.10 ! [C2: int,A2: int,B2: int] :
% 5.82/6.10 ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI1
% 5.82/6.10 thf(fact_3666_max_OcoboundedI2,axiom,
% 5.82/6.10 ! [C2: extended_enat,B2: extended_enat,A2: extended_enat] :
% 5.82/6.10 ( ( ord_le2932123472753598470d_enat @ C2 @ B2 )
% 5.82/6.10 => ( ord_le2932123472753598470d_enat @ C2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI2
% 5.82/6.10 thf(fact_3667_max_OcoboundedI2,axiom,
% 5.82/6.10 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.10 ( ( ord_less_eq_rat @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI2
% 5.82/6.10 thf(fact_3668_max_OcoboundedI2,axiom,
% 5.82/6.10 ! [C2: num,B2: num,A2: num] :
% 5.82/6.10 ( ( ord_less_eq_num @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI2
% 5.82/6.10 thf(fact_3669_max_OcoboundedI2,axiom,
% 5.82/6.10 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI2
% 5.82/6.10 thf(fact_3670_max_OcoboundedI2,axiom,
% 5.82/6.10 ! [C2: int,B2: int,A2: int] :
% 5.82/6.10 ( ( ord_less_eq_int @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.coboundedI2
% 5.82/6.10 thf(fact_3671_max_Ostrict__coboundedI2,axiom,
% 5.82/6.10 ! [C2: extended_enat,B2: extended_enat,A2: extended_enat] :
% 5.82/6.10 ( ( ord_le72135733267957522d_enat @ C2 @ B2 )
% 5.82/6.10 => ( ord_le72135733267957522d_enat @ C2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI2
% 5.82/6.10 thf(fact_3672_max_Ostrict__coboundedI2,axiom,
% 5.82/6.10 ! [C2: real,B2: real,A2: real] :
% 5.82/6.10 ( ( ord_less_real @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_real @ C2 @ ( ord_max_real @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI2
% 5.82/6.10 thf(fact_3673_max_Ostrict__coboundedI2,axiom,
% 5.82/6.10 ! [C2: rat,B2: rat,A2: rat] :
% 5.82/6.10 ( ( ord_less_rat @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI2
% 5.82/6.10 thf(fact_3674_max_Ostrict__coboundedI2,axiom,
% 5.82/6.10 ! [C2: num,B2: num,A2: num] :
% 5.82/6.10 ( ( ord_less_num @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_num @ C2 @ ( ord_max_num @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI2
% 5.82/6.10 thf(fact_3675_max_Ostrict__coboundedI2,axiom,
% 5.82/6.10 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.10 ( ( ord_less_nat @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI2
% 5.82/6.10 thf(fact_3676_max_Ostrict__coboundedI2,axiom,
% 5.82/6.10 ! [C2: int,B2: int,A2: int] :
% 5.82/6.10 ( ( ord_less_int @ C2 @ B2 )
% 5.82/6.10 => ( ord_less_int @ C2 @ ( ord_max_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI2
% 5.82/6.10 thf(fact_3677_max_Ostrict__coboundedI1,axiom,
% 5.82/6.10 ! [C2: extended_enat,A2: extended_enat,B2: extended_enat] :
% 5.82/6.10 ( ( ord_le72135733267957522d_enat @ C2 @ A2 )
% 5.82/6.10 => ( ord_le72135733267957522d_enat @ C2 @ ( ord_ma741700101516333627d_enat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI1
% 5.82/6.10 thf(fact_3678_max_Ostrict__coboundedI1,axiom,
% 5.82/6.10 ! [C2: real,A2: real,B2: real] :
% 5.82/6.10 ( ( ord_less_real @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_real @ C2 @ ( ord_max_real @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI1
% 5.82/6.10 thf(fact_3679_max_Ostrict__coboundedI1,axiom,
% 5.82/6.10 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.10 ( ( ord_less_rat @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI1
% 5.82/6.10 thf(fact_3680_max_Ostrict__coboundedI1,axiom,
% 5.82/6.10 ! [C2: num,A2: num,B2: num] :
% 5.82/6.10 ( ( ord_less_num @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_num @ C2 @ ( ord_max_num @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI1
% 5.82/6.10 thf(fact_3681_max_Ostrict__coboundedI1,axiom,
% 5.82/6.10 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.10 ( ( ord_less_nat @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI1
% 5.82/6.10 thf(fact_3682_max_Ostrict__coboundedI1,axiom,
% 5.82/6.10 ! [C2: int,A2: int,B2: int] :
% 5.82/6.10 ( ( ord_less_int @ C2 @ A2 )
% 5.82/6.10 => ( ord_less_int @ C2 @ ( ord_max_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_coboundedI1
% 5.82/6.10 thf(fact_3683_max_Ostrict__order__iff,axiom,
% 5.82/6.10 ( ord_le72135733267957522d_enat
% 5.82/6.10 = ( ^ [B6: extended_enat,A5: extended_enat] :
% 5.82/6.10 ( ( A5
% 5.82/6.10 = ( ord_ma741700101516333627d_enat @ A5 @ B6 ) )
% 5.82/6.10 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_order_iff
% 5.82/6.10 thf(fact_3684_max_Ostrict__order__iff,axiom,
% 5.82/6.10 ( ord_less_real
% 5.82/6.10 = ( ^ [B6: real,A5: real] :
% 5.82/6.10 ( ( A5
% 5.82/6.10 = ( ord_max_real @ A5 @ B6 ) )
% 5.82/6.10 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_order_iff
% 5.82/6.10 thf(fact_3685_max_Ostrict__order__iff,axiom,
% 5.82/6.10 ( ord_less_rat
% 5.82/6.10 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.10 ( ( A5
% 5.82/6.10 = ( ord_max_rat @ A5 @ B6 ) )
% 5.82/6.10 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_order_iff
% 5.82/6.10 thf(fact_3686_max_Ostrict__order__iff,axiom,
% 5.82/6.10 ( ord_less_num
% 5.82/6.10 = ( ^ [B6: num,A5: num] :
% 5.82/6.10 ( ( A5
% 5.82/6.10 = ( ord_max_num @ A5 @ B6 ) )
% 5.82/6.10 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_order_iff
% 5.82/6.10 thf(fact_3687_max_Ostrict__order__iff,axiom,
% 5.82/6.10 ( ord_less_nat
% 5.82/6.10 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.10 ( ( A5
% 5.82/6.10 = ( ord_max_nat @ A5 @ B6 ) )
% 5.82/6.10 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_order_iff
% 5.82/6.10 thf(fact_3688_max_Ostrict__order__iff,axiom,
% 5.82/6.10 ( ord_less_int
% 5.82/6.10 = ( ^ [B6: int,A5: int] :
% 5.82/6.10 ( ( A5
% 5.82/6.10 = ( ord_max_int @ A5 @ B6 ) )
% 5.82/6.10 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_order_iff
% 5.82/6.10 thf(fact_3689_max_Ostrict__boundedE,axiom,
% 5.82/6.10 ! [B2: extended_enat,C2: extended_enat,A2: extended_enat] :
% 5.82/6.10 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_le72135733267957522d_enat @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_le72135733267957522d_enat @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_boundedE
% 5.82/6.10 thf(fact_3690_max_Ostrict__boundedE,axiom,
% 5.82/6.10 ! [B2: real,C2: real,A2: real] :
% 5.82/6.10 ( ( ord_less_real @ ( ord_max_real @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_real @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_boundedE
% 5.82/6.10 thf(fact_3691_max_Ostrict__boundedE,axiom,
% 5.82/6.10 ! [B2: rat,C2: rat,A2: rat] :
% 5.82/6.10 ( ( ord_less_rat @ ( ord_max_rat @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_boundedE
% 5.82/6.10 thf(fact_3692_max_Ostrict__boundedE,axiom,
% 5.82/6.10 ! [B2: num,C2: num,A2: num] :
% 5.82/6.10 ( ( ord_less_num @ ( ord_max_num @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_num @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_boundedE
% 5.82/6.10 thf(fact_3693_max_Ostrict__boundedE,axiom,
% 5.82/6.10 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.10 ( ( ord_less_nat @ ( ord_max_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_boundedE
% 5.82/6.10 thf(fact_3694_max_Ostrict__boundedE,axiom,
% 5.82/6.10 ! [B2: int,C2: int,A2: int] :
% 5.82/6.10 ( ( ord_less_int @ ( ord_max_int @ B2 @ C2 ) @ A2 )
% 5.82/6.10 => ~ ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.10 => ~ ( ord_less_int @ C2 @ A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % max.strict_boundedE
% 5.82/6.10 thf(fact_3695_less__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: extended_enat,X2: extended_enat,Y3: extended_enat] :
% 5.82/6.10 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 5.82/6.10 | ( ord_le72135733267957522d_enat @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % less_max_iff_disj
% 5.82/6.10 thf(fact_3696_less__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.10 ( ( ord_less_real @ Z @ ( ord_max_real @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_real @ Z @ X2 )
% 5.82/6.10 | ( ord_less_real @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % less_max_iff_disj
% 5.82/6.10 thf(fact_3697_less__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_rat @ Z @ X2 )
% 5.82/6.10 | ( ord_less_rat @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % less_max_iff_disj
% 5.82/6.10 thf(fact_3698_less__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: num,X2: num,Y3: num] :
% 5.82/6.10 ( ( ord_less_num @ Z @ ( ord_max_num @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_num @ Z @ X2 )
% 5.82/6.10 | ( ord_less_num @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % less_max_iff_disj
% 5.82/6.10 thf(fact_3699_less__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: nat,X2: nat,Y3: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_nat @ Z @ X2 )
% 5.82/6.10 | ( ord_less_nat @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % less_max_iff_disj
% 5.82/6.10 thf(fact_3700_less__max__iff__disj,axiom,
% 5.82/6.10 ! [Z: int,X2: int,Y3: int] :
% 5.82/6.10 ( ( ord_less_int @ Z @ ( ord_max_int @ X2 @ Y3 ) )
% 5.82/6.10 = ( ( ord_less_int @ Z @ X2 )
% 5.82/6.10 | ( ord_less_int @ Z @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % less_max_iff_disj
% 5.82/6.10 thf(fact_3701_Bolzano,axiom,
% 5.82/6.10 ! [A2: real,B2: real,P: real > real > $o] :
% 5.82/6.10 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.10 => ( ! [A3: real,B3: real,C3: real] :
% 5.82/6.10 ( ( P @ A3 @ B3 )
% 5.82/6.10 => ( ( P @ B3 @ C3 )
% 5.82/6.10 => ( ( ord_less_eq_real @ A3 @ B3 )
% 5.82/6.10 => ( ( ord_less_eq_real @ B3 @ C3 )
% 5.82/6.10 => ( P @ A3 @ C3 ) ) ) ) )
% 5.82/6.10 => ( ! [X4: real] :
% 5.82/6.10 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.10 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.10 => ? [D5: real] :
% 5.82/6.10 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.82/6.10 & ! [A3: real,B3: real] :
% 5.82/6.10 ( ( ( ord_less_eq_real @ A3 @ X4 )
% 5.82/6.10 & ( ord_less_eq_real @ X4 @ B3 )
% 5.82/6.10 & ( ord_less_real @ ( minus_minus_real @ B3 @ A3 ) @ D5 ) )
% 5.82/6.10 => ( P @ A3 @ B3 ) ) ) ) )
% 5.82/6.10 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Bolzano
% 5.82/6.10 thf(fact_3702_vebt__maxti__hT,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 5.82/6.10 ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 5.82/6.10 @ ^ [R5: option_nat] :
% 5.82/6.10 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.10 @ ( pure_assn
% 5.82/6.10 @ ( R5
% 5.82/6.10 = ( vEBT_vebt_maxt @ T ) ) ) )
% 5.82/6.10 @ one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_maxti_hT
% 5.82/6.10 thf(fact_3703_vebt__minti__hT,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 5.82/6.10 ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 5.82/6.10 @ ^ [R5: option_nat] :
% 5.82/6.10 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.10 @ ( pure_assn
% 5.82/6.10 @ ( R5
% 5.82/6.10 = ( vEBT_vebt_mint @ T ) ) ) )
% 5.82/6.10 @ one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_minti_hT
% 5.82/6.10 thf(fact_3704_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.10 ( ( ( vEBT_T_s_u_c_c2 @ X2 @ Xa )
% 5.82/6.10 = Y3 )
% 5.82/6.10 => ( ( ? [Uu2: $o,B3: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.82/6.10 => ( ( Xa = zero_zero_nat )
% 5.82/6.10 => ( Y3 != one_one_nat ) ) )
% 5.82/6.10 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.82/6.10 => ( ? [N3: nat] :
% 5.82/6.10 ( Xa
% 5.82/6.10 = ( suc @ N3 ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) ) )
% 5.82/6.10 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) )
% 5.82/6.10 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) )
% 5.82/6.10 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) )
% 5.82/6.10 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.10 ( ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.10 => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.10 => ( Y3 = one_one_nat ) )
% 5.82/6.10 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 @ ( if_nat
% 5.82/6.10 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 != none_nat )
% 5.82/6.10 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.10 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.elims
% 5.82/6.10 thf(fact_3705_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.10 ( ( ( vEBT_T_p_r_e_d2 @ X2 @ Xa )
% 5.82/6.10 = Y3 )
% 5.82/6.10 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.10 => ( ( Xa = zero_zero_nat )
% 5.82/6.10 => ( Y3 != one_one_nat ) ) )
% 5.82/6.10 => ( ( ? [A3: $o,Uw2: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.82/6.10 => ( ( Xa
% 5.82/6.10 = ( suc @ zero_zero_nat ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) ) )
% 5.82/6.10 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.10 => ( ? [Va3: nat] :
% 5.82/6.10 ( Xa
% 5.82/6.10 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) ) )
% 5.82/6.10 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) )
% 5.82/6.10 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) )
% 5.82/6.10 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.82/6.10 => ( Y3 != one_one_nat ) )
% 5.82/6.10 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.10 ( ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.10 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.10 => ( Y3 = one_one_nat ) )
% 5.82/6.10 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 @ ( if_nat
% 5.82/6.10 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 != none_nat )
% 5.82/6.10 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.10 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.elims
% 5.82/6.10 thf(fact_3706_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 5.82/6.10 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.10 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.10 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.10 = one_one_nat ) )
% 5.82/6.10 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.82/6.10 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.10 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.10 @ ( if_nat
% 5.82/6.10 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 != none_nat )
% 5.82/6.10 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.10 @ one_one_nat ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(6)
% 5.82/6.10 thf(fact_3707_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 5.82/6.10 ! [Ma: nat,X2: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.10 ( ( ( ord_less_nat @ Ma @ X2 )
% 5.82/6.10 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.10 = one_one_nat ) )
% 5.82/6.10 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.82/6.10 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.10 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.10 @ ( if_nat
% 5.82/6.10 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 != none_nat )
% 5.82/6.10 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.10 @ one_one_nat ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(7)
% 5.82/6.10 thf(fact_3708_vebt__succ_Osimps_I1_J,axiom,
% 5.82/6.10 ! [B2: $o,Uu: $o] :
% 5.82/6.10 ( ( B2
% 5.82/6.10 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B2 ) @ zero_zero_nat )
% 5.82/6.10 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.10 & ( ~ B2
% 5.82/6.10 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B2 ) @ zero_zero_nat )
% 5.82/6.10 = none_nat ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_succ.simps(1)
% 5.82/6.10 thf(fact_3709_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J,axiom,
% 5.82/6.10 ! [A2: $o,B2: $o,Va: nat] :
% 5.82/6.10 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(3)
% 5.82/6.10 thf(fact_3710_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 5.82/6.10 ! [Uu: $o,Uv: $o] :
% 5.82/6.10 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(1)
% 5.82/6.10 thf(fact_3711_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 5.82/6.10 ! [Uv: $o,Uw: $o,N: nat] :
% 5.82/6.10 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(2)
% 5.82/6.10 thf(fact_3712_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J,axiom,
% 5.82/6.10 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.82/6.10 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(4)
% 5.82/6.10 thf(fact_3713_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 5.82/6.10 ! [Uu: $o,B2: $o] :
% 5.82/6.10 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu @ B2 ) @ zero_zero_nat )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(1)
% 5.82/6.10 thf(fact_3714_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 5.82/6.10 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.82/6.10 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(3)
% 5.82/6.10 thf(fact_3715_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 5.82/6.10 ! [A2: $o,Uw: $o] :
% 5.82/6.10 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A2 @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(2)
% 5.82/6.10 thf(fact_3716_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 5.82/6.10 ! [V: product_prod_nat_nat,Vd3: list_VEBT_VEBT,Ve3: vEBT_VEBT,Vf2: nat] :
% 5.82/6.10 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd3 @ Ve3 ) @ Vf2 )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(5)
% 5.82/6.10 thf(fact_3717_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 5.82/6.10 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd3: vEBT_VEBT,Ve3: nat] :
% 5.82/6.10 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd3 ) @ Ve3 )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(4)
% 5.82/6.10 thf(fact_3718_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 5.82/6.10 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.82/6.10 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(6)
% 5.82/6.10 thf(fact_3719_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 5.82/6.10 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.82/6.10 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(5)
% 5.82/6.10 thf(fact_3720_pred__bound__height_H,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.10 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pred_bound_height'
% 5.82/6.10 thf(fact_3721_succ_H__bound__height,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.10 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % succ'_bound_height
% 5.82/6.10 thf(fact_3722_is__succ__in__set__def,axiom,
% 5.82/6.10 ( vEBT_is_succ_in_set
% 5.82/6.10 = ( ^ [Xs2: set_nat,X3: nat,Y: nat] :
% 5.82/6.10 ( ( member_nat @ Y @ Xs2 )
% 5.82/6.10 & ( ord_less_nat @ X3 @ Y )
% 5.82/6.10 & ! [Z4: nat] :
% 5.82/6.10 ( ( member_nat @ Z4 @ Xs2 )
% 5.82/6.10 => ( ( ord_less_nat @ X3 @ Z4 )
% 5.82/6.10 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % is_succ_in_set_def
% 5.82/6.10 thf(fact_3723_pred__bound__size__univ_H,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.10 => ( ( U
% 5.82/6.10 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.10 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pred_bound_size_univ'
% 5.82/6.10 thf(fact_3724_succ__bound__size__univ_H,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.10 => ( ( U
% 5.82/6.10 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.10 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % succ_bound_size_univ'
% 5.82/6.10 thf(fact_3725_vebt__succ_Osimps_I2_J,axiom,
% 5.82/6.10 ! [Uv: $o,Uw: $o,N: nat] :
% 5.82/6.10 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.82/6.10 = none_nat ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_succ.simps(2)
% 5.82/6.10 thf(fact_3726_vebt__succ_Osimps_I3_J,axiom,
% 5.82/6.10 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.82/6.10 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.82/6.10 = none_nat ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_succ.simps(3)
% 5.82/6.10 thf(fact_3727_vebt__succ_Osimps_I4_J,axiom,
% 5.82/6.10 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd3: vEBT_VEBT,Ve3: nat] :
% 5.82/6.10 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd3 ) @ Ve3 )
% 5.82/6.10 = none_nat ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_succ.simps(4)
% 5.82/6.10 thf(fact_3728_vebt__succ_Osimps_I5_J,axiom,
% 5.82/6.10 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.82/6.10 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.82/6.10 = none_nat ) ).
% 5.82/6.10
% 5.82/6.10 % vebt_succ.simps(5)
% 5.82/6.10 thf(fact_3729_inrange,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.10 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inrange
% 5.82/6.10 thf(fact_3730_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,
% 5.82/6.10 ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ zero_zero_nat ) )
% 5.82/6.10 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(2)
% 5.82/6.10 thf(fact_3731_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,
% 5.82/6.10 ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ zero_zero_nat ) )
% 5.82/6.10 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(2)
% 5.82/6.10 thf(fact_3732_zdiff__int__split,axiom,
% 5.82/6.10 ! [P: int > $o,X2: nat,Y3: nat] :
% 5.82/6.10 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y3 ) ) )
% 5.82/6.10 = ( ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.10 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) )
% 5.82/6.10 & ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.10 => ( P @ zero_zero_int ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % zdiff_int_split
% 5.82/6.10 thf(fact_3733_heaphelp,axiom,
% 5.82/6.10 ! [Xa: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn
% 5.82/6.10 @ ( times_times_assn
% 5.82/6.10 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb ) )
% 5.82/6.10 @ ( pure_assn
% 5.82/6.10 @ ( ( none_nat = none_nat )
% 5.82/6.10 & ( N = N ) ) ) )
% 5.82/6.10 @ ( pure_assn
% 5.82/6.10 @ ( Xc
% 5.82/6.10 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa @ Xb ) ) ) )
% 5.82/6.10 @ H2 )
% 5.82/6.10 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % heaphelp
% 5.82/6.10 thf(fact_3734_heaphelp,axiom,
% 5.82/6.10 ! [Xa: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn
% 5.82/6.10 @ ( times_times_assn
% 5.82/6.10 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb ) )
% 5.82/6.10 @ ( pure_assn
% 5.82/6.10 @ ( ( none_P5556105721700978146at_nat = none_P5556105721700978146at_nat )
% 5.82/6.10 & ( N = N ) ) ) )
% 5.82/6.10 @ ( pure_assn
% 5.82/6.10 @ ( Xc
% 5.82/6.10 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa @ Xb ) ) ) )
% 5.82/6.10 @ H2 )
% 5.82/6.10 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % heaphelp
% 5.82/6.10 thf(fact_3735_nat__induct2,axiom,
% 5.82/6.10 ! [P: nat > $o,N: nat] :
% 5.82/6.10 ( ( P @ zero_zero_nat )
% 5.82/6.10 => ( ( P @ one_one_nat )
% 5.82/6.10 => ( ! [N3: nat] :
% 5.82/6.10 ( ( P @ N3 )
% 5.82/6.10 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.10 => ( P @ N ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % nat_induct2
% 5.82/6.10 thf(fact_3736_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.10 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.82/6.10 => ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.10 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.82/6.10 => ( ! [Mi2: nat,Ma2: nat] :
% 5.82/6.10 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.82/6.10 => ( ( Xa = Mi2 )
% 5.82/6.10 | ( Xa = Ma2 ) ) )
% 5.82/6.10 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [Vc2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.82/6.10 => ( ( Xa = Mi2 )
% 5.82/6.10 | ( Xa = Ma2 )
% 5.82/6.10 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.82/6.10 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [Vd2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.82/6.10 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.elims(3)
% 5.82/6.10 thf(fact_3737_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.82/6.10 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.82/6.10 = Y3 )
% 5.82/6.10 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.10 => Y3 )
% 5.82/6.10 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.82/6.10 => Y3 )
% 5.82/6.10 => ( ! [Mi2: nat,Ma2: nat] :
% 5.82/6.10 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( ~ ( ( Xa = Mi2 )
% 5.82/6.10 | ( Xa = Ma2 ) ) ) ) )
% 5.82/6.10 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [Vc2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( ~ ( ( Xa = Mi2 )
% 5.82/6.10 | ( Xa = Ma2 )
% 5.82/6.10 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.82/6.10 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [Vd2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.elims(1)
% 5.82/6.10 thf(fact_3738_buildup__nothing__in__min__max,axiom,
% 5.82/6.10 ! [N: nat,X2: nat] :
% 5.82/6.10 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % buildup_nothing_in_min_max
% 5.82/6.10 thf(fact_3739_mod__h__bot__iff_I5_J,axiom,
% 5.82/6.10 ! [P: assn,Q: assn,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.10 ( ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 5.82/6.10 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 5.82/6.10 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % mod_h_bot_iff(5)
% 5.82/6.10 thf(fact_3740_mod__pure__star__dist,axiom,
% 5.82/6.10 ! [P: assn,B2: $o,H2: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ H2 )
% 5.82/6.10 = ( ( rep_assn @ P @ H2 )
% 5.82/6.10 & B2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % mod_pure_star_dist
% 5.82/6.10 thf(fact_3741_mod__h__bot__iff_I4_J,axiom,
% 5.82/6.10 ! [Q3: array_VEBT_VEBTi,Y3: list_VEBT_VEBTi,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.10 ~ ( rep_assn @ ( snga_assn_VEBT_VEBTi @ Q3 @ Y3 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 5.82/6.10
% 5.82/6.10 % mod_h_bot_iff(4)
% 5.82/6.10 thf(fact_3742_ent__pure__post__iff,axiom,
% 5.82/6.10 ! [P: assn,Q: assn,B2: $o] :
% 5.82/6.10 ( ( entails @ P @ ( times_times_assn @ Q @ ( pure_assn @ B2 ) ) )
% 5.82/6.10 = ( ! [H: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ H )
% 5.82/6.10 => B2 )
% 5.82/6.10 & ( entails @ P @ Q ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ent_pure_post_iff
% 5.82/6.10 thf(fact_3743_ent__pure__post__iff__sng,axiom,
% 5.82/6.10 ! [P: assn,B2: $o] :
% 5.82/6.10 ( ( entails @ P @ ( pure_assn @ B2 ) )
% 5.82/6.10 = ( ! [H: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ H )
% 5.82/6.10 => B2 )
% 5.82/6.10 & ( entails @ P @ one_one_assn ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ent_pure_post_iff_sng
% 5.82/6.10 thf(fact_3744_mod__starE,axiom,
% 5.82/6.10 ! [A2: assn,B2: assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ ( times_times_assn @ A2 @ B2 ) @ H2 )
% 5.82/6.10 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A2 @ X_1 )
% 5.82/6.10 => ! [H_2: produc3658429121746597890et_nat] :
% 5.82/6.10 ~ ( rep_assn @ B2 @ H_2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % mod_starE
% 5.82/6.10 thf(fact_3745_mod__starD,axiom,
% 5.82/6.10 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 5.82/6.10 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ A @ H1 )
% 5.82/6.10 & ( rep_assn @ B @ H22 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % mod_starD
% 5.82/6.10 thf(fact_3746_ent__fwd,axiom,
% 5.82/6.10 ! [P: assn,H2: produc3658429121746597890et_nat,Q: assn] :
% 5.82/6.10 ( ( rep_assn @ P @ H2 )
% 5.82/6.10 => ( ( entails @ P @ Q )
% 5.82/6.10 => ( rep_assn @ Q @ H2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ent_fwd
% 5.82/6.10 thf(fact_3747_entailsD,axiom,
% 5.82/6.10 ! [P: assn,Q: assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( entails @ P @ Q )
% 5.82/6.10 => ( ( rep_assn @ P @ H2 )
% 5.82/6.10 => ( rep_assn @ Q @ H2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % entailsD
% 5.82/6.10 thf(fact_3748_entailsI,axiom,
% 5.82/6.10 ! [P: assn,Q: assn] :
% 5.82/6.10 ( ! [H3: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ H3 )
% 5.82/6.10 => ( rep_assn @ Q @ H3 ) )
% 5.82/6.10 => ( entails @ P @ Q ) ) ).
% 5.82/6.10
% 5.82/6.10 % entailsI
% 5.82/6.10 thf(fact_3749_entails__def,axiom,
% 5.82/6.10 ( entails
% 5.82/6.10 = ( ^ [P3: assn,Q7: assn] :
% 5.82/6.10 ! [H: produc3658429121746597890et_nat] :
% 5.82/6.10 ( ( rep_assn @ P3 @ H )
% 5.82/6.10 => ( rep_assn @ Q7 @ H ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % entails_def
% 5.82/6.10 thf(fact_3750_ex__nat__less,axiom,
% 5.82/6.10 ! [N: nat,P: nat > $o] :
% 5.82/6.10 ( ( ? [M6: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ M6 @ N )
% 5.82/6.10 & ( P @ M6 ) ) )
% 5.82/6.10 = ( ? [X3: nat] :
% 5.82/6.10 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.10 & ( P @ X3 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ex_nat_less
% 5.82/6.10 thf(fact_3751_all__nat__less,axiom,
% 5.82/6.10 ! [N: nat,P: nat > $o] :
% 5.82/6.10 ( ( ! [M6: nat] :
% 5.82/6.10 ( ( ord_less_eq_nat @ M6 @ N )
% 5.82/6.10 => ( P @ M6 ) ) )
% 5.82/6.10 = ( ! [X3: nat] :
% 5.82/6.10 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.10 => ( P @ X3 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % all_nat_less
% 5.82/6.10 thf(fact_3752_mod__emp__simp,axiom,
% 5.82/6.10 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 5.82/6.10
% 5.82/6.10 % mod_emp_simp
% 5.82/6.10 thf(fact_3753_pinf_I1_J,axiom,
% 5.82/6.10 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.82/6.10 ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(1)
% 5.82/6.10 thf(fact_3754_pinf_I1_J,axiom,
% 5.82/6.10 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.82/6.10 ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(1)
% 5.82/6.10 thf(fact_3755_pinf_I1_J,axiom,
% 5.82/6.10 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.82/6.10 ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(1)
% 5.82/6.10 thf(fact_3756_pinf_I1_J,axiom,
% 5.82/6.10 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.82/6.10 ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(1)
% 5.82/6.10 thf(fact_3757_pinf_I1_J,axiom,
% 5.82/6.10 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.82/6.10 ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(1)
% 5.82/6.10 thf(fact_3758_pinf_I2_J,axiom,
% 5.82/6.10 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.82/6.10 ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(2)
% 5.82/6.10 thf(fact_3759_pinf_I2_J,axiom,
% 5.82/6.10 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.82/6.10 ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(2)
% 5.82/6.10 thf(fact_3760_pinf_I2_J,axiom,
% 5.82/6.10 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.82/6.10 ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(2)
% 5.82/6.10 thf(fact_3761_pinf_I2_J,axiom,
% 5.82/6.10 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.82/6.10 ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(2)
% 5.82/6.10 thf(fact_3762_pinf_I2_J,axiom,
% 5.82/6.10 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.82/6.10 ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ Z5 @ X4 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(2)
% 5.82/6.10 thf(fact_3763_pinf_I3_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(3)
% 5.82/6.10 thf(fact_3764_pinf_I3_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(3)
% 5.82/6.10 thf(fact_3765_pinf_I3_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(3)
% 5.82/6.10 thf(fact_3766_pinf_I3_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(3)
% 5.82/6.10 thf(fact_3767_pinf_I3_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(3)
% 5.82/6.10 thf(fact_3768_pinf_I4_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(4)
% 5.82/6.10 thf(fact_3769_pinf_I4_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(4)
% 5.82/6.10 thf(fact_3770_pinf_I4_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(4)
% 5.82/6.10 thf(fact_3771_pinf_I4_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(4)
% 5.82/6.10 thf(fact_3772_pinf_I4_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(4)
% 5.82/6.10 thf(fact_3773_pinf_I5_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_real @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(5)
% 5.82/6.10 thf(fact_3774_pinf_I5_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_rat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(5)
% 5.82/6.10 thf(fact_3775_pinf_I5_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_num @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(5)
% 5.82/6.10 thf(fact_3776_pinf_I5_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_nat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(5)
% 5.82/6.10 thf(fact_3777_pinf_I5_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_int @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(5)
% 5.82/6.10 thf(fact_3778_pinf_I7_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_real @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(7)
% 5.82/6.10 thf(fact_3779_pinf_I7_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_rat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(7)
% 5.82/6.10 thf(fact_3780_pinf_I7_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_num @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(7)
% 5.82/6.10 thf(fact_3781_pinf_I7_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_nat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(7)
% 5.82/6.10 thf(fact_3782_pinf_I7_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_int @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(7)
% 5.82/6.10 thf(fact_3783_minf_I1_J,axiom,
% 5.82/6.10 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.82/6.10 ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(1)
% 5.82/6.10 thf(fact_3784_minf_I1_J,axiom,
% 5.82/6.10 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.82/6.10 ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(1)
% 5.82/6.10 thf(fact_3785_minf_I1_J,axiom,
% 5.82/6.10 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.82/6.10 ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(1)
% 5.82/6.10 thf(fact_3786_minf_I1_J,axiom,
% 5.82/6.10 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.82/6.10 ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(1)
% 5.82/6.10 thf(fact_3787_minf_I1_J,axiom,
% 5.82/6.10 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.82/6.10 ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 & ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(1)
% 5.82/6.10 thf(fact_3788_minf_I2_J,axiom,
% 5.82/6.10 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.82/6.10 ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: real] :
% 5.82/6.10 ! [X4: real] :
% 5.82/6.10 ( ( ord_less_real @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(2)
% 5.82/6.10 thf(fact_3789_minf_I2_J,axiom,
% 5.82/6.10 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.82/6.10 ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: rat] :
% 5.82/6.10 ! [X4: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(2)
% 5.82/6.10 thf(fact_3790_minf_I2_J,axiom,
% 5.82/6.10 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.82/6.10 ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: num] :
% 5.82/6.10 ! [X4: num] :
% 5.82/6.10 ( ( ord_less_num @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(2)
% 5.82/6.10 thf(fact_3791_minf_I2_J,axiom,
% 5.82/6.10 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.82/6.10 ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: nat] :
% 5.82/6.10 ! [X4: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(2)
% 5.82/6.10 thf(fact_3792_minf_I2_J,axiom,
% 5.82/6.10 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.82/6.10 ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ X4 @ Z5 )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 = ( Q2 @ X4 ) ) )
% 5.82/6.10 => ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P5 @ X8 )
% 5.82/6.10 | ( Q2 @ X8 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(2)
% 5.82/6.10 thf(fact_3793_minf_I3_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(3)
% 5.82/6.10 thf(fact_3794_minf_I3_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(3)
% 5.82/6.10 thf(fact_3795_minf_I3_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(3)
% 5.82/6.10 thf(fact_3796_minf_I3_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(3)
% 5.82/6.10 thf(fact_3797_minf_I3_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(3)
% 5.82/6.10 thf(fact_3798_minf_I4_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(4)
% 5.82/6.10 thf(fact_3799_minf_I4_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(4)
% 5.82/6.10 thf(fact_3800_minf_I4_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(4)
% 5.82/6.10 thf(fact_3801_minf_I4_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(4)
% 5.82/6.10 thf(fact_3802_minf_I4_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ( X8 != T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(4)
% 5.82/6.10 thf(fact_3803_minf_I5_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_real @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(5)
% 5.82/6.10 thf(fact_3804_minf_I5_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_rat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(5)
% 5.82/6.10 thf(fact_3805_minf_I5_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_num @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(5)
% 5.82/6.10 thf(fact_3806_minf_I5_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_nat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(5)
% 5.82/6.10 thf(fact_3807_minf_I5_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_int @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(5)
% 5.82/6.10 thf(fact_3808_minf_I7_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_real @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(7)
% 5.82/6.10 thf(fact_3809_minf_I7_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_rat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(7)
% 5.82/6.10 thf(fact_3810_minf_I7_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_num @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(7)
% 5.82/6.10 thf(fact_3811_minf_I7_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_nat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(7)
% 5.82/6.10 thf(fact_3812_minf_I7_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_int @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(7)
% 5.82/6.10 thf(fact_3813_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.82/6.10 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.82/6.10 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.simps(2)
% 5.82/6.10 thf(fact_3814_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.82/6.10 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X2: nat] :
% 5.82/6.10 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X2 )
% 5.82/6.10 = ( ( X2 = Mi )
% 5.82/6.10 | ( X2 = Ma ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.simps(3)
% 5.82/6.10 thf(fact_3815_pinf_I6_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_eq_real @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(6)
% 5.82/6.10 thf(fact_3816_pinf_I6_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(6)
% 5.82/6.10 thf(fact_3817_pinf_I6_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_eq_num @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(6)
% 5.82/6.10 thf(fact_3818_pinf_I6_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_eq_nat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(6)
% 5.82/6.10 thf(fact_3819_pinf_I6_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ~ ( ord_less_eq_int @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(6)
% 5.82/6.10 thf(fact_3820_pinf_I8_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_eq_real @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(8)
% 5.82/6.10 thf(fact_3821_pinf_I8_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_eq_rat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(8)
% 5.82/6.10 thf(fact_3822_pinf_I8_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_eq_num @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(8)
% 5.82/6.10 thf(fact_3823_pinf_I8_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_eq_nat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(8)
% 5.82/6.10 thf(fact_3824_pinf_I8_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.10 => ( ord_less_eq_int @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % pinf(8)
% 5.82/6.10 thf(fact_3825_minf_I6_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_eq_real @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(6)
% 5.82/6.10 thf(fact_3826_minf_I6_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_eq_rat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(6)
% 5.82/6.10 thf(fact_3827_minf_I6_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_eq_num @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(6)
% 5.82/6.10 thf(fact_3828_minf_I6_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_eq_nat @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(6)
% 5.82/6.10 thf(fact_3829_minf_I6_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ( ord_less_eq_int @ X8 @ T ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(6)
% 5.82/6.10 thf(fact_3830_minf_I8_J,axiom,
% 5.82/6.10 ! [T: real] :
% 5.82/6.10 ? [Z2: real] :
% 5.82/6.10 ! [X8: real] :
% 5.82/6.10 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_eq_real @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(8)
% 5.82/6.10 thf(fact_3831_minf_I8_J,axiom,
% 5.82/6.10 ! [T: rat] :
% 5.82/6.10 ? [Z2: rat] :
% 5.82/6.10 ! [X8: rat] :
% 5.82/6.10 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(8)
% 5.82/6.10 thf(fact_3832_minf_I8_J,axiom,
% 5.82/6.10 ! [T: num] :
% 5.82/6.10 ? [Z2: num] :
% 5.82/6.10 ! [X8: num] :
% 5.82/6.10 ( ( ord_less_num @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_eq_num @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(8)
% 5.82/6.10 thf(fact_3833_minf_I8_J,axiom,
% 5.82/6.10 ! [T: nat] :
% 5.82/6.10 ? [Z2: nat] :
% 5.82/6.10 ! [X8: nat] :
% 5.82/6.10 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_eq_nat @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(8)
% 5.82/6.10 thf(fact_3834_minf_I8_J,axiom,
% 5.82/6.10 ! [T: int] :
% 5.82/6.10 ? [Z2: int] :
% 5.82/6.10 ! [X8: int] :
% 5.82/6.10 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.10 => ~ ( ord_less_eq_int @ T @ X8 ) ) ).
% 5.82/6.10
% 5.82/6.10 % minf(8)
% 5.82/6.10 thf(fact_3835_inf__period_I1_J,axiom,
% 5.82/6.10 ! [P: real > $o,D: real,Q: real > $o] :
% 5.82/6.10 ( ! [X4: real,K2: real] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: real,K2: real] :
% 5.82/6.10 ( ( Q @ X4 )
% 5.82/6.10 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D ) ) ) )
% 5.82/6.10 => ! [X8: real,K5: real] :
% 5.82/6.10 ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P @ ( minus_minus_real @ X8 @ ( times_times_real @ K5 @ D ) ) )
% 5.82/6.10 & ( Q @ ( minus_minus_real @ X8 @ ( times_times_real @ K5 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inf_period(1)
% 5.82/6.10 thf(fact_3836_inf__period_I1_J,axiom,
% 5.82/6.10 ! [P: rat > $o,D: rat,Q: rat > $o] :
% 5.82/6.10 ( ! [X4: rat,K2: rat] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: rat,K2: rat] :
% 5.82/6.10 ( ( Q @ X4 )
% 5.82/6.10 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D ) ) ) )
% 5.82/6.10 => ! [X8: rat,K5: rat] :
% 5.82/6.10 ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K5 @ D ) ) )
% 5.82/6.10 & ( Q @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K5 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inf_period(1)
% 5.82/6.10 thf(fact_3837_inf__period_I1_J,axiom,
% 5.82/6.10 ! [P: int > $o,D: int,Q: int > $o] :
% 5.82/6.10 ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( Q @ X4 )
% 5.82/6.10 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.82/6.10 => ! [X8: int,K5: int] :
% 5.82/6.10 ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 = ( ( P @ ( minus_minus_int @ X8 @ ( times_times_int @ K5 @ D ) ) )
% 5.82/6.10 & ( Q @ ( minus_minus_int @ X8 @ ( times_times_int @ K5 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inf_period(1)
% 5.82/6.10 thf(fact_3838_inf__period_I2_J,axiom,
% 5.82/6.10 ! [P: real > $o,D: real,Q: real > $o] :
% 5.82/6.10 ( ! [X4: real,K2: real] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: real,K2: real] :
% 5.82/6.10 ( ( Q @ X4 )
% 5.82/6.10 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D ) ) ) )
% 5.82/6.10 => ! [X8: real,K5: real] :
% 5.82/6.10 ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P @ ( minus_minus_real @ X8 @ ( times_times_real @ K5 @ D ) ) )
% 5.82/6.10 | ( Q @ ( minus_minus_real @ X8 @ ( times_times_real @ K5 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inf_period(2)
% 5.82/6.10 thf(fact_3839_inf__period_I2_J,axiom,
% 5.82/6.10 ! [P: rat > $o,D: rat,Q: rat > $o] :
% 5.82/6.10 ( ! [X4: rat,K2: rat] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: rat,K2: rat] :
% 5.82/6.10 ( ( Q @ X4 )
% 5.82/6.10 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D ) ) ) )
% 5.82/6.10 => ! [X8: rat,K5: rat] :
% 5.82/6.10 ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K5 @ D ) ) )
% 5.82/6.10 | ( Q @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K5 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inf_period(2)
% 5.82/6.10 thf(fact_3840_inf__period_I2_J,axiom,
% 5.82/6.10 ! [P: int > $o,D: int,Q: int > $o] :
% 5.82/6.10 ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( Q @ X4 )
% 5.82/6.10 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.82/6.10 => ! [X8: int,K5: int] :
% 5.82/6.10 ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 = ( ( P @ ( minus_minus_int @ X8 @ ( times_times_int @ K5 @ D ) ) )
% 5.82/6.10 | ( Q @ ( minus_minus_int @ X8 @ ( times_times_int @ K5 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % inf_period(2)
% 5.82/6.10 thf(fact_3841_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,
% 5.82/6.10 ! [X2: nat] :
% 5.82/6.10 ( ( X2 != zero_zero_nat )
% 5.82/6.10 => ( ( X2
% 5.82/6.10 != ( suc @ zero_zero_nat ) )
% 5.82/6.10 => ~ ! [Va3: nat] :
% 5.82/6.10 ( X2
% 5.82/6.10 != ( suc @ ( suc @ Va3 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.cases
% 5.82/6.10 thf(fact_3842_conj__le__cong,axiom,
% 5.82/6.10 ! [X2: int,X5: int,P: $o,P5: $o] :
% 5.82/6.10 ( ( X2 = X5 )
% 5.82/6.10 => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.82/6.10 => ( P = P5 ) )
% 5.82/6.10 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.10 & P )
% 5.82/6.10 = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.82/6.10 & P5 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % conj_le_cong
% 5.82/6.10 thf(fact_3843_imp__le__cong,axiom,
% 5.82/6.10 ! [X2: int,X5: int,P: $o,P5: $o] :
% 5.82/6.10 ( ( X2 = X5 )
% 5.82/6.10 => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.82/6.10 => ( P = P5 ) )
% 5.82/6.10 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.10 => P )
% 5.82/6.10 = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.82/6.10 => P5 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % imp_le_cong
% 5.82/6.10 thf(fact_3844_VEBT__internal_Ocnt_Osimps_I1_J,axiom,
% 5.82/6.10 ! [A2: $o,B2: $o] :
% 5.82/6.10 ( ( vEBT_VEBT_cnt @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.10 = one_one_real ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.cnt.simps(1)
% 5.82/6.10 thf(fact_3845_VEBT__internal_Ocnt_H_Osimps_I1_J,axiom,
% 5.82/6.10 ! [A2: $o,B2: $o] :
% 5.82/6.10 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.10 = one_one_nat ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.cnt'.simps(1)
% 5.82/6.10 thf(fact_3846_plusinfinity,axiom,
% 5.82/6.10 ! [D2: int,P5: int > $o,P: int > $o] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P5 @ X4 )
% 5.82/6.10 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ? [X_12: int] : ( P5 @ X_12 )
% 5.82/6.10 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % plusinfinity
% 5.82/6.10 thf(fact_3847_minusinfinity,axiom,
% 5.82/6.10 ! [D2: int,P1: int > $o,P: int > $o] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P1 @ X4 )
% 5.82/6.10 = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P1 @ X4 ) ) )
% 5.82/6.10 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.82/6.10 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % minusinfinity
% 5.82/6.10 thf(fact_3848_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.82/6.10 ! [V: nat,TreeList: list_VEBT_VEBT,Vd3: vEBT_VEBT,X2: nat] :
% 5.82/6.10 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd3 ) @ X2 )
% 5.82/6.10 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.simps(5)
% 5.82/6.10 thf(fact_3849_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.82/6.10 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.82/6.10 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X2 )
% 5.82/6.10 = ( ( X2 = Mi )
% 5.82/6.10 | ( X2 = Ma )
% 5.82/6.10 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.simps(4)
% 5.82/6.10 thf(fact_3850_double__not__eq__Suc__double,axiom,
% 5.82/6.10 ! [M: nat,N: nat] :
% 5.82/6.10 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.82/6.10 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % double_not_eq_Suc_double
% 5.82/6.10 thf(fact_3851_Suc__double__not__eq__double,axiom,
% 5.82/6.10 ! [M: nat,N: nat] :
% 5.82/6.10 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.10 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.10
% 5.82/6.10 % Suc_double_not_eq_double
% 5.82/6.10 thf(fact_3852_incr__mult__lemma,axiom,
% 5.82/6.10 ! [D2: int,P: int > $o,K: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( plus_plus_int @ X4 @ D2 ) ) )
% 5.82/6.10 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ( P @ X8 )
% 5.82/6.10 => ( P @ ( plus_plus_int @ X8 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % incr_mult_lemma
% 5.82/6.10 thf(fact_3853_decr__mult__lemma,axiom,
% 5.82/6.10 ! [D2: int,P: int > $o,K: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( minus_minus_int @ X4 @ D2 ) ) )
% 5.82/6.10 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ( P @ X8 )
% 5.82/6.10 => ( P @ ( minus_minus_int @ X8 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % decr_mult_lemma
% 5.82/6.10 thf(fact_3854_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,
% 5.82/6.10 ( ( vEBT_V8646137997579335489_i_l_d @ zero_zero_nat )
% 5.82/6.10 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(1)
% 5.82/6.10 thf(fact_3855_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,
% 5.82/6.10 ( ( vEBT_V8346862874174094_d_u_p @ zero_zero_nat )
% 5.82/6.10 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(1)
% 5.82/6.10 thf(fact_3856_VEBT__internal_Ospace_H_Osimps_I1_J,axiom,
% 5.82/6.10 ! [A2: $o,B2: $o] :
% 5.82/6.10 ( ( vEBT_VEBT_space2 @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.10 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.space'.simps(1)
% 5.82/6.10 thf(fact_3857_VEBT__internal_Ospace_Osimps_I1_J,axiom,
% 5.82/6.10 ! [A2: $o,B2: $o] :
% 5.82/6.10 ( ( vEBT_VEBT_space @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.10 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.space.simps(1)
% 5.82/6.10 thf(fact_3858_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.10 ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.82/6.10 => ( ! [Mi2: nat,Ma2: nat] :
% 5.82/6.10 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.82/6.10 => ~ ( ( Xa = Mi2 )
% 5.82/6.10 | ( Xa = Ma2 ) ) )
% 5.82/6.10 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [Vc2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.82/6.10 => ~ ( ( Xa = Mi2 )
% 5.82/6.10 | ( Xa = Ma2 )
% 5.82/6.10 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.82/6.10 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [Vd2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.82/6.10 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.membermima.elims(2)
% 5.82/6.10 thf(fact_3859_member__valid__both__member__options,axiom,
% 5.82/6.10 ! [Tree: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.82/6.10 => ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.82/6.10 => ( ( vEBT_V5719532721284313246member @ Tree @ X2 )
% 5.82/6.10 | ( vEBT_VEBT_membermima @ Tree @ X2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % member_valid_both_member_options
% 5.82/6.10 thf(fact_3860_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: set_int,B2: set_int,C2: set_int,D2: set_int] :
% 5.82/6.10 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A2 @ B2 ) @ ( set_or370866239135849197et_int @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_set_int @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_set_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3861_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.10 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A2 @ B2 ) @ ( set_or633870826150836451st_rat @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3862_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.10 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A2 @ B2 ) @ ( set_or7049704709247886629st_num @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_num @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3863_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.10 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) @ ( set_or1269000886237332187st_nat @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3864_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.10 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A2 @ B2 ) @ ( set_or1266510415728281911st_int @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3865_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.10 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A2 @ B2 ) @ ( set_or189985376899183464nteger @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_le3102999989581377725nteger @ C2 @ A2 )
% 5.82/6.10 & ( ord_le3102999989581377725nteger @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3866_atLeastatMost__subset__iff,axiom,
% 5.82/6.10 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.10 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ ( set_or1222579329274155063t_real @ C2 @ D2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_real @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_subset_iff
% 5.82/6.10 thf(fact_3867_atLeastatMost__empty,axiom,
% 5.82/6.10 ! [B2: rat,A2: rat] :
% 5.82/6.10 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.10 => ( ( set_or633870826150836451st_rat @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_rat ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty
% 5.82/6.10 thf(fact_3868_atLeastatMost__empty,axiom,
% 5.82/6.10 ! [B2: num,A2: num] :
% 5.82/6.10 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.10 => ( ( set_or7049704709247886629st_num @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_num ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty
% 5.82/6.10 thf(fact_3869_atLeastatMost__empty,axiom,
% 5.82/6.10 ! [B2: nat,A2: nat] :
% 5.82/6.10 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.10 => ( ( set_or1269000886237332187st_nat @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_nat ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty
% 5.82/6.10 thf(fact_3870_atLeastatMost__empty,axiom,
% 5.82/6.10 ! [B2: int,A2: int] :
% 5.82/6.10 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.10 => ( ( set_or1266510415728281911st_int @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_int ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty
% 5.82/6.10 thf(fact_3871_atLeastatMost__empty,axiom,
% 5.82/6.10 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.10 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 5.82/6.10 => ( ( set_or189985376899183464nteger @ A2 @ B2 )
% 5.82/6.10 = bot_bo3990330152332043303nteger ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty
% 5.82/6.10 thf(fact_3872_atLeastatMost__empty,axiom,
% 5.82/6.10 ! [B2: real,A2: real] :
% 5.82/6.10 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.10 => ( ( set_or1222579329274155063t_real @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_real ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty
% 5.82/6.10 thf(fact_3873_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: set_int,B2: set_int] :
% 5.82/6.10 ( ( bot_bot_set_set_int
% 5.82/6.10 = ( set_or370866239135849197et_int @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3874_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: rat,B2: rat] :
% 5.82/6.10 ( ( bot_bot_set_rat
% 5.82/6.10 = ( set_or633870826150836451st_rat @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3875_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: num,B2: num] :
% 5.82/6.10 ( ( bot_bot_set_num
% 5.82/6.10 = ( set_or7049704709247886629st_num @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_num @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3876_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat] :
% 5.82/6.10 ( ( bot_bot_set_nat
% 5.82/6.10 = ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3877_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: int,B2: int] :
% 5.82/6.10 ( ( bot_bot_set_int
% 5.82/6.10 = ( set_or1266510415728281911st_int @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3878_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.10 ( ( bot_bo3990330152332043303nteger
% 5.82/6.10 = ( set_or189985376899183464nteger @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3879_atLeastatMost__empty__iff2,axiom,
% 5.82/6.10 ! [A2: real,B2: real] :
% 5.82/6.10 ( ( bot_bot_set_real
% 5.82/6.10 = ( set_or1222579329274155063t_real @ A2 @ B2 ) )
% 5.82/6.10 = ( ~ ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff2
% 5.82/6.10 thf(fact_3880_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: set_int,B2: set_int] :
% 5.82/6.10 ( ( ( set_or370866239135849197et_int @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_set_int )
% 5.82/6.10 = ( ~ ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3881_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: rat,B2: rat] :
% 5.82/6.10 ( ( ( set_or633870826150836451st_rat @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_rat )
% 5.82/6.10 = ( ~ ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3882_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: num,B2: num] :
% 5.82/6.10 ( ( ( set_or7049704709247886629st_num @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_num )
% 5.82/6.10 = ( ~ ( ord_less_eq_num @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3883_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat] :
% 5.82/6.10 ( ( ( set_or1269000886237332187st_nat @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_nat )
% 5.82/6.10 = ( ~ ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3884_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: int,B2: int] :
% 5.82/6.10 ( ( ( set_or1266510415728281911st_int @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_int )
% 5.82/6.10 = ( ~ ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3885_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.10 ( ( ( set_or189985376899183464nteger @ A2 @ B2 )
% 5.82/6.10 = bot_bo3990330152332043303nteger )
% 5.82/6.10 = ( ~ ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3886_atLeastatMost__empty__iff,axiom,
% 5.82/6.10 ! [A2: real,B2: real] :
% 5.82/6.10 ( ( ( set_or1222579329274155063t_real @ A2 @ B2 )
% 5.82/6.10 = bot_bot_set_real )
% 5.82/6.10 = ( ~ ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_empty_iff
% 5.82/6.10 thf(fact_3887_both__member__options__def,axiom,
% 5.82/6.10 ( vEBT_V8194947554948674370ptions
% 5.82/6.10 = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 5.82/6.10 ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 5.82/6.10 | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % both_member_options_def
% 5.82/6.10 thf(fact_3888_nat__approx__posE,axiom,
% 5.82/6.10 ! [E: rat] :
% 5.82/6.10 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.82/6.10 => ~ ! [N3: nat] :
% 5.82/6.10 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.82/6.10
% 5.82/6.10 % nat_approx_posE
% 5.82/6.10 thf(fact_3889_nat__approx__posE,axiom,
% 5.82/6.10 ! [E: real] :
% 5.82/6.10 ( ( ord_less_real @ zero_zero_real @ E )
% 5.82/6.10 => ~ ! [N3: nat] :
% 5.82/6.10 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.82/6.10
% 5.82/6.10 % nat_approx_posE
% 5.82/6.10 thf(fact_3890_buildup__nothing__in__leaf,axiom,
% 5.82/6.10 ! [N: nat,X2: nat] :
% 5.82/6.10 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % buildup_nothing_in_leaf
% 5.82/6.10 thf(fact_3891_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: set_int,H2: set_int,L4: set_int,H4: set_int] :
% 5.82/6.10 ( ( ( set_or370866239135849197et_int @ L @ H2 )
% 5.82/6.10 = ( set_or370866239135849197et_int @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 5.82/6.10 & ~ ( ord_less_eq_set_int @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3892_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: rat,H2: rat,L4: rat,H4: rat] :
% 5.82/6.10 ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 5.82/6.10 = ( set_or633870826150836451st_rat @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.82/6.10 & ~ ( ord_less_eq_rat @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3893_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: num,H2: num,L4: num,H4: num] :
% 5.82/6.10 ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 5.82/6.10 = ( set_or7049704709247886629st_num @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.82/6.10 & ~ ( ord_less_eq_num @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3894_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: nat,H2: nat,L4: nat,H4: nat] :
% 5.82/6.10 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 5.82/6.10 = ( set_or1269000886237332187st_nat @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.82/6.10 & ~ ( ord_less_eq_nat @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3895_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: int,H2: int,L4: int,H4: int] :
% 5.82/6.10 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 5.82/6.10 = ( set_or1266510415728281911st_int @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.82/6.10 & ~ ( ord_less_eq_int @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3896_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: code_integer,H2: code_integer,L4: code_integer,H4: code_integer] :
% 5.82/6.10 ( ( ( set_or189985376899183464nteger @ L @ H2 )
% 5.82/6.10 = ( set_or189985376899183464nteger @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_le3102999989581377725nteger @ L @ H2 )
% 5.82/6.10 & ~ ( ord_le3102999989581377725nteger @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3897_Icc__eq__Icc,axiom,
% 5.82/6.10 ! [L: real,H2: real,L4: real,H4: real] :
% 5.82/6.10 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 5.82/6.10 = ( set_or1222579329274155063t_real @ L4 @ H4 ) )
% 5.82/6.10 = ( ( ( L = L4 )
% 5.82/6.10 & ( H2 = H4 ) )
% 5.82/6.10 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.82/6.10 & ~ ( ord_less_eq_real @ L4 @ H4 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % Icc_eq_Icc
% 5.82/6.10 thf(fact_3898_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: set_int,L: set_int,U: set_int] :
% 5.82/6.10 ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L @ U ) )
% 5.82/6.10 = ( ( ord_less_eq_set_int @ L @ I )
% 5.82/6.10 & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3899_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: rat,L: rat,U: rat] :
% 5.82/6.10 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.82/6.10 = ( ( ord_less_eq_rat @ L @ I )
% 5.82/6.10 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3900_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: num,L: num,U: num] :
% 5.82/6.10 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.82/6.10 = ( ( ord_less_eq_num @ L @ I )
% 5.82/6.10 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3901_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: nat,L: nat,U: nat] :
% 5.82/6.10 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.82/6.10 = ( ( ord_less_eq_nat @ L @ I )
% 5.82/6.10 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3902_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: int,L: int,U: int] :
% 5.82/6.10 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.82/6.10 = ( ( ord_less_eq_int @ L @ I )
% 5.82/6.10 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3903_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: code_integer,L: code_integer,U: code_integer] :
% 5.82/6.10 ( ( member_Code_integer @ I @ ( set_or189985376899183464nteger @ L @ U ) )
% 5.82/6.10 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 5.82/6.10 & ( ord_le3102999989581377725nteger @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3904_atLeastAtMost__iff,axiom,
% 5.82/6.10 ! [I: real,L: real,U: real] :
% 5.82/6.10 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.82/6.10 = ( ( ord_less_eq_real @ L @ I )
% 5.82/6.10 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastAtMost_iff
% 5.82/6.10 thf(fact_3905_aset_I2_J,axiom,
% 5.82/6.10 ! [D: int,A: set_int,P: int > $o,Q: int > $o] :
% 5.82/6.10 ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ A )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( plus_plus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ A )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 => ( Q @ ( plus_plus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 => ( ( P @ ( plus_plus_int @ X8 @ D ) )
% 5.82/6.10 | ( Q @ ( plus_plus_int @ X8 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(2)
% 5.82/6.10 thf(fact_3906_aset_I1_J,axiom,
% 5.82/6.10 ! [D: int,A: set_int,P: int > $o,Q: int > $o] :
% 5.82/6.10 ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ A )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( plus_plus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ A )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 => ( Q @ ( plus_plus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 => ( ( P @ ( plus_plus_int @ X8 @ D ) )
% 5.82/6.10 & ( Q @ ( plus_plus_int @ X8 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(1)
% 5.82/6.10 thf(fact_3907_bset_I2_J,axiom,
% 5.82/6.10 ! [D: int,B: set_int,P: int > $o,Q: int > $o] :
% 5.82/6.10 ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ B )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( minus_minus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ B )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 => ( Q @ ( minus_minus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 | ( Q @ X8 ) )
% 5.82/6.10 => ( ( P @ ( minus_minus_int @ X8 @ D ) )
% 5.82/6.10 | ( Q @ ( minus_minus_int @ X8 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(2)
% 5.82/6.10 thf(fact_3908_bset_I1_J,axiom,
% 5.82/6.10 ! [D: int,B: set_int,P: int > $o,Q: int > $o] :
% 5.82/6.10 ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ B )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( minus_minus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ B )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( Q @ X4 )
% 5.82/6.10 => ( Q @ ( minus_minus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ( P @ X8 )
% 5.82/6.10 & ( Q @ X8 ) )
% 5.82/6.10 => ( ( P @ ( minus_minus_int @ X8 @ D ) )
% 5.82/6.10 & ( Q @ ( minus_minus_int @ X8 @ D ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(1)
% 5.82/6.10 thf(fact_3909_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.82/6.10 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.82/6.10 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.naive_member.simps(2)
% 5.82/6.10 thf(fact_3910_bounded__Max__nat,axiom,
% 5.82/6.10 ! [P: nat > $o,X2: nat,M8: nat] :
% 5.82/6.10 ( ( P @ X2 )
% 5.82/6.10 => ( ! [X4: nat] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 => ( ord_less_eq_nat @ X4 @ M8 ) )
% 5.82/6.10 => ~ ! [M5: nat] :
% 5.82/6.10 ( ( P @ M5 )
% 5.82/6.10 => ~ ! [X8: nat] :
% 5.82/6.10 ( ( P @ X8 )
% 5.82/6.10 => ( ord_less_eq_nat @ X8 @ M5 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bounded_Max_nat
% 5.82/6.10 thf(fact_3911_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.82/6.10 ! [X2: produc4471711990508489141at_nat] :
% 5.82/6.10 ~ ! [F2: nat > nat > nat,A3: nat,B3: nat,Acc: nat] :
% 5.82/6.10 ( X2
% 5.82/6.10 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % fold_atLeastAtMost_nat.cases
% 5.82/6.10 thf(fact_3912_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.82/6.10 ! [A2: $o,B2: $o,X2: nat] :
% 5.82/6.10 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.10 = ( ( ( X2 = zero_zero_nat )
% 5.82/6.10 => A2 )
% 5.82/6.10 & ( ( X2 != zero_zero_nat )
% 5.82/6.10 => ( ( ( X2 = one_one_nat )
% 5.82/6.10 => B2 )
% 5.82/6.10 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.naive_member.simps(1)
% 5.82/6.10 thf(fact_3913_aset_I7_J,axiom,
% 5.82/6.10 ! [D: int,A: set_int,T: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_int @ T @ X8 )
% 5.82/6.10 => ( ord_less_int @ T @ ( plus_plus_int @ X8 @ D ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(7)
% 5.82/6.10 thf(fact_3914_aset_I5_J,axiom,
% 5.82/6.10 ! [D: int,T: int,A: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ T @ A )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_int @ X8 @ T )
% 5.82/6.10 => ( ord_less_int @ ( plus_plus_int @ X8 @ D ) @ T ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(5)
% 5.82/6.10 thf(fact_3915_aset_I4_J,axiom,
% 5.82/6.10 ! [D: int,T: int,A: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ T @ A )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( X8 != T )
% 5.82/6.10 => ( ( plus_plus_int @ X8 @ D )
% 5.82/6.10 != T ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(4)
% 5.82/6.10 thf(fact_3916_aset_I3_J,axiom,
% 5.82/6.10 ! [D: int,T: int,A: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( X8 = T )
% 5.82/6.10 => ( ( plus_plus_int @ X8 @ D )
% 5.82/6.10 = T ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(3)
% 5.82/6.10 thf(fact_3917_bset_I7_J,axiom,
% 5.82/6.10 ! [D: int,T: int,B: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ T @ B )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_int @ T @ X8 )
% 5.82/6.10 => ( ord_less_int @ T @ ( minus_minus_int @ X8 @ D ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(7)
% 5.82/6.10 thf(fact_3918_bset_I5_J,axiom,
% 5.82/6.10 ! [D: int,B: set_int,T: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_int @ X8 @ T )
% 5.82/6.10 => ( ord_less_int @ ( minus_minus_int @ X8 @ D ) @ T ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(5)
% 5.82/6.10 thf(fact_3919_bset_I4_J,axiom,
% 5.82/6.10 ! [D: int,T: int,B: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ T @ B )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( X8 != T )
% 5.82/6.10 => ( ( minus_minus_int @ X8 @ D )
% 5.82/6.10 != T ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(4)
% 5.82/6.10 thf(fact_3920_bset_I3_J,axiom,
% 5.82/6.10 ! [D: int,T: int,B: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( X8 = T )
% 5.82/6.10 => ( ( minus_minus_int @ X8 @ D )
% 5.82/6.10 = T ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(3)
% 5.82/6.10 thf(fact_3921_periodic__finite__ex,axiom,
% 5.82/6.10 ! [D2: int,P: int > $o] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P @ X4 )
% 5.82/6.10 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 5.82/6.10 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.82/6.10 = ( ? [X3: int] :
% 5.82/6.10 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 5.82/6.10 & ( P @ X3 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % periodic_finite_ex
% 5.82/6.10 thf(fact_3922_bset_I6_J,axiom,
% 5.82/6.10 ! [D: int,B: set_int,T: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_eq_int @ X8 @ T )
% 5.82/6.10 => ( ord_less_eq_int @ ( minus_minus_int @ X8 @ D ) @ T ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(6)
% 5.82/6.10 thf(fact_3923_bset_I8_J,axiom,
% 5.82/6.10 ! [D: int,T: int,B: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ B )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_eq_int @ T @ X8 )
% 5.82/6.10 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X8 @ D ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % bset(8)
% 5.82/6.10 thf(fact_3924_aset_I6_J,axiom,
% 5.82/6.10 ! [D: int,T: int,A: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_eq_int @ X8 @ T )
% 5.82/6.10 => ( ord_less_eq_int @ ( plus_plus_int @ X8 @ D ) @ T ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(6)
% 5.82/6.10 thf(fact_3925_aset_I8_J,axiom,
% 5.82/6.10 ! [D: int,A: set_int,T: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ! [X8: int] :
% 5.82/6.10 ( ! [Xa3: int] :
% 5.82/6.10 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb3: int] :
% 5.82/6.10 ( ( member_int @ Xb3 @ A )
% 5.82/6.10 => ( X8
% 5.82/6.10 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.10 => ( ( ord_less_eq_int @ T @ X8 )
% 5.82/6.10 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X8 @ D ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % aset(8)
% 5.82/6.10 thf(fact_3926_cpmi,axiom,
% 5.82/6.10 ! [D: int,P: int > $o,P5: int > $o,B: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ X4 @ Z5 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ B )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( minus_minus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P5 @ X4 )
% 5.82/6.10 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.82/6.10 = ( ? [X3: int] :
% 5.82/6.10 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 & ( P5 @ X3 ) )
% 5.82/6.10 | ? [X3: int] :
% 5.82/6.10 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 & ? [Y: int] :
% 5.82/6.10 ( ( member_int @ Y @ B )
% 5.82/6.10 & ( P @ ( plus_plus_int @ Y @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % cpmi
% 5.82/6.10 thf(fact_3927_cppi,axiom,
% 5.82/6.10 ! [D: int,P: int > $o,P5: int > $o,A: set_int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ D )
% 5.82/6.10 => ( ? [Z5: int] :
% 5.82/6.10 ! [X4: int] :
% 5.82/6.10 ( ( ord_less_int @ Z5 @ X4 )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 = ( P5 @ X4 ) ) )
% 5.82/6.10 => ( ! [X4: int] :
% 5.82/6.10 ( ! [Xa2: int] :
% 5.82/6.10 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 => ! [Xb2: int] :
% 5.82/6.10 ( ( member_int @ Xb2 @ A )
% 5.82/6.10 => ( X4
% 5.82/6.10 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.82/6.10 => ( ( P @ X4 )
% 5.82/6.10 => ( P @ ( plus_plus_int @ X4 @ D ) ) ) )
% 5.82/6.10 => ( ! [X4: int,K2: int] :
% 5.82/6.10 ( ( P5 @ X4 )
% 5.82/6.10 = ( P5 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.82/6.10 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.82/6.10 = ( ? [X3: int] :
% 5.82/6.10 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 & ( P5 @ X3 ) )
% 5.82/6.10 | ? [X3: int] :
% 5.82/6.10 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.10 & ? [Y: int] :
% 5.82/6.10 ( ( member_int @ Y @ A )
% 5.82/6.10 & ( P @ ( minus_minus_int @ Y @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % cppi
% 5.82/6.10 thf(fact_3928_exists__least__lemma,axiom,
% 5.82/6.10 ! [P: nat > $o] :
% 5.82/6.10 ( ~ ( P @ zero_zero_nat )
% 5.82/6.10 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.82/6.10 => ? [N3: nat] :
% 5.82/6.10 ( ~ ( P @ N3 )
% 5.82/6.10 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % exists_least_lemma
% 5.82/6.10 thf(fact_3929_real__arch__simple,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ? [N3: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.82/6.10
% 5.82/6.10 % real_arch_simple
% 5.82/6.10 thf(fact_3930_real__arch__simple,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ? [N3: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.82/6.10
% 5.82/6.10 % real_arch_simple
% 5.82/6.10 thf(fact_3931_reals__Archimedean2,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ? [N3: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.82/6.10
% 5.82/6.10 % reals_Archimedean2
% 5.82/6.10 thf(fact_3932_reals__Archimedean2,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ? [N3: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.82/6.10
% 5.82/6.10 % reals_Archimedean2
% 5.82/6.10 thf(fact_3933_ex__less__of__nat__mult,axiom,
% 5.82/6.10 ! [X2: rat,Y3: rat] :
% 5.82/6.10 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.82/6.10 => ? [N3: nat] : ( ord_less_rat @ Y3 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ex_less_of_nat_mult
% 5.82/6.10 thf(fact_3934_ex__less__of__nat__mult,axiom,
% 5.82/6.10 ! [X2: real,Y3: real] :
% 5.82/6.10 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.10 => ? [N3: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ex_less_of_nat_mult
% 5.82/6.10 thf(fact_3935_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: set_int,B2: set_int,C2: set_int,D2: set_int] :
% 5.82/6.10 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A2 @ B2 ) @ ( set_or370866239135849197et_int @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_set_int @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_set_int @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_less_set_int @ C2 @ A2 )
% 5.82/6.10 | ( ord_less_set_int @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_less_eq_set_int @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3936_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.10 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A2 @ B2 ) @ ( set_or633870826150836451st_rat @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_rat @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_less_rat @ C2 @ A2 )
% 5.82/6.10 | ( ord_less_rat @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_less_eq_rat @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3937_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.10 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A2 @ B2 ) @ ( set_or7049704709247886629st_num @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_num @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_less_num @ C2 @ A2 )
% 5.82/6.10 | ( ord_less_num @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_less_eq_num @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3938_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.10 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) @ ( set_or1269000886237332187st_nat @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_nat @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_less_nat @ C2 @ A2 )
% 5.82/6.10 | ( ord_less_nat @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_less_eq_nat @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3939_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.10 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A2 @ B2 ) @ ( set_or1266510415728281911st_int @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_int @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_less_int @ C2 @ A2 )
% 5.82/6.10 | ( ord_less_int @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_less_eq_int @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3940_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.10 ( ( ord_le1307284697595431911nteger @ ( set_or189985376899183464nteger @ A2 @ B2 ) @ ( set_or189985376899183464nteger @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_le3102999989581377725nteger @ C2 @ A2 )
% 5.82/6.10 & ( ord_le3102999989581377725nteger @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_le6747313008572928689nteger @ C2 @ A2 )
% 5.82/6.10 | ( ord_le6747313008572928689nteger @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_le3102999989581377725nteger @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3941_atLeastatMost__psubset__iff,axiom,
% 5.82/6.10 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.10 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ ( set_or1222579329274155063t_real @ C2 @ D2 ) )
% 5.82/6.10 = ( ( ~ ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.10 | ( ( ord_less_eq_real @ C2 @ A2 )
% 5.82/6.10 & ( ord_less_eq_real @ B2 @ D2 )
% 5.82/6.10 & ( ( ord_less_real @ C2 @ A2 )
% 5.82/6.10 | ( ord_less_real @ B2 @ D2 ) ) ) )
% 5.82/6.10 & ( ord_less_eq_real @ C2 @ D2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % atLeastatMost_psubset_iff
% 5.82/6.10 thf(fact_3942_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.82/6.10 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.10 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S2 ) @ X2 )
% 5.82/6.10 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.10 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.naive_member.simps(3)
% 5.82/6.10 thf(fact_3943_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.10 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.82/6.10 => ( ! [A3: $o,B3: $o] :
% 5.82/6.10 ( ( X2
% 5.82/6.10 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.10 => ( ( ( Xa = zero_zero_nat )
% 5.82/6.10 => A3 )
% 5.82/6.10 & ( ( Xa != zero_zero_nat )
% 5.82/6.10 => ( ( ( Xa = one_one_nat )
% 5.82/6.10 => B3 )
% 5.82/6.10 & ( Xa = one_one_nat ) ) ) ) )
% 5.82/6.10 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.82/6.10 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [S3: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.82/6.10 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.naive_member.elims(3)
% 5.82/6.10 thf(fact_3944_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.10 ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.82/6.10 => ( ! [A3: $o,B3: $o] :
% 5.82/6.10 ( ( X2
% 5.82/6.10 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.10 => ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.10 => A3 )
% 5.82/6.10 & ( ( Xa != zero_zero_nat )
% 5.82/6.10 => ( ( ( Xa = one_one_nat )
% 5.82/6.10 => B3 )
% 5.82/6.10 & ( Xa = one_one_nat ) ) ) ) )
% 5.82/6.10 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [S3: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.82/6.10 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.naive_member.elims(2)
% 5.82/6.10 thf(fact_3945_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.82/6.10 ! [X2: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.82/6.10 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.82/6.10 = Y3 )
% 5.82/6.10 => ( ! [A3: $o,B3: $o] :
% 5.82/6.10 ( ( X2
% 5.82/6.10 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.10 => A3 )
% 5.82/6.10 & ( ( Xa != zero_zero_nat )
% 5.82/6.10 => ( ( ( Xa = one_one_nat )
% 5.82/6.10 => B3 )
% 5.82/6.10 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.82/6.10 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.82/6.10 => Y3 )
% 5.82/6.10 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.82/6.10 ( ? [S3: vEBT_VEBT] :
% 5.82/6.10 ( X2
% 5.82/6.10 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.82/6.10 => ( Y3
% 5.82/6.10 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.10 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.10 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % VEBT_internal.naive_member.elims(1)
% 5.82/6.10 thf(fact_3946_htt__def,axiom,
% 5.82/6.10 ( time_htt_VEBT_VEBTi
% 5.82/6.10 = ( ^ [P3: assn,C4: heap_T8145700208782473153_VEBTi,Q7: vEBT_VEBTi > assn,T2: nat] :
% 5.82/6.10 ( ( hoare_1429296392585015714_VEBTi @ P3 @ C4 @ Q7 )
% 5.82/6.10 & ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P3 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ C4 @ H ) @ T2 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % htt_def
% 5.82/6.10 thf(fact_3947_htt__def,axiom,
% 5.82/6.10 ( time_htt_o
% 5.82/6.10 = ( ^ [P3: assn,C4: heap_Time_Heap_o,Q7: $o > assn,T2: nat] :
% 5.82/6.10 ( ( hoare_hoare_triple_o @ P3 @ C4 @ Q7 )
% 5.82/6.10 & ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P3 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_o @ C4 @ H ) @ T2 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % htt_def
% 5.82/6.10 thf(fact_3948_htt__def,axiom,
% 5.82/6.10 ( time_htt_option_nat
% 5.82/6.10 = ( ^ [P3: assn,C4: heap_T2636463487746394924on_nat,Q7: option_nat > assn,T2: nat] :
% 5.82/6.10 ( ( hoare_7629718768684598413on_nat @ P3 @ C4 @ Q7 )
% 5.82/6.10 & ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P3 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_option_nat @ C4 @ H ) @ T2 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % htt_def
% 5.82/6.10 thf(fact_3949_htt__def,axiom,
% 5.82/6.10 ( time_htt_nat
% 5.82/6.10 = ( ^ [P3: assn,C4: heap_Time_Heap_nat,Q7: nat > assn,T2: nat] :
% 5.82/6.10 ( ( hoare_3067605981109127869le_nat @ P3 @ C4 @ Q7 )
% 5.82/6.10 & ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P3 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_nat @ C4 @ H ) @ T2 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % htt_def
% 5.82/6.10 thf(fact_3950_httI,axiom,
% 5.82/6.10 ! [P: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,T: nat] :
% 5.82/6.10 ( ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q )
% 5.82/6.10 => ( ! [H3: heap_e7401611519738050253t_unit,As2: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As2 ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ C2 @ H3 ) @ T ) )
% 5.82/6.10 => ( time_htt_VEBT_VEBTi @ P @ C2 @ Q @ T ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % httI
% 5.82/6.10 thf(fact_3951_httI,axiom,
% 5.82/6.10 ! [P: assn,C2: heap_Time_Heap_o,Q: $o > assn,T: nat] :
% 5.82/6.10 ( ( hoare_hoare_triple_o @ P @ C2 @ Q )
% 5.82/6.10 => ( ! [H3: heap_e7401611519738050253t_unit,As2: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As2 ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_o @ C2 @ H3 ) @ T ) )
% 5.82/6.10 => ( time_htt_o @ P @ C2 @ Q @ T ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % httI
% 5.82/6.10 thf(fact_3952_httI,axiom,
% 5.82/6.10 ! [P: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn,T: nat] :
% 5.82/6.10 ( ( hoare_7629718768684598413on_nat @ P @ C2 @ Q )
% 5.82/6.10 => ( ! [H3: heap_e7401611519738050253t_unit,As2: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As2 ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_option_nat @ C2 @ H3 ) @ T ) )
% 5.82/6.10 => ( time_htt_option_nat @ P @ C2 @ Q @ T ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % httI
% 5.82/6.10 thf(fact_3953_httI,axiom,
% 5.82/6.10 ! [P: assn,C2: heap_Time_Heap_nat,Q: nat > assn,T: nat] :
% 5.82/6.10 ( ( hoare_3067605981109127869le_nat @ P @ C2 @ Q )
% 5.82/6.10 => ( ! [H3: heap_e7401611519738050253t_unit,As2: set_nat] :
% 5.82/6.10 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As2 ) )
% 5.82/6.10 => ( ord_less_eq_nat @ ( time_time_nat @ C2 @ H3 ) @ T ) )
% 5.82/6.10 => ( time_htt_nat @ P @ C2 @ Q @ T ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % httI
% 5.82/6.10 thf(fact_3954_int__ops_I6_J,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat] :
% 5.82/6.10 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) )
% 5.82/6.10 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.10 = zero_zero_int ) )
% 5.82/6.10 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) )
% 5.82/6.10 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.10 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % int_ops(6)
% 5.82/6.10 thf(fact_3955_max__bot2,axiom,
% 5.82/6.10 ! [X2: set_nat] :
% 5.82/6.10 ( ( ord_max_set_nat @ X2 @ bot_bot_set_nat )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot2
% 5.82/6.10 thf(fact_3956_max__bot2,axiom,
% 5.82/6.10 ! [X2: assn] :
% 5.82/6.10 ( ( ord_max_assn @ X2 @ bot_bot_assn )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot2
% 5.82/6.10 thf(fact_3957_max__bot2,axiom,
% 5.82/6.10 ! [X2: set_int] :
% 5.82/6.10 ( ( ord_max_set_int @ X2 @ bot_bot_set_int )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot2
% 5.82/6.10 thf(fact_3958_max__bot2,axiom,
% 5.82/6.10 ! [X2: nat] :
% 5.82/6.10 ( ( ord_max_nat @ X2 @ bot_bot_nat )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot2
% 5.82/6.10 thf(fact_3959_max__bot2,axiom,
% 5.82/6.10 ! [X2: extended_enat] :
% 5.82/6.10 ( ( ord_ma741700101516333627d_enat @ X2 @ bot_bo4199563552545308370d_enat )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot2
% 5.82/6.10 thf(fact_3960_max__bot,axiom,
% 5.82/6.10 ! [X2: set_nat] :
% 5.82/6.10 ( ( ord_max_set_nat @ bot_bot_set_nat @ X2 )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot
% 5.82/6.10 thf(fact_3961_max__bot,axiom,
% 5.82/6.10 ! [X2: assn] :
% 5.82/6.10 ( ( ord_max_assn @ bot_bot_assn @ X2 )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot
% 5.82/6.10 thf(fact_3962_max__bot,axiom,
% 5.82/6.10 ! [X2: set_int] :
% 5.82/6.10 ( ( ord_max_set_int @ bot_bot_set_int @ X2 )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot
% 5.82/6.10 thf(fact_3963_max__bot,axiom,
% 5.82/6.10 ! [X2: nat] :
% 5.82/6.10 ( ( ord_max_nat @ bot_bot_nat @ X2 )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot
% 5.82/6.10 thf(fact_3964_max__bot,axiom,
% 5.82/6.10 ! [X2: extended_enat] :
% 5.82/6.10 ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X2 )
% 5.82/6.10 = X2 ) ).
% 5.82/6.10
% 5.82/6.10 % max_bot
% 5.82/6.10 thf(fact_3965_pos__mult__pos__ge,axiom,
% 5.82/6.10 ! [X2: int,N: int] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.82/6.10 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.82/6.10 => ( ord_less_eq_int @ ( times_times_int @ N @ one_one_int ) @ ( times_times_int @ N @ X2 ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % pos_mult_pos_ge
% 5.82/6.10 thf(fact_3966_heigt__uplog__rel,axiom,
% 5.82/6.10 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.10 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.10 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 5.82/6.10 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % heigt_uplog_rel
% 5.82/6.10 thf(fact_3967_order__refl,axiom,
% 5.82/6.10 ! [X2: set_int] : ( ord_less_eq_set_int @ X2 @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % order_refl
% 5.82/6.10 thf(fact_3968_order__refl,axiom,
% 5.82/6.10 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % order_refl
% 5.82/6.10 thf(fact_3969_order__refl,axiom,
% 5.82/6.10 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % order_refl
% 5.82/6.10 thf(fact_3970_order__refl,axiom,
% 5.82/6.10 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % order_refl
% 5.82/6.10 thf(fact_3971_order__refl,axiom,
% 5.82/6.10 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 5.82/6.10
% 5.82/6.10 % order_refl
% 5.82/6.10 thf(fact_3972_dual__order_Orefl,axiom,
% 5.82/6.10 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % dual_order.refl
% 5.82/6.10 thf(fact_3973_dual__order_Orefl,axiom,
% 5.82/6.10 ! [A2: rat] : ( ord_less_eq_rat @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % dual_order.refl
% 5.82/6.10 thf(fact_3974_dual__order_Orefl,axiom,
% 5.82/6.10 ! [A2: num] : ( ord_less_eq_num @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % dual_order.refl
% 5.82/6.10 thf(fact_3975_dual__order_Orefl,axiom,
% 5.82/6.10 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % dual_order.refl
% 5.82/6.10 thf(fact_3976_dual__order_Orefl,axiom,
% 5.82/6.10 ! [A2: int] : ( ord_less_eq_int @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % dual_order.refl
% 5.82/6.10 thf(fact_3977_verit__eq__simplify_I8_J,axiom,
% 5.82/6.10 ! [X22: num,Y2: num] :
% 5.82/6.10 ( ( ( bit0 @ X22 )
% 5.82/6.10 = ( bit0 @ Y2 ) )
% 5.82/6.10 = ( X22 = Y2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % verit_eq_simplify(8)
% 5.82/6.10 thf(fact_3978_star__false__right,axiom,
% 5.82/6.10 ! [P: assn] :
% 5.82/6.10 ( ( times_times_assn @ P @ bot_bot_assn )
% 5.82/6.10 = bot_bot_assn ) ).
% 5.82/6.10
% 5.82/6.10 % star_false_right
% 5.82/6.10 thf(fact_3979_star__false__left,axiom,
% 5.82/6.10 ! [P: assn] :
% 5.82/6.10 ( ( times_times_assn @ bot_bot_assn @ P )
% 5.82/6.10 = bot_bot_assn ) ).
% 5.82/6.10
% 5.82/6.10 % star_false_left
% 5.82/6.10 thf(fact_3980_assn__basic__inequalities_I3_J,axiom,
% 5.82/6.10 bot_bot_assn != one_one_assn ).
% 5.82/6.10
% 5.82/6.10 % assn_basic_inequalities(3)
% 5.82/6.10 thf(fact_3981_ent__false__iff,axiom,
% 5.82/6.10 ! [P: assn] :
% 5.82/6.10 ( ( entails @ P @ bot_bot_assn )
% 5.82/6.10 = ( ! [H: produc3658429121746597890et_nat] :
% 5.82/6.10 ~ ( rep_assn @ P @ H ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ent_false_iff
% 5.82/6.10 thf(fact_3982_snga__same__false,axiom,
% 5.82/6.10 ! [P6: array_VEBT_VEBTi,X2: list_VEBT_VEBTi,Y3: list_VEBT_VEBTi] :
% 5.82/6.10 ( ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ P6 @ X2 ) @ ( snga_assn_VEBT_VEBTi @ P6 @ Y3 ) )
% 5.82/6.10 = bot_bot_assn ) ).
% 5.82/6.10
% 5.82/6.10 % snga_same_false
% 5.82/6.10 thf(fact_3983_ceiling__numeral,axiom,
% 5.82/6.10 ! [V: num] :
% 5.82/6.10 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.82/6.10 = ( numeral_numeral_int @ V ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_numeral
% 5.82/6.10 thf(fact_3984_ceiling__numeral,axiom,
% 5.82/6.10 ! [V: num] :
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.82/6.10 = ( numeral_numeral_int @ V ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_numeral
% 5.82/6.10 thf(fact_3985_ceiling__one,axiom,
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.82/6.10 = one_one_int ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_one
% 5.82/6.10 thf(fact_3986_ceiling__one,axiom,
% 5.82/6.10 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.82/6.10 = one_one_int ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_one
% 5.82/6.10 thf(fact_3987_ceiling__le__zero,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.82/6.10 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_le_zero
% 5.82/6.10 thf(fact_3988_ceiling__le__zero,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.82/6.10 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_le_zero
% 5.82/6.10 thf(fact_3989_ceiling__le__numeral,axiom,
% 5.82/6.10 ! [X2: real,V: num] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.10 = ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_le_numeral
% 5.82/6.10 thf(fact_3990_ceiling__le__numeral,axiom,
% 5.82/6.10 ! [X2: rat,V: num] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.10 = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_le_numeral
% 5.82/6.10 thf(fact_3991_zero__less__ceiling,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.10 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % zero_less_ceiling
% 5.82/6.10 thf(fact_3992_zero__less__ceiling,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.10 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % zero_less_ceiling
% 5.82/6.10 thf(fact_3993_numeral__less__ceiling,axiom,
% 5.82/6.10 ! [V: num,X2: real] :
% 5.82/6.10 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.10 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % numeral_less_ceiling
% 5.82/6.10 thf(fact_3994_numeral__less__ceiling,axiom,
% 5.82/6.10 ! [V: num,X2: rat] :
% 5.82/6.10 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.10 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % numeral_less_ceiling
% 5.82/6.10 thf(fact_3995_ceiling__less__one,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.82/6.10 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_less_one
% 5.82/6.10 thf(fact_3996_ceiling__less__one,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.82/6.10 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_less_one
% 5.82/6.10 thf(fact_3997_one__le__ceiling,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.10 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % one_le_ceiling
% 5.82/6.10 thf(fact_3998_one__le__ceiling,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.10 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % one_le_ceiling
% 5.82/6.10 thf(fact_3999_ceiling__add__numeral,axiom,
% 5.82/6.10 ! [X2: real,V: num] :
% 5.82/6.10 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.82/6.10 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_add_numeral
% 5.82/6.10 thf(fact_4000_ceiling__add__numeral,axiom,
% 5.82/6.10 ! [X2: rat,V: num] :
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.82/6.10 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_add_numeral
% 5.82/6.10 thf(fact_4001_ceiling__le__one,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.82/6.10 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_le_one
% 5.82/6.10 thf(fact_4002_ceiling__le__one,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.82/6.10 = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_le_one
% 5.82/6.10 thf(fact_4003_one__less__ceiling,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.10 = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % one_less_ceiling
% 5.82/6.10 thf(fact_4004_one__less__ceiling,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.10 = ( ord_less_real @ one_one_real @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % one_less_ceiling
% 5.82/6.10 thf(fact_4005_ceiling__add__one,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.82/6.10 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_add_one
% 5.82/6.10 thf(fact_4006_ceiling__add__one,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.82/6.10 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_add_one
% 5.82/6.10 thf(fact_4007_ceiling__diff__numeral,axiom,
% 5.82/6.10 ! [X2: real,V: num] :
% 5.82/6.10 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.82/6.10 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_diff_numeral
% 5.82/6.10 thf(fact_4008_ceiling__diff__numeral,axiom,
% 5.82/6.10 ! [X2: rat,V: num] :
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.82/6.10 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_diff_numeral
% 5.82/6.10 thf(fact_4009_ceiling__numeral__power,axiom,
% 5.82/6.10 ! [X2: num,N: nat] :
% 5.82/6.10 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.82/6.10 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_numeral_power
% 5.82/6.10 thf(fact_4010_ceiling__numeral__power,axiom,
% 5.82/6.10 ! [X2: num,N: nat] :
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.82/6.10 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_numeral_power
% 5.82/6.10 thf(fact_4011_ceiling__diff__one,axiom,
% 5.82/6.10 ! [X2: rat] :
% 5.82/6.10 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.82/6.10 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_diff_one
% 5.82/6.10 thf(fact_4012_ceiling__diff__one,axiom,
% 5.82/6.10 ! [X2: real] :
% 5.82/6.10 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.82/6.10 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_diff_one
% 5.82/6.10 thf(fact_4013_ceiling__less__numeral,axiom,
% 5.82/6.10 ! [X2: real,V: num] :
% 5.82/6.10 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.10 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_less_numeral
% 5.82/6.10 thf(fact_4014_ceiling__less__numeral,axiom,
% 5.82/6.10 ! [X2: rat,V: num] :
% 5.82/6.10 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.10 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_less_numeral
% 5.82/6.10 thf(fact_4015_numeral__le__ceiling,axiom,
% 5.82/6.10 ! [V: num,X2: real] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.10 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % numeral_le_ceiling
% 5.82/6.10 thf(fact_4016_numeral__le__ceiling,axiom,
% 5.82/6.10 ! [V: num,X2: rat] :
% 5.82/6.10 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.10 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.82/6.10
% 5.82/6.10 % numeral_le_ceiling
% 5.82/6.10 thf(fact_4017_bot__nat__def,axiom,
% 5.82/6.10 bot_bot_nat = zero_zero_nat ).
% 5.82/6.10
% 5.82/6.10 % bot_nat_def
% 5.82/6.10 thf(fact_4018_bot__option__def,axiom,
% 5.82/6.10 bot_bot_option_nat = none_nat ).
% 5.82/6.10
% 5.82/6.10 % bot_option_def
% 5.82/6.10 thf(fact_4019_ent__false,axiom,
% 5.82/6.10 ! [P: assn] : ( entails @ bot_bot_assn @ P ) ).
% 5.82/6.10
% 5.82/6.10 % ent_false
% 5.82/6.10 thf(fact_4020_bot__enat__def,axiom,
% 5.82/6.10 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.82/6.10
% 5.82/6.10 % bot_enat_def
% 5.82/6.10 thf(fact_4021_ceiling__mono,axiom,
% 5.82/6.10 ! [Y3: real,X2: real] :
% 5.82/6.10 ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.82/6.10 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y3 ) @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_mono
% 5.82/6.10 thf(fact_4022_ceiling__mono,axiom,
% 5.82/6.10 ! [Y3: rat,X2: rat] :
% 5.82/6.10 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.10 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y3 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_mono
% 5.82/6.10 thf(fact_4023_ceiling__less__cancel,axiom,
% 5.82/6.10 ! [X2: rat,Y3: rat] :
% 5.82/6.10 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y3 ) )
% 5.82/6.10 => ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_less_cancel
% 5.82/6.10 thf(fact_4024_ceiling__less__cancel,axiom,
% 5.82/6.10 ! [X2: real,Y3: real] :
% 5.82/6.10 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y3 ) )
% 5.82/6.10 => ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_less_cancel
% 5.82/6.10 thf(fact_4025_ceiling__add__le,axiom,
% 5.82/6.10 ! [X2: rat,Y3: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y3 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_add_le
% 5.82/6.10 thf(fact_4026_ceiling__add__le,axiom,
% 5.82/6.10 ! [X2: real,Y3: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y3 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % ceiling_add_le
% 5.82/6.10 thf(fact_4027_verit__comp__simplify1_I2_J,axiom,
% 5.82/6.10 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % verit_comp_simplify1(2)
% 5.82/6.10 thf(fact_4028_verit__comp__simplify1_I2_J,axiom,
% 5.82/6.10 ! [A2: rat] : ( ord_less_eq_rat @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % verit_comp_simplify1(2)
% 5.82/6.10 thf(fact_4029_verit__comp__simplify1_I2_J,axiom,
% 5.82/6.10 ! [A2: num] : ( ord_less_eq_num @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % verit_comp_simplify1(2)
% 5.82/6.10 thf(fact_4030_verit__comp__simplify1_I2_J,axiom,
% 5.82/6.10 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % verit_comp_simplify1(2)
% 5.82/6.10 thf(fact_4031_verit__comp__simplify1_I2_J,axiom,
% 5.82/6.10 ! [A2: int] : ( ord_less_eq_int @ A2 @ A2 ) ).
% 5.82/6.10
% 5.82/6.10 % verit_comp_simplify1(2)
% 5.82/6.10 thf(fact_4032_nle__le,axiom,
% 5.82/6.10 ! [A2: rat,B2: rat] :
% 5.82/6.10 ( ( ~ ( ord_less_eq_rat @ A2 @ B2 ) )
% 5.82/6.10 = ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.10 & ( B2 != A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % nle_le
% 5.82/6.10 thf(fact_4033_nle__le,axiom,
% 5.82/6.10 ! [A2: num,B2: num] :
% 5.82/6.10 ( ( ~ ( ord_less_eq_num @ A2 @ B2 ) )
% 5.82/6.10 = ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.10 & ( B2 != A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % nle_le
% 5.82/6.10 thf(fact_4034_nle__le,axiom,
% 5.82/6.10 ! [A2: nat,B2: nat] :
% 5.82/6.10 ( ( ~ ( ord_less_eq_nat @ A2 @ B2 ) )
% 5.82/6.10 = ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.10 & ( B2 != A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % nle_le
% 5.82/6.10 thf(fact_4035_nle__le,axiom,
% 5.82/6.10 ! [A2: int,B2: int] :
% 5.82/6.10 ( ( ~ ( ord_less_eq_int @ A2 @ B2 ) )
% 5.82/6.10 = ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.10 & ( B2 != A2 ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % nle_le
% 5.82/6.10 thf(fact_4036_le__cases3,axiom,
% 5.82/6.10 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.10 ( ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ Y3 @ Z ) )
% 5.82/6.10 => ( ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ X2 @ Z ) )
% 5.82/6.10 => ( ( ( ord_less_eq_rat @ X2 @ Z )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ Z @ Y3 ) )
% 5.82/6.10 => ( ( ( ord_less_eq_rat @ Z @ Y3 )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ Y3 @ X2 ) )
% 5.82/6.10 => ( ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ Z @ X2 ) )
% 5.82/6.10 => ~ ( ( ord_less_eq_rat @ Z @ X2 )
% 5.82/6.10 => ~ ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.10
% 5.82/6.10 % le_cases3
% 5.82/6.10 thf(fact_4037_le__cases3,axiom,
% 5.82/6.10 ! [X2: num,Y3: num,Z: num] :
% 5.82/6.10 ( ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.10 => ~ ( ord_less_eq_num @ Y3 @ Z ) )
% 5.82/6.10 => ( ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.82/6.10 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 5.82/6.10 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 5.82/6.10 => ~ ( ord_less_eq_num @ Z @ Y3 ) )
% 5.82/6.10 => ( ( ( ord_less_eq_num @ Z @ Y3 )
% 5.82/6.11 => ~ ( ord_less_eq_num @ Y3 @ X2 ) )
% 5.82/6.11 => ( ( ( ord_less_eq_num @ Y3 @ Z )
% 5.82/6.11 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 5.82/6.11 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 5.82/6.11 => ~ ( ord_less_eq_num @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % le_cases3
% 5.82/6.11 thf(fact_4038_le__cases3,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.11 ( ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_eq_nat @ Y3 @ Z ) )
% 5.82/6.11 => ( ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 5.82/6.11 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 5.82/6.11 => ~ ( ord_less_eq_nat @ Z @ Y3 ) )
% 5.82/6.11 => ( ( ( ord_less_eq_nat @ Z @ Y3 )
% 5.82/6.11 => ~ ( ord_less_eq_nat @ Y3 @ X2 ) )
% 5.82/6.11 => ( ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.82/6.11 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 5.82/6.11 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 5.82/6.11 => ~ ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % le_cases3
% 5.82/6.11 thf(fact_4039_le__cases3,axiom,
% 5.82/6.11 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.11 ( ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_eq_int @ Y3 @ Z ) )
% 5.82/6.11 => ( ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_eq_int @ X2 @ Z ) )
% 5.82/6.11 => ( ( ( ord_less_eq_int @ X2 @ Z )
% 5.82/6.11 => ~ ( ord_less_eq_int @ Z @ Y3 ) )
% 5.82/6.11 => ( ( ( ord_less_eq_int @ Z @ Y3 )
% 5.82/6.11 => ~ ( ord_less_eq_int @ Y3 @ X2 ) )
% 5.82/6.11 => ( ( ( ord_less_eq_int @ Y3 @ Z )
% 5.82/6.11 => ~ ( ord_less_eq_int @ Z @ X2 ) )
% 5.82/6.11 => ~ ( ( ord_less_eq_int @ Z @ X2 )
% 5.82/6.11 => ~ ( ord_less_eq_int @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % le_cases3
% 5.82/6.11 thf(fact_4040_order__class_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [X3: set_int,Y: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.82/6.11 & ( ord_less_eq_set_int @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_class.order_eq_iff
% 5.82/6.11 thf(fact_4041_order__class_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [X3: rat,Y: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.82/6.11 & ( ord_less_eq_rat @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_class.order_eq_iff
% 5.82/6.11 thf(fact_4042_order__class_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [X3: num,Y: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X3 @ Y )
% 5.82/6.11 & ( ord_less_eq_num @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_class.order_eq_iff
% 5.82/6.11 thf(fact_4043_order__class_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [X3: nat,Y: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.82/6.11 & ( ord_less_eq_nat @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_class.order_eq_iff
% 5.82/6.11 thf(fact_4044_order__class_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [X3: int,Y: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X3 @ Y )
% 5.82/6.11 & ( ord_less_eq_int @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_class.order_eq_iff
% 5.82/6.11 thf(fact_4045_ord__eq__le__trans,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int,C2: set_int] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_set_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_trans
% 5.82/6.11 thf(fact_4046_ord__eq__le__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_trans
% 5.82/6.11 thf(fact_4047_ord__eq__le__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_trans
% 5.82/6.11 thf(fact_4048_ord__eq__le__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_trans
% 5.82/6.11 thf(fact_4049_ord__eq__le__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_trans
% 5.82/6.11 thf(fact_4050_ord__le__eq__trans,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_eq_set_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_trans
% 5.82/6.11 thf(fact_4051_ord__le__eq__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_trans
% 5.82/6.11 thf(fact_4052_ord__le__eq__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_trans
% 5.82/6.11 thf(fact_4053_ord__le__eq__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_trans
% 5.82/6.11 thf(fact_4054_ord__le__eq__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_eq_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_trans
% 5.82/6.11 thf(fact_4055_order__antisym,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.82/6.11 => ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym
% 5.82/6.11 thf(fact_4056_order__antisym,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.11 => ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym
% 5.82/6.11 thf(fact_4057_order__antisym,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.82/6.11 => ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym
% 5.82/6.11 thf(fact_4058_order__antisym,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.11 => ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym
% 5.82/6.11 thf(fact_4059_order__antisym,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.11 => ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym
% 5.82/6.11 thf(fact_4060_order_Otrans,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_set_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.trans
% 5.82/6.11 thf(fact_4061_order_Otrans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.trans
% 5.82/6.11 thf(fact_4062_order_Otrans,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.trans
% 5.82/6.11 thf(fact_4063_order_Otrans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.trans
% 5.82/6.11 thf(fact_4064_order_Otrans,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_eq_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.trans
% 5.82/6.11 thf(fact_4065_order__trans,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_eq_set_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_trans
% 5.82/6.11 thf(fact_4066_order__trans,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_eq_rat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_trans
% 5.82/6.11 thf(fact_4067_order__trans,axiom,
% 5.82/6.11 ! [X2: num,Y3: num,Z: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_num @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_eq_num @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_trans
% 5.82/6.11 thf(fact_4068_order__trans,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_trans
% 5.82/6.11 thf(fact_4069_order__trans,axiom,
% 5.82/6.11 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_eq_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_trans
% 5.82/6.11 thf(fact_4070_linorder__wlog,axiom,
% 5.82/6.11 ! [P: rat > rat > $o,A2: rat,B2: rat] :
% 5.82/6.11 ( ! [A3: rat,B3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: rat,B3: rat] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_wlog
% 5.82/6.11 thf(fact_4071_linorder__wlog,axiom,
% 5.82/6.11 ! [P: num > num > $o,A2: num,B2: num] :
% 5.82/6.11 ( ! [A3: num,B3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: num,B3: num] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_wlog
% 5.82/6.11 thf(fact_4072_linorder__wlog,axiom,
% 5.82/6.11 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 5.82/6.11 ( ! [A3: nat,B3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: nat,B3: nat] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_wlog
% 5.82/6.11 thf(fact_4073_linorder__wlog,axiom,
% 5.82/6.11 ! [P: int > int > $o,A2: int,B2: int] :
% 5.82/6.11 ( ! [A3: int,B3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: int,B3: int] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_wlog
% 5.82/6.11 thf(fact_4074_dual__order_Oeq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ B6 @ A5 )
% 5.82/6.11 & ( ord_less_eq_set_int @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.eq_iff
% 5.82/6.11 thf(fact_4075_dual__order_Oeq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ B6 @ A5 )
% 5.82/6.11 & ( ord_less_eq_rat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.eq_iff
% 5.82/6.11 thf(fact_4076_dual__order_Oeq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: num,B6: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ B6 @ A5 )
% 5.82/6.11 & ( ord_less_eq_num @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.eq_iff
% 5.82/6.11 thf(fact_4077_dual__order_Oeq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ B6 @ A5 )
% 5.82/6.11 & ( ord_less_eq_nat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.eq_iff
% 5.82/6.11 thf(fact_4078_dual__order_Oeq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: int,B6: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ B6 @ A5 )
% 5.82/6.11 & ( ord_less_eq_int @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.eq_iff
% 5.82/6.11 thf(fact_4079_dual__order_Oantisym,axiom,
% 5.82/6.11 ! [B2: set_int,A2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.antisym
% 5.82/6.11 thf(fact_4080_dual__order_Oantisym,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.antisym
% 5.82/6.11 thf(fact_4081_dual__order_Oantisym,axiom,
% 5.82/6.11 ! [B2: num,A2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.antisym
% 5.82/6.11 thf(fact_4082_dual__order_Oantisym,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.antisym
% 5.82/6.11 thf(fact_4083_dual__order_Oantisym,axiom,
% 5.82/6.11 ! [B2: int,A2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.antisym
% 5.82/6.11 thf(fact_4084_dual__order_Otrans,axiom,
% 5.82/6.11 ! [B2: set_int,A2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_set_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.trans
% 5.82/6.11 thf(fact_4085_dual__order_Otrans,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.trans
% 5.82/6.11 thf(fact_4086_dual__order_Otrans,axiom,
% 5.82/6.11 ! [B2: num,A2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_num @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.trans
% 5.82/6.11 thf(fact_4087_dual__order_Otrans,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.trans
% 5.82/6.11 thf(fact_4088_dual__order_Otrans,axiom,
% 5.82/6.11 ! [B2: int,A2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.trans
% 5.82/6.11 thf(fact_4089_antisym,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym
% 5.82/6.11 thf(fact_4090_antisym,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym
% 5.82/6.11 thf(fact_4091_antisym,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym
% 5.82/6.11 thf(fact_4092_antisym,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym
% 5.82/6.11 thf(fact_4093_antisym,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.11 => ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym
% 5.82/6.11 thf(fact_4094_Orderings_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A5 @ B6 )
% 5.82/6.11 & ( ord_less_eq_set_int @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % Orderings.order_eq_iff
% 5.82/6.11 thf(fact_4095_Orderings_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A5 @ B6 )
% 5.82/6.11 & ( ord_less_eq_rat @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % Orderings.order_eq_iff
% 5.82/6.11 thf(fact_4096_Orderings_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: num,B6: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A5 @ B6 )
% 5.82/6.11 & ( ord_less_eq_num @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % Orderings.order_eq_iff
% 5.82/6.11 thf(fact_4097_Orderings_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A5 @ B6 )
% 5.82/6.11 & ( ord_less_eq_nat @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % Orderings.order_eq_iff
% 5.82/6.11 thf(fact_4098_Orderings_Oorder__eq__iff,axiom,
% 5.82/6.11 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.82/6.11 = ( ^ [A5: int,B6: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A5 @ B6 )
% 5.82/6.11 & ( ord_less_eq_int @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % Orderings.order_eq_iff
% 5.82/6.11 thf(fact_4099_order__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: rat > rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4100_order__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: num > rat,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4101_order__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: nat > rat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4102_order__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: int > rat,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4103_order__subst1,axiom,
% 5.82/6.11 ! [A2: num,F: rat > num,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4104_order__subst1,axiom,
% 5.82/6.11 ! [A2: num,F: num > num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4105_order__subst1,axiom,
% 5.82/6.11 ! [A2: num,F: nat > num,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4106_order__subst1,axiom,
% 5.82/6.11 ! [A2: num,F: int > num,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4107_order__subst1,axiom,
% 5.82/6.11 ! [A2: nat,F: rat > nat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4108_order__subst1,axiom,
% 5.82/6.11 ! [A2: nat,F: num > nat,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst1
% 5.82/6.11 thf(fact_4109_order__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4110_order__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4111_order__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4112_order__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4113_order__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4114_order__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4115_order__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4116_order__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4117_order__subst2,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,F: nat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4118_order__subst2,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,F: nat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_subst2
% 5.82/6.11 thf(fact_4119_order__eq__refl,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ( X2 = Y3 )
% 5.82/6.11 => ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_eq_refl
% 5.82/6.11 thf(fact_4120_order__eq__refl,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( X2 = Y3 )
% 5.82/6.11 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_eq_refl
% 5.82/6.11 thf(fact_4121_order__eq__refl,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( X2 = Y3 )
% 5.82/6.11 => ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_eq_refl
% 5.82/6.11 thf(fact_4122_order__eq__refl,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( X2 = Y3 )
% 5.82/6.11 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_eq_refl
% 5.82/6.11 thf(fact_4123_order__eq__refl,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( X2 = Y3 )
% 5.82/6.11 => ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_eq_refl
% 5.82/6.11 thf(fact_4124_verit__la__disequality,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 | ~ ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 | ~ ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_la_disequality
% 5.82/6.11 thf(fact_4125_verit__la__disequality,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 | ~ ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 | ~ ( ord_less_eq_num @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_la_disequality
% 5.82/6.11 thf(fact_4126_verit__la__disequality,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 | ~ ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 | ~ ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_la_disequality
% 5.82/6.11 thf(fact_4127_verit__la__disequality,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 | ~ ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 | ~ ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_la_disequality
% 5.82/6.11 thf(fact_4128_linorder__linear,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_linear
% 5.82/6.11 thf(fact_4129_linorder__linear,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_linear
% 5.82/6.11 thf(fact_4130_linorder__linear,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_linear
% 5.82/6.11 thf(fact_4131_linorder__linear,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_linear
% 5.82/6.11 thf(fact_4132_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: rat,F: rat > rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4133_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: num,F: rat > num,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4134_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: nat,F: rat > nat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4135_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: int,F: rat > int,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4136_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: rat,F: num > rat,B2: num,C2: num] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4137_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: num,F: num > num,B2: num,C2: num] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4138_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: nat,F: num > nat,B2: num,C2: num] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4139_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: int,F: num > int,B2: num,C2: num] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4140_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: rat,F: nat > rat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4141_ord__eq__le__subst,axiom,
% 5.82/6.11 ! [A2: num,F: nat > num,B2: nat,C2: nat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_le_subst
% 5.82/6.11 thf(fact_4142_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4143_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4144_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4145_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4146_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4147_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4148_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4149_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4150_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,F: nat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4151_ord__le__eq__subst,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,F: nat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_le_eq_subst
% 5.82/6.11 thf(fact_4152_linorder__le__cases,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ~ ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_cases
% 5.82/6.11 thf(fact_4153_linorder__le__cases,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ~ ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_cases
% 5.82/6.11 thf(fact_4154_linorder__le__cases,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ~ ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_cases
% 5.82/6.11 thf(fact_4155_linorder__le__cases,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ~ ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_cases
% 5.82/6.11 thf(fact_4156_order__antisym__conv,axiom,
% 5.82/6.11 ! [Y3: set_int,X2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym_conv
% 5.82/6.11 thf(fact_4157_order__antisym__conv,axiom,
% 5.82/6.11 ! [Y3: rat,X2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym_conv
% 5.82/6.11 thf(fact_4158_order__antisym__conv,axiom,
% 5.82/6.11 ! [Y3: num,X2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym_conv
% 5.82/6.11 thf(fact_4159_order__antisym__conv,axiom,
% 5.82/6.11 ! [Y3: nat,X2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym_conv
% 5.82/6.11 thf(fact_4160_order__antisym__conv,axiom,
% 5.82/6.11 ! [Y3: int,X2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_antisym_conv
% 5.82/6.11 thf(fact_4161_order__less__imp__not__less,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_less
% 5.82/6.11 thf(fact_4162_order__less__imp__not__less,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_less
% 5.82/6.11 thf(fact_4163_order__less__imp__not__less,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_less
% 5.82/6.11 thf(fact_4164_order__less__imp__not__less,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_less
% 5.82/6.11 thf(fact_4165_order__less__imp__not__less,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_less
% 5.82/6.11 thf(fact_4166_order__less__imp__not__eq2,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( Y3 != X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq2
% 5.82/6.11 thf(fact_4167_order__less__imp__not__eq2,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( Y3 != X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq2
% 5.82/6.11 thf(fact_4168_order__less__imp__not__eq2,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( Y3 != X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq2
% 5.82/6.11 thf(fact_4169_order__less__imp__not__eq2,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( Y3 != X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq2
% 5.82/6.11 thf(fact_4170_order__less__imp__not__eq2,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( Y3 != X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq2
% 5.82/6.11 thf(fact_4171_order__less__imp__not__eq,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq
% 5.82/6.11 thf(fact_4172_order__less__imp__not__eq,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq
% 5.82/6.11 thf(fact_4173_order__less__imp__not__eq,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq
% 5.82/6.11 thf(fact_4174_order__less__imp__not__eq,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq
% 5.82/6.11 thf(fact_4175_order__less__imp__not__eq,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_not_eq
% 5.82/6.11 thf(fact_4176_linorder__less__linear,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 )
% 5.82/6.11 | ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_linear
% 5.82/6.11 thf(fact_4177_linorder__less__linear,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 )
% 5.82/6.11 | ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_linear
% 5.82/6.11 thf(fact_4178_linorder__less__linear,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 )
% 5.82/6.11 | ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_linear
% 5.82/6.11 thf(fact_4179_linorder__less__linear,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 )
% 5.82/6.11 | ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_linear
% 5.82/6.11 thf(fact_4180_linorder__less__linear,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 )
% 5.82/6.11 | ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_linear
% 5.82/6.11 thf(fact_4181_order__less__imp__triv,axiom,
% 5.82/6.11 ! [X2: real,Y3: real,P: $o] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.11 => P ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_triv
% 5.82/6.11 thf(fact_4182_order__less__imp__triv,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat,P: $o] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_rat @ Y3 @ X2 )
% 5.82/6.11 => P ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_triv
% 5.82/6.11 thf(fact_4183_order__less__imp__triv,axiom,
% 5.82/6.11 ! [X2: num,Y3: num,P: $o] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_num @ Y3 @ X2 )
% 5.82/6.11 => P ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_triv
% 5.82/6.11 thf(fact_4184_order__less__imp__triv,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat,P: $o] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_nat @ Y3 @ X2 )
% 5.82/6.11 => P ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_triv
% 5.82/6.11 thf(fact_4185_order__less__imp__triv,axiom,
% 5.82/6.11 ! [X2: int,Y3: int,P: $o] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_int @ Y3 @ X2 )
% 5.82/6.11 => P ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_triv
% 5.82/6.11 thf(fact_4186_order__less__not__sym,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_not_sym
% 5.82/6.11 thf(fact_4187_order__less__not__sym,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_not_sym
% 5.82/6.11 thf(fact_4188_order__less__not__sym,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_not_sym
% 5.82/6.11 thf(fact_4189_order__less__not__sym,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_not_sym
% 5.82/6.11 thf(fact_4190_order__less__not__sym,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_not_sym
% 5.82/6.11 thf(fact_4191_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4192_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4193_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > num,C2: num] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4194_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4195_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > int,C2: int] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_int @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4196_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > real,C2: real] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4197_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4198_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4199_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4200_order__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > int,C2: int] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_int @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst2
% 5.82/6.11 thf(fact_4201_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: real > real,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4202_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: rat > real,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4203_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: num > real,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4204_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: nat > real,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4205_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: int > real,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4206_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: real > rat,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4207_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: rat > rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4208_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: num > rat,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4209_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: nat > rat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4210_order__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: int > rat,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_subst1
% 5.82/6.11 thf(fact_4211_order__less__irrefl,axiom,
% 5.82/6.11 ! [X2: real] :
% 5.82/6.11 ~ ( ord_less_real @ X2 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_irrefl
% 5.82/6.11 thf(fact_4212_order__less__irrefl,axiom,
% 5.82/6.11 ! [X2: rat] :
% 5.82/6.11 ~ ( ord_less_rat @ X2 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_irrefl
% 5.82/6.11 thf(fact_4213_order__less__irrefl,axiom,
% 5.82/6.11 ! [X2: num] :
% 5.82/6.11 ~ ( ord_less_num @ X2 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_irrefl
% 5.82/6.11 thf(fact_4214_order__less__irrefl,axiom,
% 5.82/6.11 ! [X2: nat] :
% 5.82/6.11 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_irrefl
% 5.82/6.11 thf(fact_4215_order__less__irrefl,axiom,
% 5.82/6.11 ! [X2: int] :
% 5.82/6.11 ~ ( ord_less_int @ X2 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_irrefl
% 5.82/6.11 thf(fact_4216_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4217_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4218_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > num,C2: num] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4219_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4220_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > int,C2: int] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4221_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > real,C2: real] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4222_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4223_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4224_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4225_ord__less__eq__subst,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > int,C2: int] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ( F @ B2 )
% 5.82/6.11 = C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_subst
% 5.82/6.11 thf(fact_4226_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: real,F: real > real,B2: real,C2: real] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4227_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: rat,F: real > rat,B2: real,C2: real] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4228_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: num,F: real > num,B2: real,C2: real] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4229_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: nat,F: real > nat,B2: real,C2: real] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4230_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: int,F: real > int,B2: real,C2: real] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4231_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: real,F: rat > real,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4232_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: rat,F: rat > rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4233_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: num,F: rat > num,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4234_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: nat,F: rat > nat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4235_ord__eq__less__subst,axiom,
% 5.82/6.11 ! [A2: int,F: rat > int,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2
% 5.82/6.11 = ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_subst
% 5.82/6.11 thf(fact_4236_order__less__trans,axiom,
% 5.82/6.11 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_real @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_trans
% 5.82/6.11 thf(fact_4237_order__less__trans,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_rat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_trans
% 5.82/6.11 thf(fact_4238_order__less__trans,axiom,
% 5.82/6.11 ! [X2: num,Y3: num,Z: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_num @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_trans
% 5.82/6.11 thf(fact_4239_order__less__trans,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_nat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_trans
% 5.82/6.11 thf(fact_4240_order__less__trans,axiom,
% 5.82/6.11 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_trans
% 5.82/6.11 thf(fact_4241_order__less__asym_H,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_real @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym'
% 5.82/6.11 thf(fact_4242_order__less__asym_H,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_rat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym'
% 5.82/6.11 thf(fact_4243_order__less__asym_H,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_num @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym'
% 5.82/6.11 thf(fact_4244_order__less__asym_H,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym'
% 5.82/6.11 thf(fact_4245_order__less__asym_H,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym'
% 5.82/6.11 thf(fact_4246_linorder__neq__iff,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 = ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neq_iff
% 5.82/6.11 thf(fact_4247_linorder__neq__iff,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 = ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neq_iff
% 5.82/6.11 thf(fact_4248_linorder__neq__iff,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 = ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_num @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neq_iff
% 5.82/6.11 thf(fact_4249_linorder__neq__iff,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 = ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neq_iff
% 5.82/6.11 thf(fact_4250_linorder__neq__iff,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 = ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neq_iff
% 5.82/6.11 thf(fact_4251_order__less__asym,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym
% 5.82/6.11 thf(fact_4252_order__less__asym,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym
% 5.82/6.11 thf(fact_4253_order__less__asym,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym
% 5.82/6.11 thf(fact_4254_order__less__asym,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym
% 5.82/6.11 thf(fact_4255_order__less__asym,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ~ ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_asym
% 5.82/6.11 thf(fact_4256_linorder__neqE,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 => ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neqE
% 5.82/6.11 thf(fact_4257_linorder__neqE,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 => ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neqE
% 5.82/6.11 thf(fact_4258_linorder__neqE,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 => ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_num @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neqE
% 5.82/6.11 thf(fact_4259_linorder__neqE,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 => ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neqE
% 5.82/6.11 thf(fact_4260_linorder__neqE,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( X2 != Y3 )
% 5.82/6.11 => ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_neqE
% 5.82/6.11 thf(fact_4261_dual__order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [B2: real,A2: real] :
% 5.82/6.11 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4262_dual__order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4263_dual__order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [B2: num,A2: num] :
% 5.82/6.11 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4264_dual__order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4265_dual__order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [B2: int,A2: int] :
% 5.82/6.11 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4266_order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4267_order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4268_order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4269_order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4270_order_Ostrict__implies__not__eq,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( A2 != B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_not_eq
% 5.82/6.11 thf(fact_4271_dual__order_Ostrict__trans,axiom,
% 5.82/6.11 ! [B2: real,A2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_real @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_real @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans
% 5.82/6.11 thf(fact_4272_dual__order_Ostrict__trans,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_rat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans
% 5.82/6.11 thf(fact_4273_dual__order_Ostrict__trans,axiom,
% 5.82/6.11 ! [B2: num,A2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_num @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_num @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans
% 5.82/6.11 thf(fact_4274_dual__order_Ostrict__trans,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_nat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans
% 5.82/6.11 thf(fact_4275_dual__order_Ostrict__trans,axiom,
% 5.82/6.11 ! [B2: int,A2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans
% 5.82/6.11 thf(fact_4276_not__less__iff__gr__or__eq,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.82/6.11 = ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_less_iff_gr_or_eq
% 5.82/6.11 thf(fact_4277_not__less__iff__gr__or__eq,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.82/6.11 = ( ( ord_less_rat @ Y3 @ X2 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_less_iff_gr_or_eq
% 5.82/6.11 thf(fact_4278_not__less__iff__gr__or__eq,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.82/6.11 = ( ( ord_less_num @ Y3 @ X2 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_less_iff_gr_or_eq
% 5.82/6.11 thf(fact_4279_not__less__iff__gr__or__eq,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.82/6.11 = ( ( ord_less_nat @ Y3 @ X2 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_less_iff_gr_or_eq
% 5.82/6.11 thf(fact_4280_not__less__iff__gr__or__eq,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.82/6.11 = ( ( ord_less_int @ Y3 @ X2 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_less_iff_gr_or_eq
% 5.82/6.11 thf(fact_4281_order_Ostrict__trans,axiom,
% 5.82/6.11 ! [A2: real,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans
% 5.82/6.11 thf(fact_4282_order_Ostrict__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans
% 5.82/6.11 thf(fact_4283_order_Ostrict__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans
% 5.82/6.11 thf(fact_4284_order_Ostrict__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans
% 5.82/6.11 thf(fact_4285_order_Ostrict__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans
% 5.82/6.11 thf(fact_4286_linorder__less__wlog,axiom,
% 5.82/6.11 ! [P: real > real > $o,A2: real,B2: real] :
% 5.82/6.11 ( ! [A3: real,B3: real] :
% 5.82/6.11 ( ( ord_less_real @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: real] : ( P @ A3 @ A3 )
% 5.82/6.11 => ( ! [A3: real,B3: real] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_wlog
% 5.82/6.11 thf(fact_4287_linorder__less__wlog,axiom,
% 5.82/6.11 ! [P: rat > rat > $o,A2: rat,B2: rat] :
% 5.82/6.11 ( ! [A3: rat,B3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 5.82/6.11 => ( ! [A3: rat,B3: rat] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_wlog
% 5.82/6.11 thf(fact_4288_linorder__less__wlog,axiom,
% 5.82/6.11 ! [P: num > num > $o,A2: num,B2: num] :
% 5.82/6.11 ( ! [A3: num,B3: num] :
% 5.82/6.11 ( ( ord_less_num @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: num] : ( P @ A3 @ A3 )
% 5.82/6.11 => ( ! [A3: num,B3: num] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_wlog
% 5.82/6.11 thf(fact_4289_linorder__less__wlog,axiom,
% 5.82/6.11 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 5.82/6.11 ( ! [A3: nat,B3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 5.82/6.11 => ( ! [A3: nat,B3: nat] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_wlog
% 5.82/6.11 thf(fact_4290_linorder__less__wlog,axiom,
% 5.82/6.11 ! [P: int > int > $o,A2: int,B2: int] :
% 5.82/6.11 ( ! [A3: int,B3: int] :
% 5.82/6.11 ( ( ord_less_int @ A3 @ B3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( ! [A3: int] : ( P @ A3 @ A3 )
% 5.82/6.11 => ( ! [A3: int,B3: int] :
% 5.82/6.11 ( ( P @ B3 @ A3 )
% 5.82/6.11 => ( P @ A3 @ B3 ) )
% 5.82/6.11 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_less_wlog
% 5.82/6.11 thf(fact_4291_exists__least__iff,axiom,
% 5.82/6.11 ( ( ^ [P2: nat > $o] :
% 5.82/6.11 ? [X6: nat] : ( P2 @ X6 ) )
% 5.82/6.11 = ( ^ [P3: nat > $o] :
% 5.82/6.11 ? [N4: nat] :
% 5.82/6.11 ( ( P3 @ N4 )
% 5.82/6.11 & ! [M6: nat] :
% 5.82/6.11 ( ( ord_less_nat @ M6 @ N4 )
% 5.82/6.11 => ~ ( P3 @ M6 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % exists_least_iff
% 5.82/6.11 thf(fact_4292_dual__order_Oirrefl,axiom,
% 5.82/6.11 ! [A2: real] :
% 5.82/6.11 ~ ( ord_less_real @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.irrefl
% 5.82/6.11 thf(fact_4293_dual__order_Oirrefl,axiom,
% 5.82/6.11 ! [A2: rat] :
% 5.82/6.11 ~ ( ord_less_rat @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.irrefl
% 5.82/6.11 thf(fact_4294_dual__order_Oirrefl,axiom,
% 5.82/6.11 ! [A2: num] :
% 5.82/6.11 ~ ( ord_less_num @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.irrefl
% 5.82/6.11 thf(fact_4295_dual__order_Oirrefl,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.irrefl
% 5.82/6.11 thf(fact_4296_dual__order_Oirrefl,axiom,
% 5.82/6.11 ! [A2: int] :
% 5.82/6.11 ~ ( ord_less_int @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.irrefl
% 5.82/6.11 thf(fact_4297_dual__order_Oasym,axiom,
% 5.82/6.11 ! [B2: real,A2: real] :
% 5.82/6.11 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.11 => ~ ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.asym
% 5.82/6.11 thf(fact_4298_dual__order_Oasym,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.11 => ~ ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.asym
% 5.82/6.11 thf(fact_4299_dual__order_Oasym,axiom,
% 5.82/6.11 ! [B2: num,A2: num] :
% 5.82/6.11 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.11 => ~ ( ord_less_num @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.asym
% 5.82/6.11 thf(fact_4300_dual__order_Oasym,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.11 => ~ ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.asym
% 5.82/6.11 thf(fact_4301_dual__order_Oasym,axiom,
% 5.82/6.11 ! [B2: int,A2: int] :
% 5.82/6.11 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.11 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.asym
% 5.82/6.11 thf(fact_4302_linorder__cases,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( X2 != Y3 )
% 5.82/6.11 => ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_cases
% 5.82/6.11 thf(fact_4303_linorder__cases,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( X2 != Y3 )
% 5.82/6.11 => ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_cases
% 5.82/6.11 thf(fact_4304_linorder__cases,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( X2 != Y3 )
% 5.82/6.11 => ( ord_less_num @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_cases
% 5.82/6.11 thf(fact_4305_linorder__cases,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( X2 != Y3 )
% 5.82/6.11 => ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_cases
% 5.82/6.11 thf(fact_4306_linorder__cases,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( X2 != Y3 )
% 5.82/6.11 => ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_cases
% 5.82/6.11 thf(fact_4307_antisym__conv3,axiom,
% 5.82/6.11 ! [Y3: real,X2: real] :
% 5.82/6.11 ( ~ ( ord_less_real @ Y3 @ X2 )
% 5.82/6.11 => ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv3
% 5.82/6.11 thf(fact_4308_antisym__conv3,axiom,
% 5.82/6.11 ! [Y3: rat,X2: rat] :
% 5.82/6.11 ( ~ ( ord_less_rat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv3
% 5.82/6.11 thf(fact_4309_antisym__conv3,axiom,
% 5.82/6.11 ! [Y3: num,X2: num] :
% 5.82/6.11 ( ~ ( ord_less_num @ Y3 @ X2 )
% 5.82/6.11 => ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv3
% 5.82/6.11 thf(fact_4310_antisym__conv3,axiom,
% 5.82/6.11 ! [Y3: nat,X2: nat] :
% 5.82/6.11 ( ~ ( ord_less_nat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv3
% 5.82/6.11 thf(fact_4311_antisym__conv3,axiom,
% 5.82/6.11 ! [Y3: int,X2: int] :
% 5.82/6.11 ( ~ ( ord_less_int @ Y3 @ X2 )
% 5.82/6.11 => ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv3
% 5.82/6.11 thf(fact_4312_less__induct,axiom,
% 5.82/6.11 ! [P: nat > $o,A2: nat] :
% 5.82/6.11 ( ! [X4: nat] :
% 5.82/6.11 ( ! [Y5: nat] :
% 5.82/6.11 ( ( ord_less_nat @ Y5 @ X4 )
% 5.82/6.11 => ( P @ Y5 ) )
% 5.82/6.11 => ( P @ X4 ) )
% 5.82/6.11 => ( P @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_induct
% 5.82/6.11 thf(fact_4313_ord__less__eq__trans,axiom,
% 5.82/6.11 ! [A2: real,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_trans
% 5.82/6.11 thf(fact_4314_ord__less__eq__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_trans
% 5.82/6.11 thf(fact_4315_ord__less__eq__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_trans
% 5.82/6.11 thf(fact_4316_ord__less__eq__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_trans
% 5.82/6.11 thf(fact_4317_ord__less__eq__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( ( B2 = C2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_less_eq_trans
% 5.82/6.11 thf(fact_4318_ord__eq__less__trans,axiom,
% 5.82/6.11 ! [A2: real,B2: real,C2: real] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_trans
% 5.82/6.11 thf(fact_4319_ord__eq__less__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_trans
% 5.82/6.11 thf(fact_4320_ord__eq__less__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_trans
% 5.82/6.11 thf(fact_4321_ord__eq__less__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_trans
% 5.82/6.11 thf(fact_4322_ord__eq__less__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( A2 = B2 )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ord_eq_less_trans
% 5.82/6.11 thf(fact_4323_order_Oasym,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_real @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.asym
% 5.82/6.11 thf(fact_4324_order_Oasym,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_rat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.asym
% 5.82/6.11 thf(fact_4325_order_Oasym,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_num @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.asym
% 5.82/6.11 thf(fact_4326_order_Oasym,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.asym
% 5.82/6.11 thf(fact_4327_order_Oasym,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.asym
% 5.82/6.11 thf(fact_4328_less__imp__neq,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_imp_neq
% 5.82/6.11 thf(fact_4329_less__imp__neq,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_imp_neq
% 5.82/6.11 thf(fact_4330_less__imp__neq,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_imp_neq
% 5.82/6.11 thf(fact_4331_less__imp__neq,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_imp_neq
% 5.82/6.11 thf(fact_4332_less__imp__neq,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( X2 != Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_imp_neq
% 5.82/6.11 thf(fact_4333_dense,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ? [Z2: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Z2 )
% 5.82/6.11 & ( ord_less_real @ Z2 @ Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense
% 5.82/6.11 thf(fact_4334_dense,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ? [Z2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Z2 )
% 5.82/6.11 & ( ord_less_rat @ Z2 @ Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense
% 5.82/6.11 thf(fact_4335_gt__ex,axiom,
% 5.82/6.11 ! [X2: real] :
% 5.82/6.11 ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 5.82/6.11
% 5.82/6.11 % gt_ex
% 5.82/6.11 thf(fact_4336_gt__ex,axiom,
% 5.82/6.11 ! [X2: rat] :
% 5.82/6.11 ? [X_1: rat] : ( ord_less_rat @ X2 @ X_1 ) ).
% 5.82/6.11
% 5.82/6.11 % gt_ex
% 5.82/6.11 thf(fact_4337_gt__ex,axiom,
% 5.82/6.11 ! [X2: nat] :
% 5.82/6.11 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 5.82/6.11
% 5.82/6.11 % gt_ex
% 5.82/6.11 thf(fact_4338_gt__ex,axiom,
% 5.82/6.11 ! [X2: int] :
% 5.82/6.11 ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 5.82/6.11
% 5.82/6.11 % gt_ex
% 5.82/6.11 thf(fact_4339_lt__ex,axiom,
% 5.82/6.11 ! [X2: real] :
% 5.82/6.11 ? [Y4: real] : ( ord_less_real @ Y4 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % lt_ex
% 5.82/6.11 thf(fact_4340_lt__ex,axiom,
% 5.82/6.11 ! [X2: rat] :
% 5.82/6.11 ? [Y4: rat] : ( ord_less_rat @ Y4 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % lt_ex
% 5.82/6.11 thf(fact_4341_lt__ex,axiom,
% 5.82/6.11 ! [X2: int] :
% 5.82/6.11 ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 5.82/6.11
% 5.82/6.11 % lt_ex
% 5.82/6.11 thf(fact_4342_verit__comp__simplify1_I1_J,axiom,
% 5.82/6.11 ! [A2: real] :
% 5.82/6.11 ~ ( ord_less_real @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(1)
% 5.82/6.11 thf(fact_4343_verit__comp__simplify1_I1_J,axiom,
% 5.82/6.11 ! [A2: rat] :
% 5.82/6.11 ~ ( ord_less_rat @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(1)
% 5.82/6.11 thf(fact_4344_verit__comp__simplify1_I1_J,axiom,
% 5.82/6.11 ! [A2: num] :
% 5.82/6.11 ~ ( ord_less_num @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(1)
% 5.82/6.11 thf(fact_4345_verit__comp__simplify1_I1_J,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(1)
% 5.82/6.11 thf(fact_4346_verit__comp__simplify1_I1_J,axiom,
% 5.82/6.11 ! [A2: int] :
% 5.82/6.11 ~ ( ord_less_int @ A2 @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(1)
% 5.82/6.11 thf(fact_4347_vebt__assn__raw_Osimps_I4_J,axiom,
% 5.82/6.11 ! [Vd3: $o,Ve3: $o,V: option4927543243414619207at_nat,Va: nat,Vb: array_VEBT_VEBTi,Vc: vEBT_VEBTi] :
% 5.82/6.11 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V @ Va @ Vb @ Vc ) )
% 5.82/6.11 = bot_bot_assn ) ).
% 5.82/6.11
% 5.82/6.11 % vebt_assn_raw.simps(4)
% 5.82/6.11 thf(fact_4348_vebt__assn__raw_Osimps_I3_J,axiom,
% 5.82/6.11 ! [V: option4927543243414619207at_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,Vd3: $o,Ve3: $o] :
% 5.82/6.11 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ V @ Va @ Vb @ Vc ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 5.82/6.11 = bot_bot_assn ) ).
% 5.82/6.11
% 5.82/6.11 % vebt_assn_raw.simps(3)
% 5.82/6.11 thf(fact_4349_verit__la__generic,axiom,
% 5.82/6.11 ! [A2: int,X2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A2 @ X2 )
% 5.82/6.11 | ( A2 = X2 )
% 5.82/6.11 | ( ord_less_eq_int @ X2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_la_generic
% 5.82/6.11 thf(fact_4350_mult__ceiling__le,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.11 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A2 @ B2 ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A2 ) @ ( archim7802044766580827645g_real @ B2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % mult_ceiling_le
% 5.82/6.11 thf(fact_4351_mult__ceiling__le,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.11 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A2 @ B2 ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A2 ) @ ( archim2889992004027027881ng_rat @ B2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % mult_ceiling_le
% 5.82/6.11 thf(fact_4352_order__le__imp__less__or__eq,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_imp_less_or_eq
% 5.82/6.11 thf(fact_4353_order__le__imp__less__or__eq,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_set_int @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_imp_less_or_eq
% 5.82/6.11 thf(fact_4354_order__le__imp__less__or__eq,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_imp_less_or_eq
% 5.82/6.11 thf(fact_4355_order__le__imp__less__or__eq,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_imp_less_or_eq
% 5.82/6.11 thf(fact_4356_order__le__imp__less__or__eq,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_imp_less_or_eq
% 5.82/6.11 thf(fact_4357_order__le__imp__less__or__eq,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 | ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_imp_less_or_eq
% 5.82/6.11 thf(fact_4358_linorder__le__less__linear,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_less_linear
% 5.82/6.11 thf(fact_4359_linorder__le__less__linear,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_less_linear
% 5.82/6.11 thf(fact_4360_linorder__le__less__linear,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_less_linear
% 5.82/6.11 thf(fact_4361_linorder__le__less__linear,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_less_linear
% 5.82/6.11 thf(fact_4362_linorder__le__less__linear,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 | ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_le_less_linear
% 5.82/6.11 thf(fact_4363_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4364_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > real,C2: real] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4365_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > real,C2: real] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4366_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,F: nat > real,C2: real] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4367_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: int,B2: int,F: int > real,C2: real] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4368_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,F: real > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4369_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4370_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4371_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,F: nat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4372_order__less__le__subst2,axiom,
% 5.82/6.11 ! [A2: int,B2: int,F: int > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst2
% 5.82/6.11 thf(fact_4373_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: rat > real,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4374_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: rat > rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4375_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: num,F: rat > num,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4376_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: nat,F: rat > nat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4377_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: int,F: rat > int,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4378_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: num > real,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4379_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: num > rat,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4380_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: num,F: num > num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4381_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: nat,F: num > nat,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4382_order__less__le__subst1,axiom,
% 5.82/6.11 ! [A2: int,F: num > int,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_subst1
% 5.82/6.11 thf(fact_4383_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > real,C2: real] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4384_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4385_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4386_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4387_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,F: rat > int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_int @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4388_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > real,C2: real] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_real @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4389_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_rat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4390_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_num @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_num @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4391_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4392_order__le__less__subst2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,F: num > int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_int @ ( F @ B2 ) @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst2
% 5.82/6.11 thf(fact_4393_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: real > real,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4394_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: rat > real,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4395_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: num > real,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4396_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: nat > real,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4397_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: real,F: int > real,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_real @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4398_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: real > rat,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: real,Y4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4399_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: rat > rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: rat,Y4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4400_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: num > rat,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: num,Y4: num] :
% 5.82/6.11 ( ( ord_less_num @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4401_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: nat > rat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: nat,Y4: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4402_order__le__less__subst1,axiom,
% 5.82/6.11 ! [A2: rat,F: int > rat,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ ( F @ B2 ) )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ! [X4: int,Y4: int] :
% 5.82/6.11 ( ( ord_less_int @ X4 @ Y4 )
% 5.82/6.11 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.82/6.11 => ( ord_less_rat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_subst1
% 5.82/6.11 thf(fact_4403_order__less__le__trans,axiom,
% 5.82/6.11 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_real @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_trans
% 5.82/6.11 thf(fact_4404_order__less__le__trans,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_set_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_trans
% 5.82/6.11 thf(fact_4405_order__less__le__trans,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_trans
% 5.82/6.11 thf(fact_4406_order__less__le__trans,axiom,
% 5.82/6.11 ! [X2: num,Y3: num,Z: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_num @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_trans
% 5.82/6.11 thf(fact_4407_order__less__le__trans,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_trans
% 5.82/6.11 thf(fact_4408_order__less__le__trans,axiom,
% 5.82/6.11 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le_trans
% 5.82/6.11 thf(fact_4409_order__le__less__trans,axiom,
% 5.82/6.11 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_real @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_trans
% 5.82/6.11 thf(fact_4410_order__le__less__trans,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_set_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_set_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_trans
% 5.82/6.11 thf(fact_4411_order__le__less__trans,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_rat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_trans
% 5.82/6.11 thf(fact_4412_order__le__less__trans,axiom,
% 5.82/6.11 ! [X2: num,Y3: num,Z: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_num @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_trans
% 5.82/6.11 thf(fact_4413_order__le__less__trans,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_nat @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_trans
% 5.82/6.11 thf(fact_4414_order__le__less__trans,axiom,
% 5.82/6.11 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_int @ Y3 @ Z )
% 5.82/6.11 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less_trans
% 5.82/6.11 thf(fact_4415_order__neq__le__trans,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( A2 != B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_neq_le_trans
% 5.82/6.11 thf(fact_4416_order__neq__le__trans,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int] :
% 5.82/6.11 ( ( A2 != B2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_set_int @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_neq_le_trans
% 5.82/6.11 thf(fact_4417_order__neq__le__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( A2 != B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_neq_le_trans
% 5.82/6.11 thf(fact_4418_order__neq__le__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( A2 != B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_neq_le_trans
% 5.82/6.11 thf(fact_4419_order__neq__le__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( A2 != B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_neq_le_trans
% 5.82/6.11 thf(fact_4420_order__neq__le__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( A2 != B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_neq_le_trans
% 5.82/6.11 thf(fact_4421_order__le__neq__trans,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.11 => ( ( A2 != B2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_neq_trans
% 5.82/6.11 thf(fact_4422_order__le__neq__trans,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ( A2 != B2 )
% 5.82/6.11 => ( ord_less_set_int @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_neq_trans
% 5.82/6.11 thf(fact_4423_order__le__neq__trans,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( A2 != B2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_neq_trans
% 5.82/6.11 thf(fact_4424_order__le__neq__trans,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( A2 != B2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_neq_trans
% 5.82/6.11 thf(fact_4425_order__le__neq__trans,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( A2 != B2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_neq_trans
% 5.82/6.11 thf(fact_4426_order__le__neq__trans,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( ( A2 != B2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_neq_trans
% 5.82/6.11 thf(fact_4427_order__less__imp__le,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_le
% 5.82/6.11 thf(fact_4428_order__less__imp__le,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_le
% 5.82/6.11 thf(fact_4429_order__less__imp__le,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_le
% 5.82/6.11 thf(fact_4430_order__less__imp__le,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_le
% 5.82/6.11 thf(fact_4431_order__less__imp__le,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_le
% 5.82/6.11 thf(fact_4432_order__less__imp__le,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_imp_le
% 5.82/6.11 thf(fact_4433_linorder__not__less,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_eq_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_less
% 5.82/6.11 thf(fact_4434_linorder__not__less,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_less
% 5.82/6.11 thf(fact_4435_linorder__not__less,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_less
% 5.82/6.11 thf(fact_4436_linorder__not__less,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_less
% 5.82/6.11 thf(fact_4437_linorder__not__less,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_less
% 5.82/6.11 thf(fact_4438_linorder__not__le,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_real @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_le
% 5.82/6.11 thf(fact_4439_linorder__not__le,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_rat @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_le
% 5.82/6.11 thf(fact_4440_linorder__not__le,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_num @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_le
% 5.82/6.11 thf(fact_4441_linorder__not__le,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_nat @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_le
% 5.82/6.11 thf(fact_4442_linorder__not__le,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_int @ X2 @ Y3 ) )
% 5.82/6.11 = ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % linorder_not_le
% 5.82/6.11 thf(fact_4443_order__less__le,axiom,
% 5.82/6.11 ( ord_less_real
% 5.82/6.11 = ( ^ [X3: real,Y: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ X3 @ Y )
% 5.82/6.11 & ( X3 != Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le
% 5.82/6.11 thf(fact_4444_order__less__le,axiom,
% 5.82/6.11 ( ord_less_set_int
% 5.82/6.11 = ( ^ [X3: set_int,Y: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.82/6.11 & ( X3 != Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le
% 5.82/6.11 thf(fact_4445_order__less__le,axiom,
% 5.82/6.11 ( ord_less_rat
% 5.82/6.11 = ( ^ [X3: rat,Y: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.82/6.11 & ( X3 != Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le
% 5.82/6.11 thf(fact_4446_order__less__le,axiom,
% 5.82/6.11 ( ord_less_num
% 5.82/6.11 = ( ^ [X3: num,Y: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X3 @ Y )
% 5.82/6.11 & ( X3 != Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le
% 5.82/6.11 thf(fact_4447_order__less__le,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [X3: nat,Y: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.82/6.11 & ( X3 != Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le
% 5.82/6.11 thf(fact_4448_order__less__le,axiom,
% 5.82/6.11 ( ord_less_int
% 5.82/6.11 = ( ^ [X3: int,Y: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X3 @ Y )
% 5.82/6.11 & ( X3 != Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_less_le
% 5.82/6.11 thf(fact_4449_order__le__less,axiom,
% 5.82/6.11 ( ord_less_eq_real
% 5.82/6.11 = ( ^ [X3: real,Y: real] :
% 5.82/6.11 ( ( ord_less_real @ X3 @ Y )
% 5.82/6.11 | ( X3 = Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less
% 5.82/6.11 thf(fact_4450_order__le__less,axiom,
% 5.82/6.11 ( ord_less_eq_set_int
% 5.82/6.11 = ( ^ [X3: set_int,Y: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ X3 @ Y )
% 5.82/6.11 | ( X3 = Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less
% 5.82/6.11 thf(fact_4451_order__le__less,axiom,
% 5.82/6.11 ( ord_less_eq_rat
% 5.82/6.11 = ( ^ [X3: rat,Y: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X3 @ Y )
% 5.82/6.11 | ( X3 = Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less
% 5.82/6.11 thf(fact_4452_order__le__less,axiom,
% 5.82/6.11 ( ord_less_eq_num
% 5.82/6.11 = ( ^ [X3: num,Y: num] :
% 5.82/6.11 ( ( ord_less_num @ X3 @ Y )
% 5.82/6.11 | ( X3 = Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less
% 5.82/6.11 thf(fact_4453_order__le__less,axiom,
% 5.82/6.11 ( ord_less_eq_nat
% 5.82/6.11 = ( ^ [X3: nat,Y: nat] :
% 5.82/6.11 ( ( ord_less_nat @ X3 @ Y )
% 5.82/6.11 | ( X3 = Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less
% 5.82/6.11 thf(fact_4454_order__le__less,axiom,
% 5.82/6.11 ( ord_less_eq_int
% 5.82/6.11 = ( ^ [X3: int,Y: int] :
% 5.82/6.11 ( ( ord_less_int @ X3 @ Y )
% 5.82/6.11 | ( X3 = Y ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order_le_less
% 5.82/6.11 thf(fact_4455_dual__order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [B2: real,A2: real] :
% 5.82/6.11 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.11 => ( ord_less_eq_real @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_order
% 5.82/6.11 thf(fact_4456_dual__order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [B2: set_int,A2: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ B2 @ A2 )
% 5.82/6.11 => ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_order
% 5.82/6.11 thf(fact_4457_dual__order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.11 => ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_order
% 5.82/6.11 thf(fact_4458_dual__order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [B2: num,A2: num] :
% 5.82/6.11 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.11 => ( ord_less_eq_num @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_order
% 5.82/6.11 thf(fact_4459_dual__order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.11 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_order
% 5.82/6.11 thf(fact_4460_dual__order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [B2: int,A2: int] :
% 5.82/6.11 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.11 => ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_implies_order
% 5.82/6.11 thf(fact_4461_order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_real @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_order
% 5.82/6.11 thf(fact_4462_order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_order
% 5.82/6.11 thf(fact_4463_order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_order
% 5.82/6.11 thf(fact_4464_order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_num @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_order
% 5.82/6.11 thf(fact_4465_order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_order
% 5.82/6.11 thf(fact_4466_order_Ostrict__implies__order,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_implies_order
% 5.82/6.11 thf(fact_4467_dual__order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_real
% 5.82/6.11 = ( ^ [B6: real,A5: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ B6 @ A5 )
% 5.82/6.11 & ~ ( ord_less_eq_real @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_not
% 5.82/6.11 thf(fact_4468_dual__order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_set_int
% 5.82/6.11 = ( ^ [B6: set_int,A5: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ B6 @ A5 )
% 5.82/6.11 & ~ ( ord_less_eq_set_int @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_not
% 5.82/6.11 thf(fact_4469_dual__order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_rat
% 5.82/6.11 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ B6 @ A5 )
% 5.82/6.11 & ~ ( ord_less_eq_rat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_not
% 5.82/6.11 thf(fact_4470_dual__order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_num
% 5.82/6.11 = ( ^ [B6: num,A5: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ B6 @ A5 )
% 5.82/6.11 & ~ ( ord_less_eq_num @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_not
% 5.82/6.11 thf(fact_4471_dual__order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ B6 @ A5 )
% 5.82/6.11 & ~ ( ord_less_eq_nat @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_not
% 5.82/6.11 thf(fact_4472_dual__order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_int
% 5.82/6.11 = ( ^ [B6: int,A5: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ B6 @ A5 )
% 5.82/6.11 & ~ ( ord_less_eq_int @ A5 @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_not
% 5.82/6.11 thf(fact_4473_dual__order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [B2: real,A2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_real @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans2
% 5.82/6.11 thf(fact_4474_dual__order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [B2: set_int,A2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_set_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans2
% 5.82/6.11 thf(fact_4475_dual__order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans2
% 5.82/6.11 thf(fact_4476_dual__order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [B2: num,A2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_num @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_num @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans2
% 5.82/6.11 thf(fact_4477_dual__order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans2
% 5.82/6.11 thf(fact_4478_dual__order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [B2: int,A2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans2
% 5.82/6.11 thf(fact_4479_dual__order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [B2: real,A2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_real @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_real @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans1
% 5.82/6.11 thf(fact_4480_dual__order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [B2: set_int,A2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_set_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_set_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans1
% 5.82/6.11 thf(fact_4481_dual__order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [B2: rat,A2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_rat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_rat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans1
% 5.82/6.11 thf(fact_4482_dual__order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [B2: num,A2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_num @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_num @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans1
% 5.82/6.11 thf(fact_4483_dual__order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_nat @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_nat @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans1
% 5.82/6.11 thf(fact_4484_dual__order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [B2: int,A2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.11 => ( ( ord_less_int @ C2 @ B2 )
% 5.82/6.11 => ( ord_less_int @ C2 @ A2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_trans1
% 5.82/6.11 thf(fact_4485_dual__order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_real
% 5.82/6.11 = ( ^ [B6: real,A5: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ B6 @ A5 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_order
% 5.82/6.11 thf(fact_4486_dual__order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_set_int
% 5.82/6.11 = ( ^ [B6: set_int,A5: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ B6 @ A5 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_order
% 5.82/6.11 thf(fact_4487_dual__order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_rat
% 5.82/6.11 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ B6 @ A5 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_order
% 5.82/6.11 thf(fact_4488_dual__order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_num
% 5.82/6.11 = ( ^ [B6: num,A5: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ B6 @ A5 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_order
% 5.82/6.11 thf(fact_4489_dual__order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ B6 @ A5 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_order
% 5.82/6.11 thf(fact_4490_dual__order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_int
% 5.82/6.11 = ( ^ [B6: int,A5: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ B6 @ A5 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.strict_iff_order
% 5.82/6.11 thf(fact_4491_dual__order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_real
% 5.82/6.11 = ( ^ [B6: real,A5: real] :
% 5.82/6.11 ( ( ord_less_real @ B6 @ A5 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.order_iff_strict
% 5.82/6.11 thf(fact_4492_dual__order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_set_int
% 5.82/6.11 = ( ^ [B6: set_int,A5: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ B6 @ A5 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.order_iff_strict
% 5.82/6.11 thf(fact_4493_dual__order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_rat
% 5.82/6.11 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.11 ( ( ord_less_rat @ B6 @ A5 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.order_iff_strict
% 5.82/6.11 thf(fact_4494_dual__order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_num
% 5.82/6.11 = ( ^ [B6: num,A5: num] :
% 5.82/6.11 ( ( ord_less_num @ B6 @ A5 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.order_iff_strict
% 5.82/6.11 thf(fact_4495_dual__order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_nat
% 5.82/6.11 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.11 ( ( ord_less_nat @ B6 @ A5 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.order_iff_strict
% 5.82/6.11 thf(fact_4496_dual__order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_int
% 5.82/6.11 = ( ^ [B6: int,A5: int] :
% 5.82/6.11 ( ( ord_less_int @ B6 @ A5 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dual_order.order_iff_strict
% 5.82/6.11 thf(fact_4497_dense__le__bounded,axiom,
% 5.82/6.11 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ! [W3: real] :
% 5.82/6.11 ( ( ord_less_real @ X2 @ W3 )
% 5.82/6.11 => ( ( ord_less_real @ W3 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_real @ W3 @ Z ) ) )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_le_bounded
% 5.82/6.11 thf(fact_4498_dense__le__bounded,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ! [W3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X2 @ W3 )
% 5.82/6.11 => ( ( ord_less_rat @ W3 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_rat @ W3 @ Z ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_le_bounded
% 5.82/6.11 thf(fact_4499_dense__ge__bounded,axiom,
% 5.82/6.11 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_real @ Z @ X2 )
% 5.82/6.11 => ( ! [W3: real] :
% 5.82/6.11 ( ( ord_less_real @ Z @ W3 )
% 5.82/6.11 => ( ( ord_less_real @ W3 @ X2 )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ W3 ) ) )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_ge_bounded
% 5.82/6.11 thf(fact_4500_dense__ge__bounded,axiom,
% 5.82/6.11 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ Z @ X2 )
% 5.82/6.11 => ( ! [W3: rat] :
% 5.82/6.11 ( ( ord_less_rat @ Z @ W3 )
% 5.82/6.11 => ( ( ord_less_rat @ W3 @ X2 )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ W3 ) ) )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_ge_bounded
% 5.82/6.11 thf(fact_4501_order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_real
% 5.82/6.11 = ( ^ [A5: real,B6: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ A5 @ B6 )
% 5.82/6.11 & ~ ( ord_less_eq_real @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_not
% 5.82/6.11 thf(fact_4502_order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_set_int
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A5 @ B6 )
% 5.82/6.11 & ~ ( ord_less_eq_set_int @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_not
% 5.82/6.11 thf(fact_4503_order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_rat
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A5 @ B6 )
% 5.82/6.11 & ~ ( ord_less_eq_rat @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_not
% 5.82/6.11 thf(fact_4504_order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_num
% 5.82/6.11 = ( ^ [A5: num,B6: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A5 @ B6 )
% 5.82/6.11 & ~ ( ord_less_eq_num @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_not
% 5.82/6.11 thf(fact_4505_order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A5 @ B6 )
% 5.82/6.11 & ~ ( ord_less_eq_nat @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_not
% 5.82/6.11 thf(fact_4506_order_Ostrict__iff__not,axiom,
% 5.82/6.11 ( ord_less_int
% 5.82/6.11 = ( ^ [A5: int,B6: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A5 @ B6 )
% 5.82/6.11 & ~ ( ord_less_eq_int @ B6 @ A5 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_not
% 5.82/6.11 thf(fact_4507_order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [A2: real,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_real @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans2
% 5.82/6.11 thf(fact_4508_order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans2
% 5.82/6.11 thf(fact_4509_order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans2
% 5.82/6.11 thf(fact_4510_order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_num @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans2
% 5.82/6.11 thf(fact_4511_order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans2
% 5.82/6.11 thf(fact_4512_order_Ostrict__trans2,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_eq_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans2
% 5.82/6.11 thf(fact_4513_order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [A2: real,B2: real,C2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_real @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_real @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans1
% 5.82/6.11 thf(fact_4514_order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int,C2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_set_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans1
% 5.82/6.11 thf(fact_4515_order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_rat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans1
% 5.82/6.11 thf(fact_4516_order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [A2: num,B2: num,C2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_num @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_num @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans1
% 5.82/6.11 thf(fact_4517_order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans1
% 5.82/6.11 thf(fact_4518_order_Ostrict__trans1,axiom,
% 5.82/6.11 ! [A2: int,B2: int,C2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 => ( ( ord_less_int @ B2 @ C2 )
% 5.82/6.11 => ( ord_less_int @ A2 @ C2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_trans1
% 5.82/6.11 thf(fact_4519_order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_real
% 5.82/6.11 = ( ^ [A5: real,B6: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ A5 @ B6 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_order
% 5.82/6.11 thf(fact_4520_order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_set_int
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A5 @ B6 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_order
% 5.82/6.11 thf(fact_4521_order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_rat
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ A5 @ B6 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_order
% 5.82/6.11 thf(fact_4522_order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_num
% 5.82/6.11 = ( ^ [A5: num,B6: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ A5 @ B6 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_order
% 5.82/6.11 thf(fact_4523_order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A5 @ B6 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_order
% 5.82/6.11 thf(fact_4524_order_Ostrict__iff__order,axiom,
% 5.82/6.11 ( ord_less_int
% 5.82/6.11 = ( ^ [A5: int,B6: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ A5 @ B6 )
% 5.82/6.11 & ( A5 != B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.strict_iff_order
% 5.82/6.11 thf(fact_4525_order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_real
% 5.82/6.11 = ( ^ [A5: real,B6: real] :
% 5.82/6.11 ( ( ord_less_real @ A5 @ B6 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.order_iff_strict
% 5.82/6.11 thf(fact_4526_order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_set_int
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] :
% 5.82/6.11 ( ( ord_less_set_int @ A5 @ B6 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.order_iff_strict
% 5.82/6.11 thf(fact_4527_order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_rat
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] :
% 5.82/6.11 ( ( ord_less_rat @ A5 @ B6 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.order_iff_strict
% 5.82/6.11 thf(fact_4528_order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_num
% 5.82/6.11 = ( ^ [A5: num,B6: num] :
% 5.82/6.11 ( ( ord_less_num @ A5 @ B6 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.order_iff_strict
% 5.82/6.11 thf(fact_4529_order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.11 ( ( ord_less_nat @ A5 @ B6 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.order_iff_strict
% 5.82/6.11 thf(fact_4530_order_Oorder__iff__strict,axiom,
% 5.82/6.11 ( ord_less_eq_int
% 5.82/6.11 = ( ^ [A5: int,B6: int] :
% 5.82/6.11 ( ( ord_less_int @ A5 @ B6 )
% 5.82/6.11 | ( A5 = B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % order.order_iff_strict
% 5.82/6.11 thf(fact_4531_not__le__imp__less,axiom,
% 5.82/6.11 ! [Y3: real,X2: real] :
% 5.82/6.11 ( ~ ( ord_less_eq_real @ Y3 @ X2 )
% 5.82/6.11 => ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_le_imp_less
% 5.82/6.11 thf(fact_4532_not__le__imp__less,axiom,
% 5.82/6.11 ! [Y3: rat,X2: rat] :
% 5.82/6.11 ( ~ ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.11 => ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_le_imp_less
% 5.82/6.11 thf(fact_4533_not__le__imp__less,axiom,
% 5.82/6.11 ! [Y3: num,X2: num] :
% 5.82/6.11 ( ~ ( ord_less_eq_num @ Y3 @ X2 )
% 5.82/6.11 => ( ord_less_num @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_le_imp_less
% 5.82/6.11 thf(fact_4534_not__le__imp__less,axiom,
% 5.82/6.11 ! [Y3: nat,X2: nat] :
% 5.82/6.11 ( ~ ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.11 => ( ord_less_nat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_le_imp_less
% 5.82/6.11 thf(fact_4535_not__le__imp__less,axiom,
% 5.82/6.11 ! [Y3: int,X2: int] :
% 5.82/6.11 ( ~ ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.11 => ( ord_less_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % not_le_imp_less
% 5.82/6.11 thf(fact_4536_less__le__not__le,axiom,
% 5.82/6.11 ( ord_less_real
% 5.82/6.11 = ( ^ [X3: real,Y: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ X3 @ Y )
% 5.82/6.11 & ~ ( ord_less_eq_real @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_le_not_le
% 5.82/6.11 thf(fact_4537_less__le__not__le,axiom,
% 5.82/6.11 ( ord_less_set_int
% 5.82/6.11 = ( ^ [X3: set_int,Y: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X3 @ Y )
% 5.82/6.11 & ~ ( ord_less_eq_set_int @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_le_not_le
% 5.82/6.11 thf(fact_4538_less__le__not__le,axiom,
% 5.82/6.11 ( ord_less_rat
% 5.82/6.11 = ( ^ [X3: rat,Y: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X3 @ Y )
% 5.82/6.11 & ~ ( ord_less_eq_rat @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_le_not_le
% 5.82/6.11 thf(fact_4539_less__le__not__le,axiom,
% 5.82/6.11 ( ord_less_num
% 5.82/6.11 = ( ^ [X3: num,Y: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X3 @ Y )
% 5.82/6.11 & ~ ( ord_less_eq_num @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_le_not_le
% 5.82/6.11 thf(fact_4540_less__le__not__le,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [X3: nat,Y: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X3 @ Y )
% 5.82/6.11 & ~ ( ord_less_eq_nat @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_le_not_le
% 5.82/6.11 thf(fact_4541_less__le__not__le,axiom,
% 5.82/6.11 ( ord_less_int
% 5.82/6.11 = ( ^ [X3: int,Y: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X3 @ Y )
% 5.82/6.11 & ~ ( ord_less_eq_int @ Y @ X3 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_le_not_le
% 5.82/6.11 thf(fact_4542_dense__le,axiom,
% 5.82/6.11 ! [Y3: real,Z: real] :
% 5.82/6.11 ( ! [X4: real] :
% 5.82/6.11 ( ( ord_less_real @ X4 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_real @ X4 @ Z ) )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_le
% 5.82/6.11 thf(fact_4543_dense__le,axiom,
% 5.82/6.11 ! [Y3: rat,Z: rat] :
% 5.82/6.11 ( ! [X4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ X4 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_rat @ X4 @ Z ) )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_le
% 5.82/6.11 thf(fact_4544_dense__ge,axiom,
% 5.82/6.11 ! [Z: real,Y3: real] :
% 5.82/6.11 ( ! [X4: real] :
% 5.82/6.11 ( ( ord_less_real @ Z @ X4 )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ X4 ) )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_ge
% 5.82/6.11 thf(fact_4545_dense__ge,axiom,
% 5.82/6.11 ! [Z: rat,Y3: rat] :
% 5.82/6.11 ( ! [X4: rat] :
% 5.82/6.11 ( ( ord_less_rat @ Z @ X4 )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ X4 ) )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % dense_ge
% 5.82/6.11 thf(fact_4546_antisym__conv2,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv2
% 5.82/6.11 thf(fact_4547_antisym__conv2,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ~ ( ord_less_set_int @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv2
% 5.82/6.11 thf(fact_4548_antisym__conv2,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv2
% 5.82/6.11 thf(fact_4549_antisym__conv2,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv2
% 5.82/6.11 thf(fact_4550_antisym__conv2,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv2
% 5.82/6.11 thf(fact_4551_antisym__conv2,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv2
% 5.82/6.11 thf(fact_4552_antisym__conv1,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv1
% 5.82/6.11 thf(fact_4553_antisym__conv1,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ~ ( ord_less_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv1
% 5.82/6.11 thf(fact_4554_antisym__conv1,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv1
% 5.82/6.11 thf(fact_4555_antisym__conv1,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv1
% 5.82/6.11 thf(fact_4556_antisym__conv1,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv1
% 5.82/6.11 thf(fact_4557_antisym__conv1,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 = ( X2 = Y3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % antisym_conv1
% 5.82/6.11 thf(fact_4558_nless__le,axiom,
% 5.82/6.11 ! [A2: real,B2: real] :
% 5.82/6.11 ( ( ~ ( ord_less_real @ A2 @ B2 ) )
% 5.82/6.11 = ( ~ ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.11 | ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nless_le
% 5.82/6.11 thf(fact_4559_nless__le,axiom,
% 5.82/6.11 ! [A2: set_int,B2: set_int] :
% 5.82/6.11 ( ( ~ ( ord_less_set_int @ A2 @ B2 ) )
% 5.82/6.11 = ( ~ ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.11 | ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nless_le
% 5.82/6.11 thf(fact_4560_nless__le,axiom,
% 5.82/6.11 ! [A2: rat,B2: rat] :
% 5.82/6.11 ( ( ~ ( ord_less_rat @ A2 @ B2 ) )
% 5.82/6.11 = ( ~ ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.11 | ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nless_le
% 5.82/6.11 thf(fact_4561_nless__le,axiom,
% 5.82/6.11 ! [A2: num,B2: num] :
% 5.82/6.11 ( ( ~ ( ord_less_num @ A2 @ B2 ) )
% 5.82/6.11 = ( ~ ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.11 | ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nless_le
% 5.82/6.11 thf(fact_4562_nless__le,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( ~ ( ord_less_nat @ A2 @ B2 ) )
% 5.82/6.11 = ( ~ ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.11 | ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nless_le
% 5.82/6.11 thf(fact_4563_nless__le,axiom,
% 5.82/6.11 ! [A2: int,B2: int] :
% 5.82/6.11 ( ( ~ ( ord_less_int @ A2 @ B2 ) )
% 5.82/6.11 = ( ~ ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.11 | ( A2 = B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nless_le
% 5.82/6.11 thf(fact_4564_leI,axiom,
% 5.82/6.11 ! [X2: real,Y3: real] :
% 5.82/6.11 ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_real @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leI
% 5.82/6.11 thf(fact_4565_leI,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leI
% 5.82/6.11 thf(fact_4566_leI,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leI
% 5.82/6.11 thf(fact_4567_leI,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leI
% 5.82/6.11 thf(fact_4568_leI,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.82/6.11 => ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leI
% 5.82/6.11 thf(fact_4569_leD,axiom,
% 5.82/6.11 ! [Y3: real,X2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leD
% 5.82/6.11 thf(fact_4570_leD,axiom,
% 5.82/6.11 ! [Y3: set_int,X2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_set_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leD
% 5.82/6.11 thf(fact_4571_leD,axiom,
% 5.82/6.11 ! [Y3: rat,X2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leD
% 5.82/6.11 thf(fact_4572_leD,axiom,
% 5.82/6.11 ! [Y3: num,X2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_num @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leD
% 5.82/6.11 thf(fact_4573_leD,axiom,
% 5.82/6.11 ! [Y3: nat,X2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_nat @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leD
% 5.82/6.11 thf(fact_4574_leD,axiom,
% 5.82/6.11 ! [Y3: int,X2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.11 => ~ ( ord_less_int @ X2 @ Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % leD
% 5.82/6.11 thf(fact_4575_verit__comp__simplify1_I3_J,axiom,
% 5.82/6.11 ! [B4: real,A4: real] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 5.82/6.11 = ( ord_less_real @ A4 @ B4 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(3)
% 5.82/6.11 thf(fact_4576_verit__comp__simplify1_I3_J,axiom,
% 5.82/6.11 ! [B4: rat,A4: rat] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 5.82/6.11 = ( ord_less_rat @ A4 @ B4 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(3)
% 5.82/6.11 thf(fact_4577_verit__comp__simplify1_I3_J,axiom,
% 5.82/6.11 ! [B4: num,A4: num] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 5.82/6.11 = ( ord_less_num @ A4 @ B4 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(3)
% 5.82/6.11 thf(fact_4578_verit__comp__simplify1_I3_J,axiom,
% 5.82/6.11 ! [B4: nat,A4: nat] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 5.82/6.11 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(3)
% 5.82/6.11 thf(fact_4579_verit__comp__simplify1_I3_J,axiom,
% 5.82/6.11 ! [B4: int,A4: int] :
% 5.82/6.11 ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 5.82/6.11 = ( ord_less_int @ A4 @ B4 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_comp_simplify1(3)
% 5.82/6.11 thf(fact_4580_verit__sum__simplify,axiom,
% 5.82/6.11 ! [A2: complex] :
% 5.82/6.11 ( ( plus_plus_complex @ A2 @ zero_zero_complex )
% 5.82/6.11 = A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_sum_simplify
% 5.82/6.11 thf(fact_4581_verit__sum__simplify,axiom,
% 5.82/6.11 ! [A2: real] :
% 5.82/6.11 ( ( plus_plus_real @ A2 @ zero_zero_real )
% 5.82/6.11 = A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_sum_simplify
% 5.82/6.11 thf(fact_4582_verit__sum__simplify,axiom,
% 5.82/6.11 ! [A2: rat] :
% 5.82/6.11 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 5.82/6.11 = A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_sum_simplify
% 5.82/6.11 thf(fact_4583_verit__sum__simplify,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 5.82/6.11 = A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_sum_simplify
% 5.82/6.11 thf(fact_4584_verit__sum__simplify,axiom,
% 5.82/6.11 ! [A2: int] :
% 5.82/6.11 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 5.82/6.11 = A2 ) ).
% 5.82/6.11
% 5.82/6.11 % verit_sum_simplify
% 5.82/6.11 thf(fact_4585_verit__eq__simplify_I10_J,axiom,
% 5.82/6.11 ! [X22: num] :
% 5.82/6.11 ( one
% 5.82/6.11 != ( bit0 @ X22 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_eq_simplify(10)
% 5.82/6.11 thf(fact_4586_bot_Oextremum,axiom,
% 5.82/6.11 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum
% 5.82/6.11 thf(fact_4587_bot_Oextremum,axiom,
% 5.82/6.11 ! [A2: assn] : ( ord_less_eq_assn @ bot_bot_assn @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum
% 5.82/6.11 thf(fact_4588_bot_Oextremum,axiom,
% 5.82/6.11 ! [A2: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum
% 5.82/6.11 thf(fact_4589_bot_Oextremum,axiom,
% 5.82/6.11 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum
% 5.82/6.11 thf(fact_4590_bot_Oextremum,axiom,
% 5.82/6.11 ! [A2: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A2 ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum
% 5.82/6.11 thf(fact_4591_bot_Oextremum__unique,axiom,
% 5.82/6.11 ! [A2: set_nat] :
% 5.82/6.11 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.82/6.11 = ( A2 = bot_bot_set_nat ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_unique
% 5.82/6.11 thf(fact_4592_bot_Oextremum__unique,axiom,
% 5.82/6.11 ! [A2: assn] :
% 5.82/6.11 ( ( ord_less_eq_assn @ A2 @ bot_bot_assn )
% 5.82/6.11 = ( A2 = bot_bot_assn ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_unique
% 5.82/6.11 thf(fact_4593_bot_Oextremum__unique,axiom,
% 5.82/6.11 ! [A2: extended_enat] :
% 5.82/6.11 ( ( ord_le2932123472753598470d_enat @ A2 @ bot_bo4199563552545308370d_enat )
% 5.82/6.11 = ( A2 = bot_bo4199563552545308370d_enat ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_unique
% 5.82/6.11 thf(fact_4594_bot_Oextremum__unique,axiom,
% 5.82/6.11 ! [A2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.82/6.11 = ( A2 = bot_bot_set_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_unique
% 5.82/6.11 thf(fact_4595_bot_Oextremum__unique,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 5.82/6.11 = ( A2 = bot_bot_nat ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_unique
% 5.82/6.11 thf(fact_4596_bot_Oextremum__uniqueI,axiom,
% 5.82/6.11 ! [A2: set_nat] :
% 5.82/6.11 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.82/6.11 => ( A2 = bot_bot_set_nat ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_uniqueI
% 5.82/6.11 thf(fact_4597_bot_Oextremum__uniqueI,axiom,
% 5.82/6.11 ! [A2: assn] :
% 5.82/6.11 ( ( ord_less_eq_assn @ A2 @ bot_bot_assn )
% 5.82/6.11 => ( A2 = bot_bot_assn ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_uniqueI
% 5.82/6.11 thf(fact_4598_bot_Oextremum__uniqueI,axiom,
% 5.82/6.11 ! [A2: extended_enat] :
% 5.82/6.11 ( ( ord_le2932123472753598470d_enat @ A2 @ bot_bo4199563552545308370d_enat )
% 5.82/6.11 => ( A2 = bot_bo4199563552545308370d_enat ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_uniqueI
% 5.82/6.11 thf(fact_4599_bot_Oextremum__uniqueI,axiom,
% 5.82/6.11 ! [A2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.82/6.11 => ( A2 = bot_bot_set_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_uniqueI
% 5.82/6.11 thf(fact_4600_bot_Oextremum__uniqueI,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 5.82/6.11 => ( A2 = bot_bot_nat ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_uniqueI
% 5.82/6.11 thf(fact_4601_bot_Onot__eq__extremum,axiom,
% 5.82/6.11 ! [A2: set_nat] :
% 5.82/6.11 ( ( A2 != bot_bot_set_nat )
% 5.82/6.11 = ( ord_less_set_nat @ bot_bot_set_nat @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.not_eq_extremum
% 5.82/6.11 thf(fact_4602_bot_Onot__eq__extremum,axiom,
% 5.82/6.11 ! [A2: assn] :
% 5.82/6.11 ( ( A2 != bot_bot_assn )
% 5.82/6.11 = ( ord_less_assn @ bot_bot_assn @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.not_eq_extremum
% 5.82/6.11 thf(fact_4603_bot_Onot__eq__extremum,axiom,
% 5.82/6.11 ! [A2: extended_enat] :
% 5.82/6.11 ( ( A2 != bot_bo4199563552545308370d_enat )
% 5.82/6.11 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.not_eq_extremum
% 5.82/6.11 thf(fact_4604_bot_Onot__eq__extremum,axiom,
% 5.82/6.11 ! [A2: set_int] :
% 5.82/6.11 ( ( A2 != bot_bot_set_int )
% 5.82/6.11 = ( ord_less_set_int @ bot_bot_set_int @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.not_eq_extremum
% 5.82/6.11 thf(fact_4605_bot_Onot__eq__extremum,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ( ( A2 != bot_bot_nat )
% 5.82/6.11 = ( ord_less_nat @ bot_bot_nat @ A2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % bot.not_eq_extremum
% 5.82/6.11 thf(fact_4606_bot_Oextremum__strict,axiom,
% 5.82/6.11 ! [A2: set_nat] :
% 5.82/6.11 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_strict
% 5.82/6.11 thf(fact_4607_bot_Oextremum__strict,axiom,
% 5.82/6.11 ! [A2: assn] :
% 5.82/6.11 ~ ( ord_less_assn @ A2 @ bot_bot_assn ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_strict
% 5.82/6.11 thf(fact_4608_bot_Oextremum__strict,axiom,
% 5.82/6.11 ! [A2: extended_enat] :
% 5.82/6.11 ~ ( ord_le72135733267957522d_enat @ A2 @ bot_bo4199563552545308370d_enat ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_strict
% 5.82/6.11 thf(fact_4609_bot_Oextremum__strict,axiom,
% 5.82/6.11 ! [A2: set_int] :
% 5.82/6.11 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_strict
% 5.82/6.11 thf(fact_4610_bot_Oextremum__strict,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ~ ( ord_less_nat @ A2 @ bot_bot_nat ) ).
% 5.82/6.11
% 5.82/6.11 % bot.extremum_strict
% 5.82/6.11 thf(fact_4611_verit__eq__simplify_I14_J,axiom,
% 5.82/6.11 ! [X22: num,X33: num] :
% 5.82/6.11 ( ( bit0 @ X22 )
% 5.82/6.11 != ( bit1 @ X33 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_eq_simplify(14)
% 5.82/6.11 thf(fact_4612_verit__eq__simplify_I12_J,axiom,
% 5.82/6.11 ! [X33: num] :
% 5.82/6.11 ( one
% 5.82/6.11 != ( bit1 @ X33 ) ) ).
% 5.82/6.11
% 5.82/6.11 % verit_eq_simplify(12)
% 5.82/6.11 thf(fact_4613_max__def,axiom,
% 5.82/6.11 ( ord_ma741700101516333627d_enat
% 5.82/6.11 = ( ^ [A5: extended_enat,B6: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def
% 5.82/6.11 thf(fact_4614_max__def,axiom,
% 5.82/6.11 ( ord_max_set_int
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def
% 5.82/6.11 thf(fact_4615_max__def,axiom,
% 5.82/6.11 ( ord_max_rat
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def
% 5.82/6.11 thf(fact_4616_max__def,axiom,
% 5.82/6.11 ( ord_max_num
% 5.82/6.11 = ( ^ [A5: num,B6: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def
% 5.82/6.11 thf(fact_4617_max__def,axiom,
% 5.82/6.11 ( ord_max_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def
% 5.82/6.11 thf(fact_4618_max__def,axiom,
% 5.82/6.11 ( ord_max_int
% 5.82/6.11 = ( ^ [A5: int,B6: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def
% 5.82/6.11 thf(fact_4619_max__absorb1,axiom,
% 5.82/6.11 ! [Y3: extended_enat,X2: extended_enat] :
% 5.82/6.11 ( ( ord_le2932123472753598470d_enat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_ma741700101516333627d_enat @ X2 @ Y3 )
% 5.82/6.11 = X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb1
% 5.82/6.11 thf(fact_4620_max__absorb1,axiom,
% 5.82/6.11 ! [Y3: set_int,X2: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_max_set_int @ X2 @ Y3 )
% 5.82/6.11 = X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb1
% 5.82/6.11 thf(fact_4621_max__absorb1,axiom,
% 5.82/6.11 ! [Y3: rat,X2: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_max_rat @ X2 @ Y3 )
% 5.82/6.11 = X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb1
% 5.82/6.11 thf(fact_4622_max__absorb1,axiom,
% 5.82/6.11 ! [Y3: num,X2: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_max_num @ X2 @ Y3 )
% 5.82/6.11 = X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb1
% 5.82/6.11 thf(fact_4623_max__absorb1,axiom,
% 5.82/6.11 ! [Y3: nat,X2: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_max_nat @ X2 @ Y3 )
% 5.82/6.11 = X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb1
% 5.82/6.11 thf(fact_4624_max__absorb1,axiom,
% 5.82/6.11 ! [Y3: int,X2: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.11 => ( ( ord_max_int @ X2 @ Y3 )
% 5.82/6.11 = X2 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb1
% 5.82/6.11 thf(fact_4625_max__absorb2,axiom,
% 5.82/6.11 ! [X2: extended_enat,Y3: extended_enat] :
% 5.82/6.11 ( ( ord_le2932123472753598470d_enat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_ma741700101516333627d_enat @ X2 @ Y3 )
% 5.82/6.11 = Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb2
% 5.82/6.11 thf(fact_4626_max__absorb2,axiom,
% 5.82/6.11 ! [X2: set_int,Y3: set_int] :
% 5.82/6.11 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_max_set_int @ X2 @ Y3 )
% 5.82/6.11 = Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb2
% 5.82/6.11 thf(fact_4627_max__absorb2,axiom,
% 5.82/6.11 ! [X2: rat,Y3: rat] :
% 5.82/6.11 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_max_rat @ X2 @ Y3 )
% 5.82/6.11 = Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb2
% 5.82/6.11 thf(fact_4628_max__absorb2,axiom,
% 5.82/6.11 ! [X2: num,Y3: num] :
% 5.82/6.11 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_max_num @ X2 @ Y3 )
% 5.82/6.11 = Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb2
% 5.82/6.11 thf(fact_4629_max__absorb2,axiom,
% 5.82/6.11 ! [X2: nat,Y3: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_max_nat @ X2 @ Y3 )
% 5.82/6.11 = Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb2
% 5.82/6.11 thf(fact_4630_max__absorb2,axiom,
% 5.82/6.11 ! [X2: int,Y3: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.11 => ( ( ord_max_int @ X2 @ Y3 )
% 5.82/6.11 = Y3 ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_absorb2
% 5.82/6.11 thf(fact_4631_TBOUND__mono,axiom,
% 5.82/6.11 ! [C2: heap_T8145700208782473153_VEBTi,T: nat,T3: nat] :
% 5.82/6.11 ( ( time_T5737551269749752165_VEBTi @ C2 @ T )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T @ T3 )
% 5.82/6.11 => ( time_T5737551269749752165_VEBTi @ C2 @ T3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_mono
% 5.82/6.11 thf(fact_4632_TBOUND__mono,axiom,
% 5.82/6.11 ! [C2: heap_Time_Heap_o,T: nat,T3: nat] :
% 5.82/6.11 ( ( time_TBOUND_o @ C2 @ T )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T @ T3 )
% 5.82/6.11 => ( time_TBOUND_o @ C2 @ T3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_mono
% 5.82/6.11 thf(fact_4633_TBOUND__mono,axiom,
% 5.82/6.11 ! [C2: heap_T2636463487746394924on_nat,T: nat,T3: nat] :
% 5.82/6.11 ( ( time_T8353473612707095248on_nat @ C2 @ T )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T @ T3 )
% 5.82/6.11 => ( time_T8353473612707095248on_nat @ C2 @ T3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_mono
% 5.82/6.11 thf(fact_4634_TBOUND__mono,axiom,
% 5.82/6.11 ! [C2: heap_Time_Heap_nat,T: nat,T3: nat] :
% 5.82/6.11 ( ( time_TBOUND_nat @ C2 @ T )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T @ T3 )
% 5.82/6.11 => ( time_TBOUND_nat @ C2 @ T3 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_mono
% 5.82/6.11 thf(fact_4635_TBOUND__if__max,axiom,
% 5.82/6.11 ! [P: $o,M: heap_T8145700208782473153_VEBTi,Bm: nat,N: heap_T8145700208782473153_VEBTi,Bn: nat] :
% 5.82/6.11 ( ( P
% 5.82/6.11 => ( time_T5737551269749752165_VEBTi @ M @ Bm ) )
% 5.82/6.11 => ( ( ~ P
% 5.82/6.11 => ( time_T5737551269749752165_VEBTi @ N @ Bn ) )
% 5.82/6.11 => ( time_T5737551269749752165_VEBTi @ ( if_Hea8453224502484754311_VEBTi @ P @ M @ N ) @ ( ord_max_nat @ Bm @ Bn ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_if_max
% 5.82/6.11 thf(fact_4636_TBOUND__if__max,axiom,
% 5.82/6.11 ! [P: $o,M: heap_Time_Heap_o,Bm: nat,N: heap_Time_Heap_o,Bn: nat] :
% 5.82/6.11 ( ( P
% 5.82/6.11 => ( time_TBOUND_o @ M @ Bm ) )
% 5.82/6.11 => ( ( ~ P
% 5.82/6.11 => ( time_TBOUND_o @ N @ Bn ) )
% 5.82/6.11 => ( time_TBOUND_o @ ( if_Heap_Time_Heap_o @ P @ M @ N ) @ ( ord_max_nat @ Bm @ Bn ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_if_max
% 5.82/6.11 thf(fact_4637_TBOUND__if__max,axiom,
% 5.82/6.11 ! [P: $o,M: heap_T2636463487746394924on_nat,Bm: nat,N: heap_T2636463487746394924on_nat,Bn: nat] :
% 5.82/6.11 ( ( P
% 5.82/6.11 => ( time_T8353473612707095248on_nat @ M @ Bm ) )
% 5.82/6.11 => ( ( ~ P
% 5.82/6.11 => ( time_T8353473612707095248on_nat @ N @ Bn ) )
% 5.82/6.11 => ( time_T8353473612707095248on_nat @ ( if_Hea5867803462524415986on_nat @ P @ M @ N ) @ ( ord_max_nat @ Bm @ Bn ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_if_max
% 5.82/6.11 thf(fact_4638_TBOUND__if__max,axiom,
% 5.82/6.11 ! [P: $o,M: heap_Time_Heap_nat,Bm: nat,N: heap_Time_Heap_nat,Bn: nat] :
% 5.82/6.11 ( ( P
% 5.82/6.11 => ( time_TBOUND_nat @ M @ Bm ) )
% 5.82/6.11 => ( ( ~ P
% 5.82/6.11 => ( time_TBOUND_nat @ N @ Bn ) )
% 5.82/6.11 => ( time_TBOUND_nat @ ( if_Hea2662716070787841314ap_nat @ P @ M @ N ) @ ( ord_max_nat @ Bm @ Bn ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_if_max
% 5.82/6.11 thf(fact_4639_max__def__raw,axiom,
% 5.82/6.11 ( ord_ma741700101516333627d_enat
% 5.82/6.11 = ( ^ [A5: extended_enat,B6: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def_raw
% 5.82/6.11 thf(fact_4640_max__def__raw,axiom,
% 5.82/6.11 ( ord_max_set_int
% 5.82/6.11 = ( ^ [A5: set_int,B6: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def_raw
% 5.82/6.11 thf(fact_4641_max__def__raw,axiom,
% 5.82/6.11 ( ord_max_rat
% 5.82/6.11 = ( ^ [A5: rat,B6: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def_raw
% 5.82/6.11 thf(fact_4642_max__def__raw,axiom,
% 5.82/6.11 ( ord_max_num
% 5.82/6.11 = ( ^ [A5: num,B6: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def_raw
% 5.82/6.11 thf(fact_4643_max__def__raw,axiom,
% 5.82/6.11 ( ord_max_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def_raw
% 5.82/6.11 thf(fact_4644_max__def__raw,axiom,
% 5.82/6.11 ( ord_max_int
% 5.82/6.11 = ( ^ [A5: int,B6: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B6 ) @ B6 @ A5 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % max_def_raw
% 5.82/6.11 thf(fact_4645_int__ops_I3_J,axiom,
% 5.82/6.11 ! [N: num] :
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.82/6.11 = ( numeral_numeral_int @ N ) ) ).
% 5.82/6.11
% 5.82/6.11 % int_ops(3)
% 5.82/6.11 thf(fact_4646_nat__int__comparison_I2_J,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nat_int_comparison(2)
% 5.82/6.11 thf(fact_4647_nat__int__comparison_I3_J,axiom,
% 5.82/6.11 ( ord_less_eq_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nat_int_comparison(3)
% 5.82/6.11 thf(fact_4648_int__ops_I2_J,axiom,
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.82/6.11 = one_one_int ) ).
% 5.82/6.11
% 5.82/6.11 % int_ops(2)
% 5.82/6.11 thf(fact_4649_int__plus,axiom,
% 5.82/6.11 ! [N: nat,M: nat] :
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.82/6.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % int_plus
% 5.82/6.11 thf(fact_4650_int__ops_I5_J,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % int_ops(5)
% 5.82/6.11 thf(fact_4651_int__ops_I7_J,axiom,
% 5.82/6.11 ! [A2: nat,B2: nat] :
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A2 @ B2 ) )
% 5.82/6.11 = ( times_times_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % int_ops(7)
% 5.82/6.11 thf(fact_4652_TBOUNDD,axiom,
% 5.82/6.11 ! [M: heap_T8145700208782473153_VEBTi,T: nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.11 ( ( time_T5737551269749752165_VEBTi @ M @ T )
% 5.82/6.11 => ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ M @ H2 ) @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDD
% 5.82/6.11 thf(fact_4653_TBOUNDD,axiom,
% 5.82/6.11 ! [M: heap_Time_Heap_o,T: nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.11 ( ( time_TBOUND_o @ M @ T )
% 5.82/6.11 => ( ord_less_eq_nat @ ( time_time_o @ M @ H2 ) @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDD
% 5.82/6.11 thf(fact_4654_TBOUNDD,axiom,
% 5.82/6.11 ! [M: heap_T2636463487746394924on_nat,T: nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.11 ( ( time_T8353473612707095248on_nat @ M @ T )
% 5.82/6.11 => ( ord_less_eq_nat @ ( time_time_option_nat @ M @ H2 ) @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDD
% 5.82/6.11 thf(fact_4655_TBOUNDD,axiom,
% 5.82/6.11 ! [M: heap_Time_Heap_nat,T: nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.11 ( ( time_TBOUND_nat @ M @ T )
% 5.82/6.11 => ( ord_less_eq_nat @ ( time_time_nat @ M @ H2 ) @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDD
% 5.82/6.11 thf(fact_4656_TBOUNDI,axiom,
% 5.82/6.11 ! [M: heap_T8145700208782473153_VEBTi,T: nat] :
% 5.82/6.11 ( ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ M @ H3 ) @ T )
% 5.82/6.11 => ( time_T5737551269749752165_VEBTi @ M @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDI
% 5.82/6.11 thf(fact_4657_TBOUNDI,axiom,
% 5.82/6.11 ! [M: heap_Time_Heap_o,T: nat] :
% 5.82/6.11 ( ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_o @ M @ H3 ) @ T )
% 5.82/6.11 => ( time_TBOUND_o @ M @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDI
% 5.82/6.11 thf(fact_4658_TBOUNDI,axiom,
% 5.82/6.11 ! [M: heap_T2636463487746394924on_nat,T: nat] :
% 5.82/6.11 ( ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_option_nat @ M @ H3 ) @ T )
% 5.82/6.11 => ( time_T8353473612707095248on_nat @ M @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDI
% 5.82/6.11 thf(fact_4659_TBOUNDI,axiom,
% 5.82/6.11 ! [M: heap_Time_Heap_nat,T: nat] :
% 5.82/6.11 ( ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_nat @ M @ H3 ) @ T )
% 5.82/6.11 => ( time_TBOUND_nat @ M @ T ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUNDI
% 5.82/6.11 thf(fact_4660_TBOUND__def,axiom,
% 5.82/6.11 ( time_T5737551269749752165_VEBTi
% 5.82/6.11 = ( ^ [M6: heap_T8145700208782473153_VEBTi,T2: nat] :
% 5.82/6.11 ! [H: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ M6 @ H ) @ T2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_def
% 5.82/6.11 thf(fact_4661_TBOUND__def,axiom,
% 5.82/6.11 ( time_TBOUND_o
% 5.82/6.11 = ( ^ [M6: heap_Time_Heap_o,T2: nat] :
% 5.82/6.11 ! [H: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_o @ M6 @ H ) @ T2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_def
% 5.82/6.11 thf(fact_4662_TBOUND__def,axiom,
% 5.82/6.11 ( time_T8353473612707095248on_nat
% 5.82/6.11 = ( ^ [M6: heap_T2636463487746394924on_nat,T2: nat] :
% 5.82/6.11 ! [H: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_option_nat @ M6 @ H ) @ T2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_def
% 5.82/6.11 thf(fact_4663_TBOUND__def,axiom,
% 5.82/6.11 ( time_TBOUND_nat
% 5.82/6.11 = ( ^ [M6: heap_Time_Heap_nat,T2: nat] :
% 5.82/6.11 ! [H: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_nat @ M6 @ H ) @ T2 ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % TBOUND_def
% 5.82/6.11 thf(fact_4664_ceiling__log__nat__eq__if,axiom,
% 5.82/6.11 ! [B2: nat,N: nat,K: nat] :
% 5.82/6.11 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.82/6.11 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.11 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.82/6.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ceiling_log_nat_eq_if
% 5.82/6.11 thf(fact_4665_ceiling__log2__div2,axiom,
% 5.82/6.11 ! [N: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.11 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.82/6.11 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ceiling_log2_div2
% 5.82/6.11 thf(fact_4666_norm__pre__pure__iff__htt_H,axiom,
% 5.82/6.11 ! [B2: $o,P: assn,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_VEBT_VEBTi @ ( times_times_assn @ ( pure_assn @ B2 ) @ P ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_VEBT_VEBTi @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt'
% 5.82/6.11 thf(fact_4667_norm__pre__pure__iff__htt_H,axiom,
% 5.82/6.11 ! [B2: $o,P: assn,F: heap_Time_Heap_o,Q: $o > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_o @ ( times_times_assn @ ( pure_assn @ B2 ) @ P ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_o @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt'
% 5.82/6.11 thf(fact_4668_norm__pre__pure__iff__htt_H,axiom,
% 5.82/6.11 ! [B2: $o,P: assn,F: heap_T2636463487746394924on_nat,Q: option_nat > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_option_nat @ ( times_times_assn @ ( pure_assn @ B2 ) @ P ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_option_nat @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt'
% 5.82/6.11 thf(fact_4669_norm__pre__pure__iff__htt_H,axiom,
% 5.82/6.11 ! [B2: $o,P: assn,F: heap_Time_Heap_nat,Q: nat > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_nat @ ( times_times_assn @ ( pure_assn @ B2 ) @ P ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_nat @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt'
% 5.82/6.11 thf(fact_4670_norm__pre__pure__iff__htt,axiom,
% 5.82/6.11 ! [P: assn,B2: $o,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_VEBT_VEBTi @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_VEBT_VEBTi @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt
% 5.82/6.11 thf(fact_4671_norm__pre__pure__iff__htt,axiom,
% 5.82/6.11 ! [P: assn,B2: $o,F: heap_Time_Heap_o,Q: $o > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_o @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_o @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt
% 5.82/6.11 thf(fact_4672_norm__pre__pure__iff__htt,axiom,
% 5.82/6.11 ! [P: assn,B2: $o,F: heap_T2636463487746394924on_nat,Q: option_nat > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_option_nat @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_option_nat @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt
% 5.82/6.11 thf(fact_4673_norm__pre__pure__iff__htt,axiom,
% 5.82/6.11 ! [P: assn,B2: $o,F: heap_Time_Heap_nat,Q: nat > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_nat @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ F @ Q @ T )
% 5.82/6.11 = ( B2
% 5.82/6.11 => ( time_htt_nat @ P @ F @ Q @ T ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % norm_pre_pure_iff_htt
% 5.82/6.11 thf(fact_4674_nat__less__as__int,axiom,
% 5.82/6.11 ( ord_less_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nat_less_as_int
% 5.82/6.11 thf(fact_4675_nat__leq__as__int,axiom,
% 5.82/6.11 ( ord_less_eq_nat
% 5.82/6.11 = ( ^ [A5: nat,B6: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % nat_leq_as_int
% 5.82/6.11 thf(fact_4676_ceiling__log__nat__eq__powr__iff,axiom,
% 5.82/6.11 ! [B2: nat,K: nat,N: nat] :
% 5.82/6.11 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.11 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.11 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.82/6.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.82/6.11 = ( ( ord_less_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.82/6.11 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % ceiling_log_nat_eq_powr_iff
% 5.82/6.11 thf(fact_4677_htt__cons__rule,axiom,
% 5.82/6.11 ! [P5: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,T3: nat,P: assn,Q: vEBT_VEBTi > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_VEBT_VEBTi @ P5 @ C2 @ Q2 @ T3 )
% 5.82/6.11 => ( ( entails @ P @ P5 )
% 5.82/6.11 => ( ! [X4: vEBT_VEBTi] : ( entails @ ( Q2 @ X4 ) @ ( Q @ X4 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T3 @ T )
% 5.82/6.11 => ( time_htt_VEBT_VEBTi @ P @ C2 @ Q @ T ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_cons_rule
% 5.82/6.11 thf(fact_4678_htt__cons__rule,axiom,
% 5.82/6.11 ! [P5: assn,C2: heap_Time_Heap_o,Q2: $o > assn,T3: nat,P: assn,Q: $o > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_o @ P5 @ C2 @ Q2 @ T3 )
% 5.82/6.11 => ( ( entails @ P @ P5 )
% 5.82/6.11 => ( ! [X4: $o] : ( entails @ ( Q2 @ X4 ) @ ( Q @ X4 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T3 @ T )
% 5.82/6.11 => ( time_htt_o @ P @ C2 @ Q @ T ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_cons_rule
% 5.82/6.11 thf(fact_4679_htt__cons__rule,axiom,
% 5.82/6.11 ! [P5: assn,C2: heap_T2636463487746394924on_nat,Q2: option_nat > assn,T3: nat,P: assn,Q: option_nat > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_option_nat @ P5 @ C2 @ Q2 @ T3 )
% 5.82/6.11 => ( ( entails @ P @ P5 )
% 5.82/6.11 => ( ! [X4: option_nat] : ( entails @ ( Q2 @ X4 ) @ ( Q @ X4 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T3 @ T )
% 5.82/6.11 => ( time_htt_option_nat @ P @ C2 @ Q @ T ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_cons_rule
% 5.82/6.11 thf(fact_4680_htt__cons__rule,axiom,
% 5.82/6.11 ! [P5: assn,C2: heap_Time_Heap_nat,Q2: nat > assn,T3: nat,P: assn,Q: nat > assn,T: nat] :
% 5.82/6.11 ( ( time_htt_nat @ P5 @ C2 @ Q2 @ T3 )
% 5.82/6.11 => ( ( entails @ P @ P5 )
% 5.82/6.11 => ( ! [X4: nat] : ( entails @ ( Q2 @ X4 ) @ ( Q @ X4 ) )
% 5.82/6.11 => ( ( ord_less_eq_nat @ T3 @ T )
% 5.82/6.11 => ( time_htt_nat @ P @ C2 @ Q @ T ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_cons_rule
% 5.82/6.11 thf(fact_4681_int__Suc,axiom,
% 5.82/6.11 ! [N: nat] :
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.82/6.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % int_Suc
% 5.82/6.11 thf(fact_4682_int__ops_I4_J,axiom,
% 5.82/6.11 ! [A2: nat] :
% 5.82/6.11 ( ( semiri1314217659103216013at_int @ ( suc @ A2 ) )
% 5.82/6.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ one_one_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % int_ops(4)
% 5.82/6.11 thf(fact_4683_less__1__helper,axiom,
% 5.82/6.11 ! [N: int,M: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ N @ M )
% 5.82/6.11 => ( ord_less_int @ ( minus_minus_int @ N @ one_one_int ) @ M ) ) ).
% 5.82/6.11
% 5.82/6.11 % less_1_helper
% 5.82/6.11 thf(fact_4684_htt__vebt__memberi__invar__vebt,axiom,
% 5.82/6.11 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.11 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.11 => ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X2 )
% 5.82/6.11 @ ^ [R5: $o] :
% 5.82/6.11 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.11 @ ( pure_assn
% 5.82/6.11 @ ( R5
% 5.82/6.11 = ( vEBT_vebt_member @ T @ X2 ) ) ) )
% 5.82/6.11 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_vebt_memberi_invar_vebt
% 5.82/6.11 thf(fact_4685_htt__vebt__inserti__invar__vebt,axiom,
% 5.82/6.11 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.11 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.11 => ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X2 ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X2 ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_vebt_inserti_invar_vebt
% 5.82/6.11 thf(fact_4686_htt__vebt__predi,axiom,
% 5.82/6.11 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.11 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.11 => ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_predi @ Ti @ X2 )
% 5.82/6.11 @ ^ [R5: option_nat] :
% 5.82/6.11 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.11 @ ( pure_assn
% 5.82/6.11 @ ( R5
% 5.82/6.11 = ( vEBT_vebt_pred @ T @ X2 ) ) ) )
% 5.82/6.11 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_vebt_predi
% 5.82/6.11 thf(fact_4687_htt__vebt__succi,axiom,
% 5.82/6.11 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X2: nat] :
% 5.82/6.11 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.11 => ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_succi @ Ti @ X2 )
% 5.82/6.11 @ ^ [R5: option_nat] :
% 5.82/6.11 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 5.82/6.11 @ ( pure_assn
% 5.82/6.11 @ ( R5
% 5.82/6.11 = ( vEBT_vebt_succ @ T @ X2 ) ) ) )
% 5.82/6.11 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % htt_vebt_succi
% 5.82/6.11 thf(fact_4688_log__ceil__idem,axiom,
% 5.82/6.11 ! [X2: real] :
% 5.82/6.11 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.11 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.82/6.11 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % log_ceil_idem
% 5.82/6.11 thf(fact_4689_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,
% 5.82/6.11 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.11 ( ( ( vEBT_V1232361888498592333_e_t_e @ X2 @ Xa )
% 5.82/6.11 = Y3 )
% 5.82/6.11 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.11 => ( ! [A3: $o,B3: $o] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.11 => ( ( Xa = zero_zero_nat )
% 5.82/6.11 => ( ( Y3 = one_one_nat )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.11 => ( ! [A3: $o,B3: $o] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.11 => ( ( Xa
% 5.82/6.11 = ( suc @ zero_zero_nat ) )
% 5.82/6.11 => ( ( Y3 = one_one_nat )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.82/6.11 => ( ! [A3: $o,B3: $o] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.11 => ! [N3: nat] :
% 5.82/6.11 ( ( Xa
% 5.82/6.11 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.11 => ( ( Y3 = one_one_nat )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.82/6.11 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.11 => ( ( Y3 = one_one_nat )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.11 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 5.82/6.11 => ( ( Y3 = one_one_nat )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.11 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 5.82/6.11 => ( ( Y3 = one_one_nat )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.11 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.11 ( ( X2
% 5.82/6.11 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.11 => ( ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.11 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.11 => ( Y3 = one_one_nat ) )
% 5.82/6.11 & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.11 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.11 => ( ( ( ( Xa = Mi2 )
% 5.82/6.11 & ( Xa = Ma2 ) )
% 5.82/6.11 => ( Y3 = one_one_nat ) )
% 5.82/6.11 & ( ~ ( ( Xa = Mi2 )
% 5.82/6.11 & ( Xa = Ma2 ) )
% 5.82/6.11 => ( Y3
% 5.82/6.11 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) )
% 5.82/6.11 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.pelims
% 5.82/6.11 thf(fact_4690_of__int__numeral,axiom,
% 5.82/6.11 ! [K: num] :
% 5.82/6.11 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.82/6.11 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_numeral
% 5.82/6.11 thf(fact_4691_of__int__numeral,axiom,
% 5.82/6.11 ! [K: num] :
% 5.82/6.11 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.82/6.11 = ( numeral_numeral_real @ K ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_numeral
% 5.82/6.11 thf(fact_4692_of__int__numeral,axiom,
% 5.82/6.11 ! [K: num] :
% 5.82/6.11 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.82/6.11 = ( numeral_numeral_rat @ K ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_numeral
% 5.82/6.11 thf(fact_4693_of__int__numeral,axiom,
% 5.82/6.11 ! [K: num] :
% 5.82/6.11 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.82/6.11 = ( numeral_numeral_int @ K ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_numeral
% 5.82/6.11 thf(fact_4694_of__int__eq__numeral__iff,axiom,
% 5.82/6.11 ! [Z: int,N: num] :
% 5.82/6.11 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.82/6.11 = ( numera6690914467698888265omplex @ N ) )
% 5.82/6.11 = ( Z
% 5.82/6.11 = ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_numeral_iff
% 5.82/6.11 thf(fact_4695_of__int__eq__numeral__iff,axiom,
% 5.82/6.11 ! [Z: int,N: num] :
% 5.82/6.11 ( ( ( ring_1_of_int_real @ Z )
% 5.82/6.11 = ( numeral_numeral_real @ N ) )
% 5.82/6.11 = ( Z
% 5.82/6.11 = ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_numeral_iff
% 5.82/6.11 thf(fact_4696_of__int__eq__numeral__iff,axiom,
% 5.82/6.11 ! [Z: int,N: num] :
% 5.82/6.11 ( ( ( ring_1_of_int_rat @ Z )
% 5.82/6.11 = ( numeral_numeral_rat @ N ) )
% 5.82/6.11 = ( Z
% 5.82/6.11 = ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_numeral_iff
% 5.82/6.11 thf(fact_4697_of__int__eq__numeral__iff,axiom,
% 5.82/6.11 ! [Z: int,N: num] :
% 5.82/6.11 ( ( ( ring_1_of_int_int @ Z )
% 5.82/6.11 = ( numeral_numeral_int @ N ) )
% 5.82/6.11 = ( Z
% 5.82/6.11 = ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_numeral_iff
% 5.82/6.11 thf(fact_4698_of__int__le__iff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.11 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_le_iff
% 5.82/6.11 thf(fact_4699_of__int__le__iff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.11 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_le_iff
% 5.82/6.11 thf(fact_4700_of__int__le__iff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.11 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_le_iff
% 5.82/6.11 thf(fact_4701_of__int__less__iff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.11 = ( ord_less_int @ W @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_less_iff
% 5.82/6.11 thf(fact_4702_of__int__less__iff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.11 = ( ord_less_int @ W @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_less_iff
% 5.82/6.11 thf(fact_4703_of__int__less__iff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.11 = ( ord_less_int @ W @ Z ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_less_iff
% 5.82/6.11 thf(fact_4704_of__int__eq__1__iff,axiom,
% 5.82/6.11 ! [Z: int] :
% 5.82/6.11 ( ( ( ring_1_of_int_int @ Z )
% 5.82/6.11 = one_one_int )
% 5.82/6.11 = ( Z = one_one_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_1_iff
% 5.82/6.11 thf(fact_4705_of__int__eq__1__iff,axiom,
% 5.82/6.11 ! [Z: int] :
% 5.82/6.11 ( ( ( ring_1_of_int_real @ Z )
% 5.82/6.11 = one_one_real )
% 5.82/6.11 = ( Z = one_one_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_1_iff
% 5.82/6.11 thf(fact_4706_of__int__eq__1__iff,axiom,
% 5.82/6.11 ! [Z: int] :
% 5.82/6.11 ( ( ( ring_1_of_int_rat @ Z )
% 5.82/6.11 = one_one_rat )
% 5.82/6.11 = ( Z = one_one_int ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_eq_1_iff
% 5.82/6.11 thf(fact_4707_of__int__1,axiom,
% 5.82/6.11 ( ( ring_1_of_int_int @ one_one_int )
% 5.82/6.11 = one_one_int ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_1
% 5.82/6.11 thf(fact_4708_of__int__1,axiom,
% 5.82/6.11 ( ( ring_1_of_int_real @ one_one_int )
% 5.82/6.11 = one_one_real ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_1
% 5.82/6.11 thf(fact_4709_of__int__1,axiom,
% 5.82/6.11 ( ( ring_1_of_int_rat @ one_one_int )
% 5.82/6.11 = one_one_rat ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_1
% 5.82/6.11 thf(fact_4710_of__int__add,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.82/6.11 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_add
% 5.82/6.11 thf(fact_4711_of__int__add,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.82/6.11 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_add
% 5.82/6.11 thf(fact_4712_of__int__add,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.82/6.11 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_add
% 5.82/6.11 thf(fact_4713_of__int__mult,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.82/6.11 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_mult
% 5.82/6.11 thf(fact_4714_of__int__mult,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.82/6.11 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_mult
% 5.82/6.11 thf(fact_4715_of__int__mult,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.11 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.82/6.11 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.82/6.11
% 5.82/6.11 % of_int_mult
% 5.82/6.11 thf(fact_4716_nat__numeral,axiom,
% 5.82/6.11 ! [K: num] :
% 5.82/6.11 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.82/6.11 = ( numeral_numeral_nat @ K ) ) ).
% 5.82/6.11
% 5.82/6.11 % nat_numeral
% 5.82/6.11 thf(fact_4717_of__int__diff,axiom,
% 5.82/6.11 ! [W: int,Z: int] :
% 5.82/6.12 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.82/6.12 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_diff
% 5.82/6.12 thf(fact_4718_of__int__diff,axiom,
% 5.82/6.12 ! [W: int,Z: int] :
% 5.82/6.12 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.82/6.12 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_diff
% 5.82/6.12 thf(fact_4719_of__int__diff,axiom,
% 5.82/6.12 ! [W: int,Z: int] :
% 5.82/6.12 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.82/6.12 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_diff
% 5.82/6.12 thf(fact_4720_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ( ring_1_of_int_rat @ X2 )
% 5.82/6.12 = ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) )
% 5.82/6.12 = ( X2
% 5.82/6.12 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4721_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ( ring_1_of_int_real @ X2 )
% 5.82/6.12 = ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) )
% 5.82/6.12 = ( X2
% 5.82/6.12 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4722_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ( ring_1_of_int_int @ X2 )
% 5.82/6.12 = ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) )
% 5.82/6.12 = ( X2
% 5.82/6.12 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4723_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ( ring_17405671764205052669omplex @ X2 )
% 5.82/6.12 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B2 ) @ W ) )
% 5.82/6.12 = ( X2
% 5.82/6.12 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4724_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ( ring_18347121197199848620nteger @ X2 )
% 5.82/6.12 = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B2 ) @ W ) )
% 5.82/6.12 = ( X2
% 5.82/6.12 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4725_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W )
% 5.82/6.12 = ( ring_1_of_int_rat @ X2 ) )
% 5.82/6.12 = ( ( power_power_int @ B2 @ W )
% 5.82/6.12 = X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4726_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W )
% 5.82/6.12 = ( ring_1_of_int_real @ X2 ) )
% 5.82/6.12 = ( ( power_power_int @ B2 @ W )
% 5.82/6.12 = X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4727_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W )
% 5.82/6.12 = ( ring_1_of_int_int @ X2 ) )
% 5.82/6.12 = ( ( power_power_int @ B2 @ W )
% 5.82/6.12 = X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4728_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B2 ) @ W )
% 5.82/6.12 = ( ring_17405671764205052669omplex @ X2 ) )
% 5.82/6.12 = ( ( power_power_int @ B2 @ W )
% 5.82/6.12 = X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4729_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B2 ) @ W )
% 5.82/6.12 = ( ring_18347121197199848620nteger @ X2 ) )
% 5.82/6.12 = ( ( power_power_int @ B2 @ W )
% 5.82/6.12 = X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4730_of__int__power,axiom,
% 5.82/6.12 ! [Z: int,N: nat] :
% 5.82/6.12 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.82/6.12 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power
% 5.82/6.12 thf(fact_4731_of__int__power,axiom,
% 5.82/6.12 ! [Z: int,N: nat] :
% 5.82/6.12 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.82/6.12 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power
% 5.82/6.12 thf(fact_4732_of__int__power,axiom,
% 5.82/6.12 ! [Z: int,N: nat] :
% 5.82/6.12 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.82/6.12 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power
% 5.82/6.12 thf(fact_4733_of__int__power,axiom,
% 5.82/6.12 ! [Z: int,N: nat] :
% 5.82/6.12 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.82/6.12 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power
% 5.82/6.12 thf(fact_4734_of__int__power,axiom,
% 5.82/6.12 ! [Z: int,N: nat] :
% 5.82/6.12 ( ( ring_18347121197199848620nteger @ ( power_power_int @ Z @ N ) )
% 5.82/6.12 = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ Z ) @ N ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power
% 5.82/6.12 thf(fact_4735_nat__1,axiom,
% 5.82/6.12 ( ( nat2 @ one_one_int )
% 5.82/6.12 = ( suc @ zero_zero_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_1
% 5.82/6.12 thf(fact_4736_nat__le__0,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.82/6.12 => ( ( nat2 @ Z )
% 5.82/6.12 = zero_zero_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_le_0
% 5.82/6.12 thf(fact_4737_nat__0__iff,axiom,
% 5.82/6.12 ! [I: int] :
% 5.82/6.12 ( ( ( nat2 @ I )
% 5.82/6.12 = zero_zero_nat )
% 5.82/6.12 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_0_iff
% 5.82/6.12 thf(fact_4738_zless__nat__conj,axiom,
% 5.82/6.12 ! [W: int,Z: int] :
% 5.82/6.12 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.12 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % zless_nat_conj
% 5.82/6.12 thf(fact_4739_int__nat__eq,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.82/6.12 = Z ) )
% 5.82/6.12 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.82/6.12 = zero_zero_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % int_nat_eq
% 5.82/6.12 thf(fact_4740_ceiling__add__of__int,axiom,
% 5.82/6.12 ! [X2: rat,Z: int] :
% 5.82/6.12 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.82/6.12 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_add_of_int
% 5.82/6.12 thf(fact_4741_ceiling__add__of__int,axiom,
% 5.82/6.12 ! [X2: real,Z: int] :
% 5.82/6.12 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.82/6.12 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_add_of_int
% 5.82/6.12 thf(fact_4742_ceiling__diff__of__int,axiom,
% 5.82/6.12 ! [X2: rat,Z: int] :
% 5.82/6.12 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.82/6.12 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_diff_of_int
% 5.82/6.12 thf(fact_4743_ceiling__diff__of__int,axiom,
% 5.82/6.12 ! [X2: real,Z: int] :
% 5.82/6.12 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.82/6.12 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_diff_of_int
% 5.82/6.12 thf(fact_4744_of__int__le__0__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_0_iff
% 5.82/6.12 thf(fact_4745_of__int__le__0__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_0_iff
% 5.82/6.12 thf(fact_4746_of__int__le__0__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_0_iff
% 5.82/6.12 thf(fact_4747_of__int__0__le__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_0_le_iff
% 5.82/6.12 thf(fact_4748_of__int__0__le__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_0_le_iff
% 5.82/6.12 thf(fact_4749_of__int__0__le__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_0_le_iff
% 5.82/6.12 thf(fact_4750_of__int__numeral__le__iff,axiom,
% 5.82/6.12 ! [N: num,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_numeral_le_iff
% 5.82/6.12 thf(fact_4751_of__int__numeral__le__iff,axiom,
% 5.82/6.12 ! [N: num,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_numeral_le_iff
% 5.82/6.12 thf(fact_4752_of__int__numeral__le__iff,axiom,
% 5.82/6.12 ! [N: num,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_numeral_le_iff
% 5.82/6.12 thf(fact_4753_of__int__le__numeral__iff,axiom,
% 5.82/6.12 ! [Z: int,N: num] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_iff
% 5.82/6.12 thf(fact_4754_of__int__le__numeral__iff,axiom,
% 5.82/6.12 ! [Z: int,N: num] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_iff
% 5.82/6.12 thf(fact_4755_of__int__le__numeral__iff,axiom,
% 5.82/6.12 ! [Z: int,N: num] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_iff
% 5.82/6.12 thf(fact_4756_of__int__0__less__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_0_less_iff
% 5.82/6.12 thf(fact_4757_of__int__0__less__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_0_less_iff
% 5.82/6.12 thf(fact_4758_of__int__0__less__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.12 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_0_less_iff
% 5.82/6.12 thf(fact_4759_of__int__less__0__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.82/6.12 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_0_iff
% 5.82/6.12 thf(fact_4760_of__int__less__0__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.82/6.12 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_0_iff
% 5.82/6.12 thf(fact_4761_of__int__less__0__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.82/6.12 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_0_iff
% 5.82/6.12 thf(fact_4762_of__int__less__numeral__iff,axiom,
% 5.82/6.12 ! [Z: int,N: num] :
% 5.82/6.12 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.82/6.12 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_iff
% 5.82/6.12 thf(fact_4763_of__int__less__numeral__iff,axiom,
% 5.82/6.12 ! [Z: int,N: num] :
% 5.82/6.12 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.82/6.12 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_iff
% 5.82/6.12 thf(fact_4764_of__int__less__numeral__iff,axiom,
% 5.82/6.12 ! [Z: int,N: num] :
% 5.82/6.12 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.82/6.12 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_iff
% 5.82/6.12 thf(fact_4765_of__int__numeral__less__iff,axiom,
% 5.82/6.12 ! [N: num,Z: int] :
% 5.82/6.12 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_numeral_less_iff
% 5.82/6.12 thf(fact_4766_of__int__numeral__less__iff,axiom,
% 5.82/6.12 ! [N: num,Z: int] :
% 5.82/6.12 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_numeral_less_iff
% 5.82/6.12 thf(fact_4767_of__int__numeral__less__iff,axiom,
% 5.82/6.12 ! [N: num,Z: int] :
% 5.82/6.12 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.12 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_numeral_less_iff
% 5.82/6.12 thf(fact_4768_of__int__1__le__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_1_le_iff
% 5.82/6.12 thf(fact_4769_of__int__1__le__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_1_le_iff
% 5.82/6.12 thf(fact_4770_of__int__1__le__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_1_le_iff
% 5.82/6.12 thf(fact_4771_of__int__le__1__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_1_iff
% 5.82/6.12 thf(fact_4772_of__int__le__1__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_1_iff
% 5.82/6.12 thf(fact_4773_of__int__le__1__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.82/6.12 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_1_iff
% 5.82/6.12 thf(fact_4774_of__int__less__1__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.82/6.12 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_1_iff
% 5.82/6.12 thf(fact_4775_of__int__less__1__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.82/6.12 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_1_iff
% 5.82/6.12 thf(fact_4776_of__int__less__1__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.82/6.12 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_1_iff
% 5.82/6.12 thf(fact_4777_of__int__1__less__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_1_less_iff
% 5.82/6.12 thf(fact_4778_of__int__1__less__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_1_less_iff
% 5.82/6.12 thf(fact_4779_of__int__1__less__iff,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.82/6.12 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_1_less_iff
% 5.82/6.12 thf(fact_4780_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [Y3: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ( ring_18347121197199848620nteger @ Y3 )
% 5.82/6.12 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 5.82/6.12 = ( Y3
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4781_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [Y3: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ( ring_17405671764205052669omplex @ Y3 )
% 5.82/6.12 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.82/6.12 = ( Y3
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4782_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [Y3: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ( ring_1_of_int_real @ Y3 )
% 5.82/6.12 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.82/6.12 = ( Y3
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4783_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [Y3: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ( ring_1_of_int_rat @ Y3 )
% 5.82/6.12 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.82/6.12 = ( Y3
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4784_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [Y3: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ( ring_1_of_int_int @ Y3 )
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.82/6.12 = ( Y3
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_eq_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4785_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,Y3: int] :
% 5.82/6.12 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 5.82/6.12 = ( ring_18347121197199848620nteger @ Y3 ) )
% 5.82/6.12 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = Y3 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4786_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,Y3: int] :
% 5.82/6.12 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.82/6.12 = ( ring_17405671764205052669omplex @ Y3 ) )
% 5.82/6.12 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = Y3 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4787_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,Y3: int] :
% 5.82/6.12 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.82/6.12 = ( ring_1_of_int_real @ Y3 ) )
% 5.82/6.12 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = Y3 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4788_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,Y3: int] :
% 5.82/6.12 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.82/6.12 = ( ring_1_of_int_rat @ Y3 ) )
% 5.82/6.12 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = Y3 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4789_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,Y3: int] :
% 5.82/6.12 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = ( ring_1_of_int_int @ Y3 ) )
% 5.82/6.12 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = Y3 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_eq_of_int_cancel_iff
% 5.82/6.12 thf(fact_4790_of__int__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4791_of__int__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4792_of__int__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4793_of__int__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4794_of__int__le__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4795_of__int__le__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B2 ) @ W ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4796_of__int__le__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4797_of__int__le__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4798_of__int__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4799_of__int__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4800_of__int__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4801_of__int__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: int,B2: int,W: nat] :
% 5.82/6.12 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) )
% 5.82/6.12 = ( ord_less_int @ X2 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4802_of__int__less__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B2 ) @ W ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4803_of__int__less__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4804_of__int__less__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4805_of__int__less__of__int__power__cancel__iff,axiom,
% 5.82/6.12 ! [B2: int,W: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_of_int_power_cancel_iff
% 5.82/6.12 thf(fact_4806_zero__less__nat__eq,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % zero_less_nat_eq
% 5.82/6.12 thf(fact_4807_diff__nat__numeral,axiom,
% 5.82/6.12 ! [V: num,V3: num] :
% 5.82/6.12 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.82/6.12 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % diff_nat_numeral
% 5.82/6.12 thf(fact_4808_of__nat__nat,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_nat
% 5.82/6.12 thf(fact_4809_of__nat__nat,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_nat
% 5.82/6.12 thf(fact_4810_of__nat__nat,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ring_1_of_int_int @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_nat
% 5.82/6.12 thf(fact_4811_numeral__power__eq__nat__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,Y3: int] :
% 5.82/6.12 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.82/6.12 = ( nat2 @ Y3 ) )
% 5.82/6.12 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.82/6.12 = Y3 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_eq_nat_cancel_iff
% 5.82/6.12 thf(fact_4812_nat__eq__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [Y3: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ( nat2 @ Y3 )
% 5.82/6.12 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.82/6.12 = ( Y3
% 5.82/6.12 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_eq_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4813_nat__ceiling__le__eq,axiom,
% 5.82/6.12 ! [X2: real,A2: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A2 )
% 5.82/6.12 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_ceiling_le_eq
% 5.82/6.12 thf(fact_4814_one__less__nat__eq,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % one_less_nat_eq
% 5.82/6.12 thf(fact_4815_numeral__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4816_numeral__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4817_numeral__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4818_numeral__power__le__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_le_of_int_cancel_iff
% 5.82/6.12 thf(fact_4819_of__int__le__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4820_of__int__le__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A2 ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4821_of__int__le__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4822_of__int__le__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A2 ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_le_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4823_of__int__less__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4824_of__int__less__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_real @ ( ring_1_of_int_real @ A2 ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4825_of__int__less__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4826_of__int__less__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_int @ ( ring_1_of_int_int @ A2 ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_less_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4827_numeral__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4828_numeral__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4829_numeral__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4830_numeral__power__less__of__int__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_less_of_int_cancel_iff
% 5.82/6.12 thf(fact_4831_nat__numeral__diff__1,axiom,
% 5.82/6.12 ! [V: num] :
% 5.82/6.12 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.82/6.12 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_numeral_diff_1
% 5.82/6.12 thf(fact_4832_numeral__power__less__nat__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A2 ) )
% 5.82/6.12 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_less_nat_cancel_iff
% 5.82/6.12 thf(fact_4833_nat__less__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_nat @ ( nat2 @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_less_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4834_nat__le__numeral__power__cancel__iff,axiom,
% 5.82/6.12 ! [A2: int,X2: num,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( nat2 @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.82/6.12 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_le_numeral_power_cancel_iff
% 5.82/6.12 thf(fact_4835_numeral__power__le__nat__cancel__iff,axiom,
% 5.82/6.12 ! [X2: num,N: nat,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A2 ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % numeral_power_le_nat_cancel_iff
% 5.82/6.12 thf(fact_4836_ex__le__of__int,axiom,
% 5.82/6.12 ! [X2: real] :
% 5.82/6.12 ? [Z2: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ex_le_of_int
% 5.82/6.12 thf(fact_4837_ex__le__of__int,axiom,
% 5.82/6.12 ! [X2: rat] :
% 5.82/6.12 ? [Z2: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ex_le_of_int
% 5.82/6.12 thf(fact_4838_ex__of__int__less,axiom,
% 5.82/6.12 ! [X2: real] :
% 5.82/6.12 ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X2 ) ).
% 5.82/6.12
% 5.82/6.12 % ex_of_int_less
% 5.82/6.12 thf(fact_4839_ex__of__int__less,axiom,
% 5.82/6.12 ! [X2: rat] :
% 5.82/6.12 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ).
% 5.82/6.12
% 5.82/6.12 % ex_of_int_less
% 5.82/6.12 thf(fact_4840_ex__less__of__int,axiom,
% 5.82/6.12 ! [X2: real] :
% 5.82/6.12 ? [Z2: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ex_less_of_int
% 5.82/6.12 thf(fact_4841_ex__less__of__int,axiom,
% 5.82/6.12 ! [X2: rat] :
% 5.82/6.12 ? [Z2: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ex_less_of_int
% 5.82/6.12 thf(fact_4842_mult__of__int__commute,axiom,
% 5.82/6.12 ! [X2: int,Y3: real] :
% 5.82/6.12 ( ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ Y3 )
% 5.82/6.12 = ( times_times_real @ Y3 @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % mult_of_int_commute
% 5.82/6.12 thf(fact_4843_mult__of__int__commute,axiom,
% 5.82/6.12 ! [X2: int,Y3: rat] :
% 5.82/6.12 ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y3 )
% 5.82/6.12 = ( times_times_rat @ Y3 @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % mult_of_int_commute
% 5.82/6.12 thf(fact_4844_mult__of__int__commute,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y3 )
% 5.82/6.12 = ( times_times_int @ Y3 @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % mult_of_int_commute
% 5.82/6.12 thf(fact_4845_of__int__max,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( ring_1_of_int_real @ ( ord_max_int @ X2 @ Y3 ) )
% 5.82/6.12 = ( ord_max_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ Y3 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_max
% 5.82/6.12 thf(fact_4846_of__int__max,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( ring_1_of_int_rat @ ( ord_max_int @ X2 @ Y3 ) )
% 5.82/6.12 = ( ord_max_rat @ ( ring_1_of_int_rat @ X2 ) @ ( ring_1_of_int_rat @ Y3 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_max
% 5.82/6.12 thf(fact_4847_of__int__max,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( ring_1_of_int_int @ ( ord_max_int @ X2 @ Y3 ) )
% 5.82/6.12 = ( ord_max_int @ ( ring_1_of_int_int @ X2 ) @ ( ring_1_of_int_int @ Y3 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_max
% 5.82/6.12 thf(fact_4848_nat__numeral__as__int,axiom,
% 5.82/6.12 ( numeral_numeral_nat
% 5.82/6.12 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_numeral_as_int
% 5.82/6.12 thf(fact_4849_nat__mono,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.82/6.12 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_mono
% 5.82/6.12 thf(fact_4850_nat__one__as__int,axiom,
% 5.82/6.12 ( one_one_nat
% 5.82/6.12 = ( nat2 @ one_one_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_one_as_int
% 5.82/6.12 thf(fact_4851_ex__nat,axiom,
% 5.82/6.12 ( ( ^ [P2: nat > $o] :
% 5.82/6.12 ? [X6: nat] : ( P2 @ X6 ) )
% 5.82/6.12 = ( ^ [P3: nat > $o] :
% 5.82/6.12 ? [X3: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.82/6.12 & ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ex_nat
% 5.82/6.12 thf(fact_4852_all__nat,axiom,
% 5.82/6.12 ( ( ^ [P2: nat > $o] :
% 5.82/6.12 ! [X6: nat] : ( P2 @ X6 ) )
% 5.82/6.12 = ( ^ [P3: nat > $o] :
% 5.82/6.12 ! [X3: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.82/6.12 => ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % all_nat
% 5.82/6.12 thf(fact_4853_eq__nat__nat__iff,axiom,
% 5.82/6.12 ! [Z: int,Z6: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.82/6.12 => ( ( ( nat2 @ Z )
% 5.82/6.12 = ( nat2 @ Z6 ) )
% 5.82/6.12 = ( Z = Z6 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % eq_nat_nat_iff
% 5.82/6.12 thf(fact_4854_le__of__int__ceiling,axiom,
% 5.82/6.12 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % le_of_int_ceiling
% 5.82/6.12 thf(fact_4855_le__of__int__ceiling,axiom,
% 5.82/6.12 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % le_of_int_ceiling
% 5.82/6.12 thf(fact_4856_nat__mono__iff,axiom,
% 5.82/6.12 ! [Z: int,W: int] :
% 5.82/6.12 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_mono_iff
% 5.82/6.12 thf(fact_4857_zless__nat__eq__int__zless,axiom,
% 5.82/6.12 ! [M: nat,Z: int] :
% 5.82/6.12 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % zless_nat_eq_int_zless
% 5.82/6.12 thf(fact_4858_nat__le__iff,axiom,
% 5.82/6.12 ! [X2: int,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 5.82/6.12 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_le_iff
% 5.82/6.12 thf(fact_4859_of__nat__ceiling,axiom,
% 5.82/6.12 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_ceiling
% 5.82/6.12 thf(fact_4860_of__nat__ceiling,axiom,
% 5.82/6.12 ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_ceiling
% 5.82/6.12 thf(fact_4861_nat__int__add,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) )
% 5.82/6.12 = ( plus_plus_nat @ A2 @ B2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_int_add
% 5.82/6.12 thf(fact_4862_int__eq__iff,axiom,
% 5.82/6.12 ! [M: nat,Z: int] :
% 5.82/6.12 ( ( ( semiri1314217659103216013at_int @ M )
% 5.82/6.12 = Z )
% 5.82/6.12 = ( ( M
% 5.82/6.12 = ( nat2 @ Z ) )
% 5.82/6.12 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % int_eq_iff
% 5.82/6.12 thf(fact_4863_nat__0__le,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.82/6.12 = Z ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_0_le
% 5.82/6.12 thf(fact_4864_ceiling__le__iff,axiom,
% 5.82/6.12 ! [X2: real,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.82/6.12 = ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_le_iff
% 5.82/6.12 thf(fact_4865_ceiling__le__iff,axiom,
% 5.82/6.12 ! [X2: rat,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.82/6.12 = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_le_iff
% 5.82/6.12 thf(fact_4866_ceiling__le,axiom,
% 5.82/6.12 ! [X2: real,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A2 ) )
% 5.82/6.12 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_le
% 5.82/6.12 thf(fact_4867_ceiling__le,axiom,
% 5.82/6.12 ! [X2: rat,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A2 ) )
% 5.82/6.12 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ A2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_le
% 5.82/6.12 thf(fact_4868_less__ceiling__iff,axiom,
% 5.82/6.12 ! [Z: int,X2: rat] :
% 5.82/6.12 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.12 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % less_ceiling_iff
% 5.82/6.12 thf(fact_4869_less__ceiling__iff,axiom,
% 5.82/6.12 ! [Z: int,X2: real] :
% 5.82/6.12 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.12 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % less_ceiling_iff
% 5.82/6.12 thf(fact_4870_int__minus,axiom,
% 5.82/6.12 ! [N: nat,M: nat] :
% 5.82/6.12 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.12 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % int_minus
% 5.82/6.12 thf(fact_4871_real__of__int__div4,axiom,
% 5.82/6.12 ! [N: int,X2: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % real_of_int_div4
% 5.82/6.12 thf(fact_4872_real__nat__ceiling__ge,axiom,
% 5.82/6.12 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % real_nat_ceiling_ge
% 5.82/6.12 thf(fact_4873_nat__plus__as__int,axiom,
% 5.82/6.12 ( plus_plus_nat
% 5.82/6.12 = ( ^ [A5: nat,B6: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_plus_as_int
% 5.82/6.12 thf(fact_4874_nat__times__as__int,axiom,
% 5.82/6.12 ( times_times_nat
% 5.82/6.12 = ( ^ [A5: nat,B6: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_times_as_int
% 5.82/6.12 thf(fact_4875_nat__minus__as__int,axiom,
% 5.82/6.12 ( minus_minus_nat
% 5.82/6.12 = ( ^ [A5: nat,B6: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_minus_as_int
% 5.82/6.12 thf(fact_4876_nat__div__as__int,axiom,
% 5.82/6.12 ( divide_divide_nat
% 5.82/6.12 = ( ^ [A5: nat,B6: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_div_as_int
% 5.82/6.12 thf(fact_4877_of__int__nonneg,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_nonneg
% 5.82/6.12 thf(fact_4878_of__int__nonneg,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_nonneg
% 5.82/6.12 thf(fact_4879_of__int__nonneg,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_nonneg
% 5.82/6.12 thf(fact_4880_of__int__pos,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_pos
% 5.82/6.12 thf(fact_4881_of__int__pos,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_pos
% 5.82/6.12 thf(fact_4882_of__int__pos,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_pos
% 5.82/6.12 thf(fact_4883_floor__exists,axiom,
% 5.82/6.12 ! [X2: real] :
% 5.82/6.12 ? [Z2: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X2 )
% 5.82/6.12 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % floor_exists
% 5.82/6.12 thf(fact_4884_floor__exists,axiom,
% 5.82/6.12 ! [X2: rat] :
% 5.82/6.12 ? [Z2: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 )
% 5.82/6.12 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % floor_exists
% 5.82/6.12 thf(fact_4885_floor__exists1,axiom,
% 5.82/6.12 ! [X2: real] :
% 5.82/6.12 ? [X4: int] :
% 5.82/6.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X2 )
% 5.82/6.12 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.82/6.12 & ! [Y5: int] :
% 5.82/6.12 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X2 )
% 5.82/6.12 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.82/6.12 => ( Y5 = X4 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % floor_exists1
% 5.82/6.12 thf(fact_4886_floor__exists1,axiom,
% 5.82/6.12 ! [X2: rat] :
% 5.82/6.12 ? [X4: int] :
% 5.82/6.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X2 )
% 5.82/6.12 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.82/6.12 & ! [Y5: int] :
% 5.82/6.12 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X2 )
% 5.82/6.12 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.82/6.12 => ( Y5 = X4 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % floor_exists1
% 5.82/6.12 thf(fact_4887_of__int__ceiling__le__add__one,axiom,
% 5.82/6.12 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_ceiling_le_add_one
% 5.82/6.12 thf(fact_4888_of__int__ceiling__le__add__one,axiom,
% 5.82/6.12 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_ceiling_le_add_one
% 5.82/6.12 thf(fact_4889_of__int__ceiling__diff__one__le,axiom,
% 5.82/6.12 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_ceiling_diff_one_le
% 5.82/6.12 thf(fact_4890_of__int__ceiling__diff__one__le,axiom,
% 5.82/6.12 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 5.82/6.12
% 5.82/6.12 % of_int_ceiling_diff_one_le
% 5.82/6.12 thf(fact_4891_of__nat__less__of__int__iff,axiom,
% 5.82/6.12 ! [N: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_less_of_int_iff
% 5.82/6.12 thf(fact_4892_of__nat__less__of__int__iff,axiom,
% 5.82/6.12 ! [N: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_less_of_int_iff
% 5.82/6.12 thf(fact_4893_of__nat__less__of__int__iff,axiom,
% 5.82/6.12 ! [N: nat,X2: int] :
% 5.82/6.12 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 5.82/6.12 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_less_of_int_iff
% 5.82/6.12 thf(fact_4894_nat__less__eq__zless,axiom,
% 5.82/6.12 ! [W: int,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.82/6.12 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_less_eq_zless
% 5.82/6.12 thf(fact_4895_nat__eq__iff,axiom,
% 5.82/6.12 ! [W: int,M: nat] :
% 5.82/6.12 ( ( ( nat2 @ W )
% 5.82/6.12 = M )
% 5.82/6.12 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.82/6.12 => ( W
% 5.82/6.12 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.82/6.12 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.82/6.12 => ( M = zero_zero_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_eq_iff
% 5.82/6.12 thf(fact_4896_nat__eq__iff2,axiom,
% 5.82/6.12 ! [M: nat,W: int] :
% 5.82/6.12 ( ( M
% 5.82/6.12 = ( nat2 @ W ) )
% 5.82/6.12 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.82/6.12 => ( W
% 5.82/6.12 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.82/6.12 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.82/6.12 => ( M = zero_zero_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_eq_iff2
% 5.82/6.12 thf(fact_4897_nat__le__eq__zle,axiom,
% 5.82/6.12 ! [W: int,Z: int] :
% 5.82/6.12 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.82/6.12 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.82/6.12 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.82/6.12 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_le_eq_zle
% 5.82/6.12 thf(fact_4898_nat__add__distrib,axiom,
% 5.82/6.12 ! [Z: int,Z6: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.82/6.12 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.82/6.12 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_add_distrib
% 5.82/6.12 thf(fact_4899_le__nat__iff,axiom,
% 5.82/6.12 ! [K: int,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.12 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.82/6.12 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % le_nat_iff
% 5.82/6.12 thf(fact_4900_Suc__as__int,axiom,
% 5.82/6.12 ( suc
% 5.82/6.12 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Suc_as_int
% 5.82/6.12 thf(fact_4901_nat__mult__distrib,axiom,
% 5.82/6.12 ! [Z: int,Z6: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.82/6.12 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_mult_distrib
% 5.82/6.12 thf(fact_4902_nat__diff__distrib_H,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.12 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.12 => ( ( nat2 @ ( minus_minus_int @ X2 @ Y3 ) )
% 5.82/6.12 = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_diff_distrib'
% 5.82/6.12 thf(fact_4903_nat__diff__distrib,axiom,
% 5.82/6.12 ! [Z6: int,Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.82/6.12 => ( ( ord_less_eq_int @ Z6 @ Z )
% 5.82/6.12 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 5.82/6.12 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_diff_distrib
% 5.82/6.12 thf(fact_4904_nat__div__distrib,axiom,
% 5.82/6.12 ! [X2: int,Y3: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.12 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y3 ) )
% 5.82/6.12 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_div_distrib
% 5.82/6.12 thf(fact_4905_nat__div__distrib_H,axiom,
% 5.82/6.12 ! [Y3: int,X2: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.12 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y3 ) )
% 5.82/6.12 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_div_distrib'
% 5.82/6.12 thf(fact_4906_nat__power__eq,axiom,
% 5.82/6.12 ! [Z: int,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.82/6.12 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_power_eq
% 5.82/6.12 thf(fact_4907_int__le__real__less,axiom,
% 5.82/6.12 ( ord_less_eq_int
% 5.82/6.12 = ( ^ [N4: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N4 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % int_le_real_less
% 5.82/6.12 thf(fact_4908_int__less__real__le,axiom,
% 5.82/6.12 ( ord_less_int
% 5.82/6.12 = ( ^ [N4: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N4 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % int_less_real_le
% 5.82/6.12 thf(fact_4909_nat__2,axiom,
% 5.82/6.12 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.12 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_2
% 5.82/6.12 thf(fact_4910_ceiling__split,axiom,
% 5.82/6.12 ! [P: int > $o,T: real] :
% 5.82/6.12 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.82/6.12 = ( ! [I4: int] :
% 5.82/6.12 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 5.82/6.12 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 5.82/6.12 => ( P @ I4 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_split
% 5.82/6.12 thf(fact_4911_ceiling__split,axiom,
% 5.82/6.12 ! [P: int > $o,T: rat] :
% 5.82/6.12 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.82/6.12 = ( ! [I4: int] :
% 5.82/6.12 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 5.82/6.12 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.82/6.12 => ( P @ I4 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_split
% 5.82/6.12 thf(fact_4912_ceiling__eq__iff,axiom,
% 5.82/6.12 ! [X2: real,A2: int] :
% 5.82/6.12 ( ( ( archim7802044766580827645g_real @ X2 )
% 5.82/6.12 = A2 )
% 5.82/6.12 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A2 ) @ one_one_real ) @ X2 )
% 5.82/6.12 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_eq_iff
% 5.82/6.12 thf(fact_4913_ceiling__eq__iff,axiom,
% 5.82/6.12 ! [X2: rat,A2: int] :
% 5.82/6.12 ( ( ( archim2889992004027027881ng_rat @ X2 )
% 5.82/6.12 = A2 )
% 5.82/6.12 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A2 ) @ one_one_rat ) @ X2 )
% 5.82/6.12 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_eq_iff
% 5.82/6.12 thf(fact_4914_ceiling__unique,axiom,
% 5.82/6.12 ! [Z: int,X2: real] :
% 5.82/6.12 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 )
% 5.82/6.12 => ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) )
% 5.82/6.12 => ( ( archim7802044766580827645g_real @ X2 )
% 5.82/6.12 = Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_unique
% 5.82/6.12 thf(fact_4915_ceiling__unique,axiom,
% 5.82/6.12 ! [Z: int,X2: rat] :
% 5.82/6.12 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 )
% 5.82/6.12 => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) )
% 5.82/6.12 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.82/6.12 = Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_unique
% 5.82/6.12 thf(fact_4916_ceiling__correct,axiom,
% 5.82/6.12 ! [X2: real] :
% 5.82/6.12 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) @ one_one_real ) @ X2 )
% 5.82/6.12 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_correct
% 5.82/6.12 thf(fact_4917_ceiling__correct,axiom,
% 5.82/6.12 ! [X2: rat] :
% 5.82/6.12 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 5.82/6.12 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_correct
% 5.82/6.12 thf(fact_4918_ceiling__less__iff,axiom,
% 5.82/6.12 ! [X2: real,Z: int] :
% 5.82/6.12 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.82/6.12 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_less_iff
% 5.82/6.12 thf(fact_4919_ceiling__less__iff,axiom,
% 5.82/6.12 ! [X2: rat,Z: int] :
% 5.82/6.12 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.82/6.12 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_less_iff
% 5.82/6.12 thf(fact_4920_le__ceiling__iff,axiom,
% 5.82/6.12 ! [Z: int,X2: rat] :
% 5.82/6.12 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.82/6.12 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % le_ceiling_iff
% 5.82/6.12 thf(fact_4921_le__ceiling__iff,axiom,
% 5.82/6.12 ! [Z: int,X2: real] :
% 5.82/6.12 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.82/6.12 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.82/6.12
% 5.82/6.12 % le_ceiling_iff
% 5.82/6.12 thf(fact_4922_Suc__nat__eq__nat__zadd1,axiom,
% 5.82/6.12 ! [Z: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.12 => ( ( suc @ ( nat2 @ Z ) )
% 5.82/6.12 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Suc_nat_eq_nat_zadd1
% 5.82/6.12 thf(fact_4923_nat__less__iff,axiom,
% 5.82/6.12 ! [W: int,M: nat] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.82/6.12 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.82/6.12 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % nat_less_iff
% 5.82/6.12 thf(fact_4924_real__of__int__div2,axiom,
% 5.82/6.12 ! [N: int,X2: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % real_of_int_div2
% 5.82/6.12 thf(fact_4925_real__of__int__div3,axiom,
% 5.82/6.12 ! [N: int,X2: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.82/6.12
% 5.82/6.12 % real_of_int_div3
% 5.82/6.12 thf(fact_4926_diff__nat__eq__if,axiom,
% 5.82/6.12 ! [Z6: int,Z: int] :
% 5.82/6.12 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 5.82/6.12 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.82/6.12 = ( nat2 @ Z ) ) )
% 5.82/6.12 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 5.82/6.12 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.82/6.12 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % diff_nat_eq_if
% 5.82/6.12 thf(fact_4927_ceiling__divide__upper,axiom,
% 5.82/6.12 ! [Q3: real,P6: real] :
% 5.82/6.12 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.82/6.12 => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_divide_upper
% 5.82/6.12 thf(fact_4928_ceiling__divide__upper,axiom,
% 5.82/6.12 ! [Q3: rat,P6: rat] :
% 5.82/6.12 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.82/6.12 => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_divide_upper
% 5.82/6.12 thf(fact_4929_ceiling__divide__lower,axiom,
% 5.82/6.12 ! [Q3: real,P6: real] :
% 5.82/6.12 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.82/6.12 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P6 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_divide_lower
% 5.82/6.12 thf(fact_4930_ceiling__divide__lower,axiom,
% 5.82/6.12 ! [Q3: rat,P6: rat] :
% 5.82/6.12 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.82/6.12 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P6 ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_divide_lower
% 5.82/6.12 thf(fact_4931_ceiling__eq,axiom,
% 5.82/6.12 ! [N: int,X2: real] :
% 5.82/6.12 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.82/6.12 => ( ( ord_less_eq_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.82/6.12 => ( ( archim7802044766580827645g_real @ X2 )
% 5.82/6.12 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_eq
% 5.82/6.12 thf(fact_4932_ceiling__eq,axiom,
% 5.82/6.12 ! [N: int,X2: rat] :
% 5.82/6.12 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X2 )
% 5.82/6.12 => ( ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.82/6.12 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.82/6.12 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ceiling_eq
% 5.82/6.12 thf(fact_4933_Abs__fnat__hom__add,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( plus_plus_rat @ ( semiri681578069525770553at_rat @ A2 ) @ ( semiri681578069525770553at_rat @ B2 ) )
% 5.82/6.12 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Abs_fnat_hom_add
% 5.82/6.12 thf(fact_4934_Abs__fnat__hom__add,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( plus_plus_real @ ( semiri5074537144036343181t_real @ A2 ) @ ( semiri5074537144036343181t_real @ B2 ) )
% 5.82/6.12 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Abs_fnat_hom_add
% 5.82/6.12 thf(fact_4935_Abs__fnat__hom__add,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) )
% 5.82/6.12 = ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Abs_fnat_hom_add
% 5.82/6.12 thf(fact_4936_Abs__fnat__hom__add,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ A2 ) @ ( semiri1316708129612266289at_nat @ B2 ) )
% 5.82/6.12 = ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Abs_fnat_hom_add
% 5.82/6.12 thf(fact_4937_of__nat__gt__0,axiom,
% 5.82/6.12 ! [K: nat] :
% 5.82/6.12 ( ( ( semiri8010041392384452111omplex @ K )
% 5.82/6.12 != zero_zero_complex )
% 5.82/6.12 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_gt_0
% 5.82/6.12 thf(fact_4938_of__nat__gt__0,axiom,
% 5.82/6.12 ! [K: nat] :
% 5.82/6.12 ( ( ( semiri681578069525770553at_rat @ K )
% 5.82/6.12 != zero_zero_rat )
% 5.82/6.12 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_gt_0
% 5.82/6.12 thf(fact_4939_of__nat__gt__0,axiom,
% 5.82/6.12 ! [K: nat] :
% 5.82/6.12 ( ( ( semiri5074537144036343181t_real @ K )
% 5.82/6.12 != zero_zero_real )
% 5.82/6.12 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_gt_0
% 5.82/6.12 thf(fact_4940_of__nat__gt__0,axiom,
% 5.82/6.12 ! [K: nat] :
% 5.82/6.12 ( ( ( semiri1314217659103216013at_int @ K )
% 5.82/6.12 != zero_zero_int )
% 5.82/6.12 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_gt_0
% 5.82/6.12 thf(fact_4941_of__nat__gt__0,axiom,
% 5.82/6.12 ! [K: nat] :
% 5.82/6.12 ( ( ( semiri1316708129612266289at_nat @ K )
% 5.82/6.12 != zero_zero_nat )
% 5.82/6.12 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % of_nat_gt_0
% 5.82/6.12 thf(fact_4942_vebt__delete_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 5.82/6.12 ( ( ( vEBT_vebt_delete @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Leaf @ $false @ B3 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ $false ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ! [N3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.82/6.12 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.82/6.12 & ( ~ ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.12 => ( ( ( ( Xa = Mi2 )
% 5.82/6.12 & ( Xa = Ma2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.82/6.12 & ( ~ ( ( Xa = Mi2 )
% 5.82/6.12 & ( Xa = Ma2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_Node
% 5.82/6.12 @ ( some_P7363390416028606310at_nat
% 5.82/6.12 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( Xa = Mi2 )
% 5.82/6.12 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.12 = Ma2 ) )
% 5.82/6.12 & ( ( Xa != Mi2 )
% 5.82/6.12 => ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 5.82/6.12 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ Ma2 ) ) )
% 5.82/6.12 @ ( suc @ ( suc @ Va3 ) )
% 5.82/6.12 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_Node
% 5.82/6.12 @ ( some_P7363390416028606310at_nat
% 5.82/6.12 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa = Mi2 ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ Mi2 )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( Xa = Mi2 )
% 5.82/6.12 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.12 = Ma2 ) )
% 5.82/6.12 & ( ( Xa != Mi2 )
% 5.82/6.12 => ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ Ma2 ) ) )
% 5.82/6.12 @ ( suc @ ( suc @ Va3 ) )
% 5.82/6.12 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ Summary2 ) )
% 5.82/6.12 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_delete.pelims
% 5.82/6.12 thf(fact_4943_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_s_u_c_c2 @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [Uv2: $o,Uw2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ! [N3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ N3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.82/6.12 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( Y3 = one_one_nat ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.12 @ one_one_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.pelims
% 5.82/6.12 thf(fact_4944_vebt__insert_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 5.82/6.12 ( ( ( vEBT_vebt_insert @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.82/6.12 & ( ( Xa != one_one_nat )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( if_VEBT_VEBT
% 5.82/6.12 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 & ~ ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.82/6.12 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_insert.pelims
% 5.82/6.12 thf(fact_4945_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_p_r_e_d2 @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,Uw2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ! [Va3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.82/6.12 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( ( ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( Y3 = one_one_nat ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.12 @ one_one_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.pelims
% 5.82/6.12 thf(fact_4946_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 & ~ ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.12 @ one_one_nat ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 5.82/6.12 thf(fact_4947_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 5.82/6.12 thf(fact_4948_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( Xa = Mi2 ) @ zero_zero_nat
% 5.82/6.12 @ ( if_nat @ ( Xa = Ma2 ) @ zero_zero_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ zero_zero_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ zero_zero_nat
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ Mi2 @ Xa )
% 5.82/6.12 & ( ord_less_nat @ Xa @ Ma2 ) )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.82/6.12 @ zero_zero_nat ) ) ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 5.82/6.12 thf(fact_4949_vebt__member_Opelims_I1_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.82/6.12 ( ( ( vEBT_vebt_member @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => A3 )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => B3 )
% 5.82/6.12 & ( Xa = one_one_nat ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( ~ Y3
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( ~ Y3
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.12 => ( ~ Y3
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( Xa != Mi2 )
% 5.82/6.12 => ( ( Xa != Ma2 )
% 5.82/6.12 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_member.pelims(1)
% 5.82/6.12 thf(fact_4950_vebt__member_Opelims_I3_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.12 ( ~ ( vEBT_vebt_member @ X2 @ Xa )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) )
% 5.82/6.12 => ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => A3 )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => B3 )
% 5.82/6.12 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.82/6.12 => ( ( Xa != Mi2 )
% 5.82/6.12 => ( ( Xa != Ma2 )
% 5.82/6.12 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_member.pelims(3)
% 5.82/6.12 thf(fact_4951_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.82/6.12 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => A3 )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => B3 )
% 5.82/6.12 & ( Xa = one_one_nat ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( ~ Y3
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % VEBT_internal.naive_member.pelims(1)
% 5.82/6.12 thf(fact_4952_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.12 ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => A3 )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => B3 )
% 5.82/6.12 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.82/6.12 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % VEBT_internal.naive_member.pelims(2)
% 5.82/6.12 thf(fact_4953_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.12 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) )
% 5.82/6.12 => ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => A3 )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => B3 )
% 5.82/6.12 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) )
% 5.82/6.12 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa ) )
% 5.82/6.12 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % VEBT_internal.naive_member.pelims(3)
% 5.82/6.12 thf(fact_4954_vebt__member_Opelims_I2_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.12 ( ( vEBT_vebt_member @ X2 @ Xa )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( ( Xa = zero_zero_nat )
% 5.82/6.12 => A3 )
% 5.82/6.12 & ( ( Xa != zero_zero_nat )
% 5.82/6.12 => ( ( ( Xa = one_one_nat )
% 5.82/6.12 => B3 )
% 5.82/6.12 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( Xa != Mi2 )
% 5.82/6.12 => ( ( Xa != Ma2 )
% 5.82/6.12 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_member.pelims(2)
% 5.82/6.12 thf(fact_4955_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.12 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) )
% 5.82/6.12 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa ) )
% 5.82/6.12 => ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa ) )
% 5.82/6.12 => ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 )
% 5.82/6.12 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.82/6.12 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa ) )
% 5.82/6.12 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % VEBT_internal.membermima.pelims(3)
% 5.82/6.12 thf(fact_4956_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.82/6.12 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ( ~ Y3
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.82/6.12 => ( ~ Y3
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 )
% 5.82/6.12 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % VEBT_internal.membermima.pelims(1)
% 5.82/6.12 thf(fact_4957_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.82/6.12 ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 )
% 5.82/6.12 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.82/6.12 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa ) )
% 5.82/6.12 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % VEBT_internal.membermima.pelims(2)
% 5.82/6.12 thf(fact_4958_set__bit__0,axiom,
% 5.82/6.12 ! [A2: int] :
% 5.82/6.12 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A2 )
% 5.82/6.12 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_bit_0
% 5.82/6.12 thf(fact_4959_set__bit__0,axiom,
% 5.82/6.12 ! [A2: nat] :
% 5.82/6.12 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A2 )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_bit_0
% 5.82/6.12 thf(fact_4960_pred__less__length__list,axiom,
% 5.82/6.12 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.12 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.82/6.12 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % pred_less_length_list
% 5.82/6.12 thf(fact_4961_pred__lesseq__max,axiom,
% 5.82/6.12 ! [Deg: nat,X2: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.12 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.82/6.12 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % pred_lesseq_max
% 5.82/6.12 thf(fact_4962_add__shift,axiom,
% 5.82/6.12 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.12 ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.82/6.12 = Z )
% 5.82/6.12 = ( ( vEBT_VEBT_add @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.82/6.12 = ( some_nat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % add_shift
% 5.82/6.12 thf(fact_4963_mul__shift,axiom,
% 5.82/6.12 ! [X2: nat,Y3: nat,Z: nat] :
% 5.82/6.12 ( ( ( times_times_nat @ X2 @ Y3 )
% 5.82/6.12 = Z )
% 5.82/6.12 = ( ( vEBT_VEBT_mul @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.82/6.12 = ( some_nat @ Z ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % mul_shift
% 5.82/6.12 thf(fact_4964_add__def,axiom,
% 5.82/6.12 ( vEBT_VEBT_add
% 5.82/6.12 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % add_def
% 5.82/6.12 thf(fact_4965_mul__def,axiom,
% 5.82/6.12 ( vEBT_VEBT_mul
% 5.82/6.12 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % mul_def
% 5.82/6.12 thf(fact_4966_set__bit__nonnegative__int__iff,axiom,
% 5.82/6.12 ! [N: nat,K: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.82/6.12 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_bit_nonnegative_int_iff
% 5.82/6.12 thf(fact_4967_succ__less__length__list,axiom,
% 5.82/6.12 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.12 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.82/6.12 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ none_nat
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % succ_less_length_list
% 5.82/6.12 thf(fact_4968_succ__greatereq__min,axiom,
% 5.82/6.12 ! [Deg: nat,Mi: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.82/6.12 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.82/6.12 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ none_nat
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % succ_greatereq_min
% 5.82/6.12 thf(fact_4969_set__bit__greater__eq,axiom,
% 5.82/6.12 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_bit_greater_eq
% 5.82/6.12 thf(fact_4970_vebt__pred_Osimps_I7_J,axiom,
% 5.82/6.12 ! [Ma: nat,X2: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.12 ( ( ( ord_less_nat @ Ma @ X2 )
% 5.82/6.12 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( some_nat @ Ma ) ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.82/6.12 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_pred.simps(7)
% 5.82/6.12 thf(fact_4971_vebt__succ_Osimps_I6_J,axiom,
% 5.82/6.12 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.12 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.12 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( some_nat @ Mi ) ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.82/6.12 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ none_nat
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_succ.simps(6)
% 5.82/6.12 thf(fact_4972_vebt__pred_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 5.82/6.12 ( ( ( vEBT_vebt_pred @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( Y3 != none_nat ) ) )
% 5.82/6.12 => ( ! [A3: $o] :
% 5.82/6.12 ( ? [Uw2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ~ ( ( A3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.12 & ( ~ A3
% 5.82/6.12 => ( Y3 = none_nat ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ? [Va3: nat] :
% 5.82/6.12 ( Xa
% 5.82/6.12 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.12 => ~ ( ( B3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.12 & ( ~ B3
% 5.82/6.12 => ( ( A3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.12 & ( ~ A3
% 5.82/6.12 => ( Y3 = none_nat ) ) ) ) ) ) )
% 5.82/6.12 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.82/6.12 => ( Y3 != none_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.82/6.12 => ( Y3 != none_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.82/6.12 => ( Y3 != none_nat ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ Ma2 ) ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_pred.elims
% 5.82/6.12 thf(fact_4973_vebt__succ_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 5.82/6.12 ( ( ( vEBT_vebt_succ @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ! [Uu2: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ~ ( ( B3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.12 & ( ~ B3
% 5.82/6.12 => ( Y3 = none_nat ) ) ) ) )
% 5.82/6.12 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( ? [N3: nat] :
% 5.82/6.12 ( Xa
% 5.82/6.12 = ( suc @ N3 ) )
% 5.82/6.12 => ( Y3 != none_nat ) ) )
% 5.82/6.12 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( Y3 != none_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.82/6.12 => ( Y3 != none_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.82/6.12 => ( Y3 != none_nat ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ Mi2 ) ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ none_nat
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_succ.elims
% 5.82/6.12 thf(fact_4974_vebt__succ_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 5.82/6.12 ( ( ( vEBT_vebt_succ @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( ( B3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.12 & ( ~ B3
% 5.82/6.12 => ( Y3 = none_nat ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [Uv2: $o,Uw2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ! [N3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ N3 ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.82/6.12 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ Mi2 ) ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ none_nat
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_succ.pelims
% 5.82/6.12 thf(fact_4975_vebt__pred_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 5.82/6.12 ( ( ( vEBT_vebt_pred @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,Uw2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( ( ( A3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.12 & ( ~ A3
% 5.82/6.12 => ( Y3 = none_nat ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ! [Va3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.12 => ( ( ( B3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.12 & ( ~ B3
% 5.82/6.12 => ( ( A3
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.12 & ( ~ A3
% 5.82/6.12 => ( Y3 = none_nat ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.82/6.12 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.82/6.12 => ( ( Y3 = none_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( ( ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( some_nat @ Ma2 ) ) )
% 5.82/6.12 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.82/6.12 => ( Y3
% 5.82/6.12 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( if_option_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.82/6.12 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ none_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % vebt_pred.pelims
% 5.82/6.12 thf(fact_4976_succ__bound__size__univ,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ( U
% 5.82/6.12 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.12 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X2 ) ) @ ( 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 ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % succ_bound_size_univ
% 5.82/6.12 thf(fact_4977_insert__bound__size__univ,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ( U
% 5.82/6.12 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.12 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_bound_size_univ
% 5.82/6.12 thf(fact_4978_pred__bound__size__univ,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ( U
% 5.82/6.12 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.12 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X2 ) ) @ ( 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 ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % pred_bound_size_univ
% 5.82/6.12 thf(fact_4979_delete__correct,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X2 ) )
% 5.82/6.12 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % delete_correct
% 5.82/6.12 thf(fact_4980_delete__correct_H,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X2 ) )
% 5.82/6.12 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % delete_correct'
% 5.82/6.12 thf(fact_4981_insert__subset,axiom,
% 5.82/6.12 ! [X2: nat,A: set_nat,B: set_nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ A ) @ B )
% 5.82/6.12 = ( ( member_nat @ X2 @ B )
% 5.82/6.12 & ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_subset
% 5.82/6.12 thf(fact_4982_insert__subset,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A ) @ B )
% 5.82/6.12 = ( ( member_VEBT_VEBT @ X2 @ B )
% 5.82/6.12 & ( ord_le4337996190870823476T_VEBT @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_subset
% 5.82/6.12 thf(fact_4983_insert__subset,axiom,
% 5.82/6.12 ! [X2: real,A: set_real,B: set_real] :
% 5.82/6.12 ( ( ord_less_eq_set_real @ ( insert_real @ X2 @ A ) @ B )
% 5.82/6.12 = ( ( member_real @ X2 @ B )
% 5.82/6.12 & ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_subset
% 5.82/6.12 thf(fact_4984_insert__subset,axiom,
% 5.82/6.12 ! [X2: int,A: set_int,B: set_int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ ( insert_int @ X2 @ A ) @ B )
% 5.82/6.12 = ( ( member_int @ X2 @ B )
% 5.82/6.12 & ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_subset
% 5.82/6.12 thf(fact_4985_Diff__insert0,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ B ) )
% 5.82/6.12 = ( minus_5127226145743854075T_VEBT @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert0
% 5.82/6.12 thf(fact_4986_Diff__insert0,axiom,
% 5.82/6.12 ! [X2: real,A: set_real,B: set_real] :
% 5.82/6.12 ( ~ ( member_real @ X2 @ A )
% 5.82/6.12 => ( ( minus_minus_set_real @ A @ ( insert_real @ X2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_real @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert0
% 5.82/6.12 thf(fact_4987_Diff__insert0,axiom,
% 5.82/6.12 ! [X2: int,A: set_int,B: set_int] :
% 5.82/6.12 ( ~ ( member_int @ X2 @ A )
% 5.82/6.12 => ( ( minus_minus_set_int @ A @ ( insert_int @ X2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_int @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert0
% 5.82/6.12 thf(fact_4988_Diff__insert0,axiom,
% 5.82/6.12 ! [X2: nat,A: set_nat,B: set_nat] :
% 5.82/6.12 ( ~ ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_nat @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert0
% 5.82/6.12 thf(fact_4989_insert__Diff1,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,B: set_VEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ( member_VEBT_VEBT @ X2 @ B )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_5127226145743854075T_VEBT @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff1
% 5.82/6.12 thf(fact_4990_insert__Diff1,axiom,
% 5.82/6.12 ! [X2: real,B: set_real,A: set_real] :
% 5.82/6.12 ( ( member_real @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_minus_set_real @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff1
% 5.82/6.12 thf(fact_4991_insert__Diff1,axiom,
% 5.82/6.12 ! [X2: int,B: set_int,A: set_int] :
% 5.82/6.12 ( ( member_int @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_minus_set_int @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff1
% 5.82/6.12 thf(fact_4992_insert__Diff1,axiom,
% 5.82/6.12 ! [X2: nat,B: set_nat,A: set_nat] :
% 5.82/6.12 ( ( member_nat @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_minus_set_nat @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff1
% 5.82/6.12 thf(fact_4993_singleton__conv2,axiom,
% 5.82/6.12 ! [A2: vEBT_VEBT] :
% 5.82/6.12 ( ( collect_VEBT_VEBT
% 5.82/6.12 @ ( ^ [Y6: vEBT_VEBT,Z3: vEBT_VEBT] : ( Y6 = Z3 )
% 5.82/6.12 @ A2 ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv2
% 5.82/6.12 thf(fact_4994_singleton__conv2,axiom,
% 5.82/6.12 ! [A2: complex] :
% 5.82/6.12 ( ( collect_complex
% 5.82/6.12 @ ( ^ [Y6: complex,Z3: complex] : ( Y6 = Z3 )
% 5.82/6.12 @ A2 ) )
% 5.82/6.12 = ( insert_complex @ A2 @ bot_bot_set_complex ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv2
% 5.82/6.12 thf(fact_4995_singleton__conv2,axiom,
% 5.82/6.12 ! [A2: product_prod_int_int] :
% 5.82/6.12 ( ( collec213857154873943460nt_int
% 5.82/6.12 @ ( ^ [Y6: product_prod_int_int,Z3: product_prod_int_int] : ( Y6 = Z3 )
% 5.82/6.12 @ A2 ) )
% 5.82/6.12 = ( insert5033312907999012233nt_int @ A2 @ bot_bo1796632182523588997nt_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv2
% 5.82/6.12 thf(fact_4996_singleton__conv2,axiom,
% 5.82/6.12 ! [A2: nat] :
% 5.82/6.12 ( ( collect_nat
% 5.82/6.12 @ ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.82/6.12 @ A2 ) )
% 5.82/6.12 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv2
% 5.82/6.12 thf(fact_4997_singleton__conv2,axiom,
% 5.82/6.12 ! [A2: int] :
% 5.82/6.12 ( ( collect_int
% 5.82/6.12 @ ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.82/6.12 @ A2 ) )
% 5.82/6.12 = ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv2
% 5.82/6.12 thf(fact_4998_singleton__conv,axiom,
% 5.82/6.12 ! [A2: vEBT_VEBT] :
% 5.82/6.12 ( ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [X3: vEBT_VEBT] : ( X3 = A2 ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv
% 5.82/6.12 thf(fact_4999_singleton__conv,axiom,
% 5.82/6.12 ! [A2: complex] :
% 5.82/6.12 ( ( collect_complex
% 5.82/6.12 @ ^ [X3: complex] : ( X3 = A2 ) )
% 5.82/6.12 = ( insert_complex @ A2 @ bot_bot_set_complex ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv
% 5.82/6.12 thf(fact_5000_singleton__conv,axiom,
% 5.82/6.12 ! [A2: product_prod_int_int] :
% 5.82/6.12 ( ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [X3: product_prod_int_int] : ( X3 = A2 ) )
% 5.82/6.12 = ( insert5033312907999012233nt_int @ A2 @ bot_bo1796632182523588997nt_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv
% 5.82/6.12 thf(fact_5001_singleton__conv,axiom,
% 5.82/6.12 ! [A2: nat] :
% 5.82/6.12 ( ( collect_nat
% 5.82/6.12 @ ^ [X3: nat] : ( X3 = A2 ) )
% 5.82/6.12 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv
% 5.82/6.12 thf(fact_5002_singleton__conv,axiom,
% 5.82/6.12 ! [A2: int] :
% 5.82/6.12 ( ( collect_int
% 5.82/6.12 @ ^ [X3: int] : ( X3 = A2 ) )
% 5.82/6.12 = ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_conv
% 5.82/6.12 thf(fact_5003_singleton__insert__inj__eq,axiom,
% 5.82/6.12 ! [B2: vEBT_VEBT,A2: vEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ( insert_VEBT_VEBT @ B2 @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ A ) )
% 5.82/6.12 = ( ( A2 = B2 )
% 5.82/6.12 & ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ B2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_insert_inj_eq
% 5.82/6.12 thf(fact_5004_singleton__insert__inj__eq,axiom,
% 5.82/6.12 ! [B2: nat,A2: nat,A: set_nat] :
% 5.82/6.12 ( ( ( insert_nat @ B2 @ bot_bot_set_nat )
% 5.82/6.12 = ( insert_nat @ A2 @ A ) )
% 5.82/6.12 = ( ( A2 = B2 )
% 5.82/6.12 & ( ord_less_eq_set_nat @ A @ ( insert_nat @ B2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_insert_inj_eq
% 5.82/6.12 thf(fact_5005_singleton__insert__inj__eq,axiom,
% 5.82/6.12 ! [B2: int,A2: int,A: set_int] :
% 5.82/6.12 ( ( ( insert_int @ B2 @ bot_bot_set_int )
% 5.82/6.12 = ( insert_int @ A2 @ A ) )
% 5.82/6.12 = ( ( A2 = B2 )
% 5.82/6.12 & ( ord_less_eq_set_int @ A @ ( insert_int @ B2 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_insert_inj_eq
% 5.82/6.12 thf(fact_5006_singleton__insert__inj__eq_H,axiom,
% 5.82/6.12 ! [A2: vEBT_VEBT,A: set_VEBT_VEBT,B2: vEBT_VEBT] :
% 5.82/6.12 ( ( ( insert_VEBT_VEBT @ A2 @ A )
% 5.82/6.12 = ( insert_VEBT_VEBT @ B2 @ bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.12 = ( ( A2 = B2 )
% 5.82/6.12 & ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ B2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_insert_inj_eq'
% 5.82/6.12 thf(fact_5007_singleton__insert__inj__eq_H,axiom,
% 5.82/6.12 ! [A2: nat,A: set_nat,B2: nat] :
% 5.82/6.12 ( ( ( insert_nat @ A2 @ A )
% 5.82/6.12 = ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 5.82/6.12 = ( ( A2 = B2 )
% 5.82/6.12 & ( ord_less_eq_set_nat @ A @ ( insert_nat @ B2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_insert_inj_eq'
% 5.82/6.12 thf(fact_5008_singleton__insert__inj__eq_H,axiom,
% 5.82/6.12 ! [A2: int,A: set_int,B2: int] :
% 5.82/6.12 ( ( ( insert_int @ A2 @ A )
% 5.82/6.12 = ( insert_int @ B2 @ bot_bot_set_int ) )
% 5.82/6.12 = ( ( A2 = B2 )
% 5.82/6.12 & ( ord_less_eq_set_int @ A @ ( insert_int @ B2 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % singleton_insert_inj_eq'
% 5.82/6.12 thf(fact_5009_insert__Diff__single,axiom,
% 5.82/6.12 ! [A2: vEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ( insert_VEBT_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_single
% 5.82/6.12 thf(fact_5010_insert__Diff__single,axiom,
% 5.82/6.12 ! [A2: int,A: set_int] :
% 5.82/6.12 ( ( insert_int @ A2 @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.12 = ( insert_int @ A2 @ A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_single
% 5.82/6.12 thf(fact_5011_insert__Diff__single,axiom,
% 5.82/6.12 ! [A2: nat,A: set_nat] :
% 5.82/6.12 ( ( insert_nat @ A2 @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.12 = ( insert_nat @ A2 @ A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_single
% 5.82/6.12 thf(fact_5012_insert__compr,axiom,
% 5.82/6.12 ( insert_VEBT_VEBT
% 5.82/6.12 = ( ^ [A5: vEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.82/6.12 ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.12 ( ( X3 = A5 )
% 5.82/6.12 | ( member_VEBT_VEBT @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_compr
% 5.82/6.12 thf(fact_5013_insert__compr,axiom,
% 5.82/6.12 ( insert_real
% 5.82/6.12 = ( ^ [A5: real,B5: set_real] :
% 5.82/6.12 ( collect_real
% 5.82/6.12 @ ^ [X3: real] :
% 5.82/6.12 ( ( X3 = A5 )
% 5.82/6.12 | ( member_real @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_compr
% 5.82/6.12 thf(fact_5014_insert__compr,axiom,
% 5.82/6.12 ( insert_nat
% 5.82/6.12 = ( ^ [A5: nat,B5: set_nat] :
% 5.82/6.12 ( collect_nat
% 5.82/6.12 @ ^ [X3: nat] :
% 5.82/6.12 ( ( X3 = A5 )
% 5.82/6.12 | ( member_nat @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_compr
% 5.82/6.12 thf(fact_5015_insert__compr,axiom,
% 5.82/6.12 ( insert_int
% 5.82/6.12 = ( ^ [A5: int,B5: set_int] :
% 5.82/6.12 ( collect_int
% 5.82/6.12 @ ^ [X3: int] :
% 5.82/6.12 ( ( X3 = A5 )
% 5.82/6.12 | ( member_int @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_compr
% 5.82/6.12 thf(fact_5016_insert__compr,axiom,
% 5.82/6.12 ( insert_complex
% 5.82/6.12 = ( ^ [A5: complex,B5: set_complex] :
% 5.82/6.12 ( collect_complex
% 5.82/6.12 @ ^ [X3: complex] :
% 5.82/6.12 ( ( X3 = A5 )
% 5.82/6.12 | ( member_complex @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_compr
% 5.82/6.12 thf(fact_5017_insert__compr,axiom,
% 5.82/6.12 ( insert5033312907999012233nt_int
% 5.82/6.12 = ( ^ [A5: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 5.82/6.12 ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [X3: product_prod_int_int] :
% 5.82/6.12 ( ( X3 = A5 )
% 5.82/6.12 | ( member5262025264175285858nt_int @ X3 @ B5 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_compr
% 5.82/6.12 thf(fact_5018_insert__Collect,axiom,
% 5.82/6.12 ! [A2: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.12 ( ( insert_VEBT_VEBT @ A2 @ ( collect_VEBT_VEBT @ P ) )
% 5.82/6.12 = ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [U2: vEBT_VEBT] :
% 5.82/6.12 ( ( U2 != A2 )
% 5.82/6.12 => ( P @ U2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Collect
% 5.82/6.12 thf(fact_5019_insert__Collect,axiom,
% 5.82/6.12 ! [A2: nat,P: nat > $o] :
% 5.82/6.12 ( ( insert_nat @ A2 @ ( collect_nat @ P ) )
% 5.82/6.12 = ( collect_nat
% 5.82/6.12 @ ^ [U2: nat] :
% 5.82/6.12 ( ( U2 != A2 )
% 5.82/6.12 => ( P @ U2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Collect
% 5.82/6.12 thf(fact_5020_insert__Collect,axiom,
% 5.82/6.12 ! [A2: int,P: int > $o] :
% 5.82/6.12 ( ( insert_int @ A2 @ ( collect_int @ P ) )
% 5.82/6.12 = ( collect_int
% 5.82/6.12 @ ^ [U2: int] :
% 5.82/6.12 ( ( U2 != A2 )
% 5.82/6.12 => ( P @ U2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Collect
% 5.82/6.12 thf(fact_5021_insert__Collect,axiom,
% 5.82/6.12 ! [A2: complex,P: complex > $o] :
% 5.82/6.12 ( ( insert_complex @ A2 @ ( collect_complex @ P ) )
% 5.82/6.12 = ( collect_complex
% 5.82/6.12 @ ^ [U2: complex] :
% 5.82/6.12 ( ( U2 != A2 )
% 5.82/6.12 => ( P @ U2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Collect
% 5.82/6.12 thf(fact_5022_insert__Collect,axiom,
% 5.82/6.12 ! [A2: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.82/6.12 ( ( insert5033312907999012233nt_int @ A2 @ ( collec213857154873943460nt_int @ P ) )
% 5.82/6.12 = ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [U2: product_prod_int_int] :
% 5.82/6.12 ( ( U2 != A2 )
% 5.82/6.12 => ( P @ U2 ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Collect
% 5.82/6.12 thf(fact_5023_insert__mono,axiom,
% 5.82/6.12 ! [C: set_nat,D: set_nat,A2: nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ C @ D )
% 5.82/6.12 => ( ord_less_eq_set_nat @ ( insert_nat @ A2 @ C ) @ ( insert_nat @ A2 @ D ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_mono
% 5.82/6.12 thf(fact_5024_insert__mono,axiom,
% 5.82/6.12 ! [C: set_VEBT_VEBT,D: set_VEBT_VEBT,A2: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ C @ D )
% 5.82/6.12 => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ A2 @ C ) @ ( insert_VEBT_VEBT @ A2 @ D ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_mono
% 5.82/6.12 thf(fact_5025_insert__mono,axiom,
% 5.82/6.12 ! [C: set_int,D: set_int,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ C @ D )
% 5.82/6.12 => ( ord_less_eq_set_int @ ( insert_int @ A2 @ C ) @ ( insert_int @ A2 @ D ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_mono
% 5.82/6.12 thf(fact_5026_subset__insert,axiom,
% 5.82/6.12 ! [X2: nat,A: set_nat,B: set_nat] :
% 5.82/6.12 ( ~ ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ X2 @ B ) )
% 5.82/6.12 = ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert
% 5.82/6.12 thf(fact_5027_subset__insert,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ B ) )
% 5.82/6.12 = ( ord_le4337996190870823476T_VEBT @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert
% 5.82/6.12 thf(fact_5028_subset__insert,axiom,
% 5.82/6.12 ! [X2: real,A: set_real,B: set_real] :
% 5.82/6.12 ( ~ ( member_real @ X2 @ A )
% 5.82/6.12 => ( ( ord_less_eq_set_real @ A @ ( insert_real @ X2 @ B ) )
% 5.82/6.12 = ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert
% 5.82/6.12 thf(fact_5029_subset__insert,axiom,
% 5.82/6.12 ! [X2: int,A: set_int,B: set_int] :
% 5.82/6.12 ( ~ ( member_int @ X2 @ A )
% 5.82/6.12 => ( ( ord_less_eq_set_int @ A @ ( insert_int @ X2 @ B ) )
% 5.82/6.12 = ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert
% 5.82/6.12 thf(fact_5030_subset__insertI,axiom,
% 5.82/6.12 ! [B: set_nat,A2: nat] : ( ord_less_eq_set_nat @ B @ ( insert_nat @ A2 @ B ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insertI
% 5.82/6.12 thf(fact_5031_subset__insertI,axiom,
% 5.82/6.12 ! [B: set_VEBT_VEBT,A2: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ B @ ( insert_VEBT_VEBT @ A2 @ B ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insertI
% 5.82/6.12 thf(fact_5032_subset__insertI,axiom,
% 5.82/6.12 ! [B: set_int,A2: int] : ( ord_less_eq_set_int @ B @ ( insert_int @ A2 @ B ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insertI
% 5.82/6.12 thf(fact_5033_subset__insertI2,axiom,
% 5.82/6.12 ! [A: set_nat,B: set_nat,B2: nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.12 => ( ord_less_eq_set_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insertI2
% 5.82/6.12 thf(fact_5034_subset__insertI2,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,B2: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.12 => ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ B2 @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insertI2
% 5.82/6.12 thf(fact_5035_subset__insertI2,axiom,
% 5.82/6.12 ! [A: set_int,B: set_int,B2: int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.12 => ( ord_less_eq_set_int @ A @ ( insert_int @ B2 @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insertI2
% 5.82/6.12 thf(fact_5036_insert__Diff__if,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,B: set_VEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ( member_VEBT_VEBT @ X2 @ B )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_5127226145743854075T_VEBT @ A @ B ) ) )
% 5.82/6.12 & ( ~ ( member_VEBT_VEBT @ X2 @ B )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A ) @ B )
% 5.82/6.12 = ( insert_VEBT_VEBT @ X2 @ ( minus_5127226145743854075T_VEBT @ A @ B ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_if
% 5.82/6.12 thf(fact_5037_insert__Diff__if,axiom,
% 5.82/6.12 ! [X2: real,B: set_real,A: set_real] :
% 5.82/6.12 ( ( ( member_real @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_minus_set_real @ A @ B ) ) )
% 5.82/6.12 & ( ~ ( member_real @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A ) @ B )
% 5.82/6.12 = ( insert_real @ X2 @ ( minus_minus_set_real @ A @ B ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_if
% 5.82/6.12 thf(fact_5038_insert__Diff__if,axiom,
% 5.82/6.12 ! [X2: int,B: set_int,A: set_int] :
% 5.82/6.12 ( ( ( member_int @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_minus_set_int @ A @ B ) ) )
% 5.82/6.12 & ( ~ ( member_int @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A ) @ B )
% 5.82/6.12 = ( insert_int @ X2 @ ( minus_minus_set_int @ A @ B ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_if
% 5.82/6.12 thf(fact_5039_insert__Diff__if,axiom,
% 5.82/6.12 ! [X2: nat,B: set_nat,A: set_nat] :
% 5.82/6.12 ( ( ( member_nat @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A ) @ B )
% 5.82/6.12 = ( minus_minus_set_nat @ A @ B ) ) )
% 5.82/6.12 & ( ~ ( member_nat @ X2 @ B )
% 5.82/6.12 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A ) @ B )
% 5.82/6.12 = ( insert_nat @ X2 @ ( minus_minus_set_nat @ A @ B ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff_if
% 5.82/6.12 thf(fact_5040_Collect__conv__if2,axiom,
% 5.82/6.12 ! [P: vEBT_VEBT > $o,A2: vEBT_VEBT] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if2
% 5.82/6.12 thf(fact_5041_Collect__conv__if2,axiom,
% 5.82/6.12 ! [P: complex > $o,A2: complex] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_complex
% 5.82/6.12 @ ^ [X3: complex] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_complex
% 5.82/6.12 @ ^ [X3: complex] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bot_set_complex ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if2
% 5.82/6.12 thf(fact_5042_Collect__conv__if2,axiom,
% 5.82/6.12 ! [P: product_prod_int_int > $o,A2: product_prod_int_int] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [X3: product_prod_int_int] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert5033312907999012233nt_int @ A2 @ bot_bo1796632182523588997nt_int ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [X3: product_prod_int_int] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bo1796632182523588997nt_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if2
% 5.82/6.12 thf(fact_5043_Collect__conv__if2,axiom,
% 5.82/6.12 ! [P: nat > $o,A2: nat] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_nat
% 5.82/6.12 @ ^ [X3: nat] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_nat
% 5.82/6.12 @ ^ [X3: nat] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bot_set_nat ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if2
% 5.82/6.12 thf(fact_5044_Collect__conv__if2,axiom,
% 5.82/6.12 ! [P: int > $o,A2: int] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_int
% 5.82/6.12 @ ^ [X3: int] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_int
% 5.82/6.12 @ ^ [X3: int] :
% 5.82/6.12 ( ( A2 = X3 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bot_set_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if2
% 5.82/6.12 thf(fact_5045_Collect__conv__if,axiom,
% 5.82/6.12 ! [P: vEBT_VEBT > $o,A2: vEBT_VEBT] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_VEBT_VEBT
% 5.82/6.12 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if
% 5.82/6.12 thf(fact_5046_Collect__conv__if,axiom,
% 5.82/6.12 ! [P: complex > $o,A2: complex] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_complex
% 5.82/6.12 @ ^ [X3: complex] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_complex
% 5.82/6.12 @ ^ [X3: complex] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bot_set_complex ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if
% 5.82/6.12 thf(fact_5047_Collect__conv__if,axiom,
% 5.82/6.12 ! [P: product_prod_int_int > $o,A2: product_prod_int_int] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [X3: product_prod_int_int] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert5033312907999012233nt_int @ A2 @ bot_bo1796632182523588997nt_int ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collec213857154873943460nt_int
% 5.82/6.12 @ ^ [X3: product_prod_int_int] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bo1796632182523588997nt_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if
% 5.82/6.12 thf(fact_5048_Collect__conv__if,axiom,
% 5.82/6.12 ! [P: nat > $o,A2: nat] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_nat
% 5.82/6.12 @ ^ [X3: nat] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_nat
% 5.82/6.12 @ ^ [X3: nat] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bot_set_nat ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if
% 5.82/6.12 thf(fact_5049_Collect__conv__if,axiom,
% 5.82/6.12 ! [P: int > $o,A2: int] :
% 5.82/6.12 ( ( ( P @ A2 )
% 5.82/6.12 => ( ( collect_int
% 5.82/6.12 @ ^ [X3: int] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.12 & ( ~ ( P @ A2 )
% 5.82/6.12 => ( ( collect_int
% 5.82/6.12 @ ^ [X3: int] :
% 5.82/6.12 ( ( X3 = A2 )
% 5.82/6.12 & ( P @ X3 ) ) )
% 5.82/6.12 = bot_bot_set_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Collect_conv_if
% 5.82/6.12 thf(fact_5050_subset__singletonD,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.12 => ( ( A = bot_bo8194388402131092736T_VEBT )
% 5.82/6.12 | ( A
% 5.82/6.12 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_singletonD
% 5.82/6.12 thf(fact_5051_subset__singletonD,axiom,
% 5.82/6.12 ! [A: set_nat,X2: nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.82/6.12 => ( ( A = bot_bot_set_nat )
% 5.82/6.12 | ( A
% 5.82/6.12 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_singletonD
% 5.82/6.12 thf(fact_5052_subset__singletonD,axiom,
% 5.82/6.12 ! [A: set_int,X2: int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.82/6.12 => ( ( A = bot_bot_set_int )
% 5.82/6.12 | ( A
% 5.82/6.12 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_singletonD
% 5.82/6.12 thf(fact_5053_subset__singleton__iff,axiom,
% 5.82/6.12 ! [X: set_VEBT_VEBT,A2: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ X @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.12 = ( ( X = bot_bo8194388402131092736T_VEBT )
% 5.82/6.12 | ( X
% 5.82/6.12 = ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_singleton_iff
% 5.82/6.12 thf(fact_5054_subset__singleton__iff,axiom,
% 5.82/6.12 ! [X: set_nat,A2: nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ X @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 5.82/6.12 = ( ( X = bot_bot_set_nat )
% 5.82/6.12 | ( X
% 5.82/6.12 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_singleton_iff
% 5.82/6.12 thf(fact_5055_subset__singleton__iff,axiom,
% 5.82/6.12 ! [X: set_int,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ X @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 5.82/6.12 = ( ( X = bot_bot_set_int )
% 5.82/6.12 | ( X
% 5.82/6.12 = ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_singleton_iff
% 5.82/6.12 thf(fact_5056_Diff__insert,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,A2: vEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ B ) )
% 5.82/6.12 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ B ) @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert
% 5.82/6.12 thf(fact_5057_Diff__insert,axiom,
% 5.82/6.12 ! [A: set_int,A2: int,B: set_int] :
% 5.82/6.12 ( ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_int @ ( minus_minus_set_int @ A @ B ) @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert
% 5.82/6.12 thf(fact_5058_Diff__insert,axiom,
% 5.82/6.12 ! [A: set_nat,A2: nat,B: set_nat] :
% 5.82/6.12 ( ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert
% 5.82/6.12 thf(fact_5059_insert__Diff,axiom,
% 5.82/6.12 ! [A2: vEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.12 => ( ( insert_VEBT_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff
% 5.82/6.12 thf(fact_5060_insert__Diff,axiom,
% 5.82/6.12 ! [A2: real,A: set_real] :
% 5.82/6.12 ( ( member_real @ A2 @ A )
% 5.82/6.12 => ( ( insert_real @ A2 @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff
% 5.82/6.12 thf(fact_5061_insert__Diff,axiom,
% 5.82/6.12 ! [A2: int,A: set_int] :
% 5.82/6.12 ( ( member_int @ A2 @ A )
% 5.82/6.12 => ( ( insert_int @ A2 @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff
% 5.82/6.12 thf(fact_5062_insert__Diff,axiom,
% 5.82/6.12 ! [A2: nat,A: set_nat] :
% 5.82/6.12 ( ( member_nat @ A2 @ A )
% 5.82/6.12 => ( ( insert_nat @ A2 @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_Diff
% 5.82/6.12 thf(fact_5063_Diff__insert2,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,A2: vEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ B ) )
% 5.82/6.12 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) @ B ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert2
% 5.82/6.12 thf(fact_5064_Diff__insert2,axiom,
% 5.82/6.12 ! [A: set_int,A2: int,B: set_int] :
% 5.82/6.12 ( ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ B ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert2
% 5.82/6.12 thf(fact_5065_Diff__insert2,axiom,
% 5.82/6.12 ! [A: set_nat,A2: nat,B: set_nat] :
% 5.82/6.12 ( ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B ) )
% 5.82/6.12 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ B ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert2
% 5.82/6.12 thf(fact_5066_Diff__insert__absorb,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A ) @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert_absorb
% 5.82/6.12 thf(fact_5067_Diff__insert__absorb,axiom,
% 5.82/6.12 ! [X2: real,A: set_real] :
% 5.82/6.12 ( ~ ( member_real @ X2 @ A )
% 5.82/6.12 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A ) @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert_absorb
% 5.82/6.12 thf(fact_5068_Diff__insert__absorb,axiom,
% 5.82/6.12 ! [X2: int,A: set_int] :
% 5.82/6.12 ( ~ ( member_int @ X2 @ A )
% 5.82/6.12 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A ) @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert_absorb
% 5.82/6.12 thf(fact_5069_Diff__insert__absorb,axiom,
% 5.82/6.12 ! [X2: nat,A: set_nat] :
% 5.82/6.12 ( ~ ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.82/6.12 = A ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_insert_absorb
% 5.82/6.12 thf(fact_5070_set__minus__singleton__eq,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,X: set_VEBT_VEBT] :
% 5.82/6.12 ( ~ ( member_VEBT_VEBT @ X2 @ X )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ X @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.12 = X ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_minus_singleton_eq
% 5.82/6.12 thf(fact_5071_set__minus__singleton__eq,axiom,
% 5.82/6.12 ! [X2: real,X: set_real] :
% 5.82/6.12 ( ~ ( member_real @ X2 @ X )
% 5.82/6.12 => ( ( minus_minus_set_real @ X @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.82/6.12 = X ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_minus_singleton_eq
% 5.82/6.12 thf(fact_5072_set__minus__singleton__eq,axiom,
% 5.82/6.12 ! [X2: int,X: set_int] :
% 5.82/6.12 ( ~ ( member_int @ X2 @ X )
% 5.82/6.12 => ( ( minus_minus_set_int @ X @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.82/6.12 = X ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_minus_singleton_eq
% 5.82/6.12 thf(fact_5073_set__minus__singleton__eq,axiom,
% 5.82/6.12 ! [X2: nat,X: set_nat] :
% 5.82/6.12 ( ~ ( member_nat @ X2 @ X )
% 5.82/6.12 => ( ( minus_minus_set_nat @ X @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.82/6.12 = X ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_minus_singleton_eq
% 5.82/6.12 thf(fact_5074_insert__minus__eq,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT,A: set_VEBT_VEBT] :
% 5.82/6.12 ( ( X2 != Y3 )
% 5.82/6.12 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A ) @ ( insert_VEBT_VEBT @ Y3 @ bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ X2 @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ Y3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_minus_eq
% 5.82/6.12 thf(fact_5075_insert__minus__eq,axiom,
% 5.82/6.12 ! [X2: int,Y3: int,A: set_int] :
% 5.82/6.12 ( ( X2 != Y3 )
% 5.82/6.12 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A ) @ ( insert_int @ Y3 @ bot_bot_set_int ) )
% 5.82/6.12 = ( insert_int @ X2 @ ( minus_minus_set_int @ A @ ( insert_int @ Y3 @ bot_bot_set_int ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_minus_eq
% 5.82/6.12 thf(fact_5076_insert__minus__eq,axiom,
% 5.82/6.12 ! [X2: nat,Y3: nat,A: set_nat] :
% 5.82/6.12 ( ( X2 != Y3 )
% 5.82/6.12 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A ) @ ( insert_nat @ Y3 @ bot_bot_set_nat ) )
% 5.82/6.12 = ( insert_nat @ X2 @ ( minus_minus_set_nat @ A @ ( insert_nat @ Y3 @ bot_bot_set_nat ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_minus_eq
% 5.82/6.12 thf(fact_5077_subset__Diff__insert,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,X2: vEBT_VEBT,C: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ B @ ( insert_VEBT_VEBT @ X2 @ C ) ) )
% 5.82/6.12 = ( ( ord_le4337996190870823476T_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ B @ C ) )
% 5.82/6.12 & ~ ( member_VEBT_VEBT @ X2 @ A ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_Diff_insert
% 5.82/6.12 thf(fact_5078_subset__Diff__insert,axiom,
% 5.82/6.12 ! [A: set_real,B: set_real,X2: real,C: set_real] :
% 5.82/6.12 ( ( ord_less_eq_set_real @ A @ ( minus_minus_set_real @ B @ ( insert_real @ X2 @ C ) ) )
% 5.82/6.12 = ( ( ord_less_eq_set_real @ A @ ( minus_minus_set_real @ B @ C ) )
% 5.82/6.12 & ~ ( member_real @ X2 @ A ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_Diff_insert
% 5.82/6.12 thf(fact_5079_subset__Diff__insert,axiom,
% 5.82/6.12 ! [A: set_nat,B: set_nat,X2: nat,C: set_nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ A @ ( minus_minus_set_nat @ B @ ( insert_nat @ X2 @ C ) ) )
% 5.82/6.12 = ( ( ord_less_eq_set_nat @ A @ ( minus_minus_set_nat @ B @ C ) )
% 5.82/6.12 & ~ ( member_nat @ X2 @ A ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_Diff_insert
% 5.82/6.12 thf(fact_5080_subset__Diff__insert,axiom,
% 5.82/6.12 ! [A: set_int,B: set_int,X2: int,C: set_int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ A @ ( minus_minus_set_int @ B @ ( insert_int @ X2 @ C ) ) )
% 5.82/6.12 = ( ( ord_less_eq_set_int @ A @ ( minus_minus_set_int @ B @ C ) )
% 5.82/6.12 & ~ ( member_int @ X2 @ A ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_Diff_insert
% 5.82/6.12 thf(fact_5081_Diff__single__insert,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B )
% 5.82/6.12 => ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_single_insert
% 5.82/6.12 thf(fact_5082_Diff__single__insert,axiom,
% 5.82/6.12 ! [A: set_nat,X2: nat,B: set_nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B )
% 5.82/6.12 => ( ord_less_eq_set_nat @ A @ ( insert_nat @ X2 @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_single_insert
% 5.82/6.12 thf(fact_5083_Diff__single__insert,axiom,
% 5.82/6.12 ! [A: set_int,X2: int,B: set_int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B )
% 5.82/6.12 => ( ord_less_eq_set_int @ A @ ( insert_int @ X2 @ B ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Diff_single_insert
% 5.82/6.12 thf(fact_5084_subset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ord_le4337996190870823476T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ord_le4337996190870823476T_VEBT @ A @ B ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert_iff
% 5.82/6.12 thf(fact_5085_subset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_real,X2: real,B: set_real] :
% 5.82/6.12 ( ( ord_less_eq_set_real @ A @ ( insert_real @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_real @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_real @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_real @ A @ B ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert_iff
% 5.82/6.12 thf(fact_5086_subset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_nat,X2: nat,B: set_nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_nat @ A @ B ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert_iff
% 5.82/6.12 thf(fact_5087_subset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_int,X2: int,B: set_int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ A @ ( insert_int @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_int @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_int @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_int @ A @ B ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % subset_insert_iff
% 5.82/6.12 thf(fact_5088_atLeast0__atMost__Suc,axiom,
% 5.82/6.12 ! [N: nat] :
% 5.82/6.12 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.82/6.12 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeast0_atMost_Suc
% 5.82/6.12 thf(fact_5089_Icc__eq__insert__lb__nat,axiom,
% 5.82/6.12 ! [M: nat,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.12 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.82/6.12 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % Icc_eq_insert_lb_nat
% 5.82/6.12 thf(fact_5090_atLeastAtMostSuc__conv,axiom,
% 5.82/6.12 ! [M: nat,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.12 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.82/6.12 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastAtMostSuc_conv
% 5.82/6.12 thf(fact_5091_atLeastAtMost__insertL,axiom,
% 5.82/6.12 ! [M: nat,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.12 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.82/6.12 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastAtMost_insertL
% 5.82/6.12 thf(fact_5092_remove__subset,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,S: set_VEBT_VEBT] :
% 5.82/6.12 ( ( member_VEBT_VEBT @ X2 @ S )
% 5.82/6.12 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ S ) ) ).
% 5.82/6.12
% 5.82/6.12 % remove_subset
% 5.82/6.12 thf(fact_5093_remove__subset,axiom,
% 5.82/6.12 ! [X2: real,S: set_real] :
% 5.82/6.12 ( ( member_real @ X2 @ S )
% 5.82/6.12 => ( ord_less_set_real @ ( minus_minus_set_real @ S @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ S ) ) ).
% 5.82/6.12
% 5.82/6.12 % remove_subset
% 5.82/6.12 thf(fact_5094_remove__subset,axiom,
% 5.82/6.12 ! [X2: int,S: set_int] :
% 5.82/6.12 ( ( member_int @ X2 @ S )
% 5.82/6.12 => ( ord_less_set_int @ ( minus_minus_set_int @ S @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ S ) ) ).
% 5.82/6.12
% 5.82/6.12 % remove_subset
% 5.82/6.12 thf(fact_5095_remove__subset,axiom,
% 5.82/6.12 ! [X2: nat,S: set_nat] :
% 5.82/6.12 ( ( member_nat @ X2 @ S )
% 5.82/6.12 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ S ) ) ).
% 5.82/6.12
% 5.82/6.12 % remove_subset
% 5.82/6.12 thf(fact_5096_set__update__subset__insert,axiom,
% 5.82/6.12 ! [Xs: list_VEBT_VEBTi,I: nat,X2: vEBT_VEBTi] : ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) ) @ ( insert_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ Xs ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_update_subset_insert
% 5.82/6.12 thf(fact_5097_set__update__subset__insert,axiom,
% 5.82/6.12 ! [Xs: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) ) @ ( insert_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_update_subset_insert
% 5.82/6.12 thf(fact_5098_set__update__subset__insert,axiom,
% 5.82/6.12 ! [Xs: list_nat,I: nat,X2: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X2 ) ) @ ( insert_nat @ X2 @ ( set_nat2 @ Xs ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_update_subset_insert
% 5.82/6.12 thf(fact_5099_set__update__subset__insert,axiom,
% 5.82/6.12 ! [Xs: list_o,I: nat,X2: $o] : ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X2 ) ) @ ( insert_o @ X2 @ ( set_o2 @ Xs ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_update_subset_insert
% 5.82/6.12 thf(fact_5100_set__update__subset__insert,axiom,
% 5.82/6.12 ! [Xs: list_real,I: nat,X2: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X2 ) ) @ ( insert_real @ X2 @ ( set_real2 @ Xs ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_update_subset_insert
% 5.82/6.12 thf(fact_5101_set__update__subset__insert,axiom,
% 5.82/6.12 ! [Xs: list_int,I: nat,X2: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X2 ) ) @ ( insert_int @ X2 @ ( set_int2 @ Xs ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % set_update_subset_insert
% 5.82/6.12 thf(fact_5102_psubset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.12 ( ( ord_le3480810397992357184T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_VEBT_VEBT @ X2 @ B )
% 5.82/6.12 => ( ord_le3480810397992357184T_VEBT @ A @ B ) )
% 5.82/6.12 & ( ~ ( member_VEBT_VEBT @ X2 @ B )
% 5.82/6.12 => ( ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.12 => ( ord_le4337996190870823476T_VEBT @ A @ B ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % psubset_insert_iff
% 5.82/6.12 thf(fact_5103_psubset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_real,X2: real,B: set_real] :
% 5.82/6.12 ( ( ord_less_set_real @ A @ ( insert_real @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_real @ X2 @ B )
% 5.82/6.12 => ( ord_less_set_real @ A @ B ) )
% 5.82/6.12 & ( ~ ( member_real @ X2 @ B )
% 5.82/6.12 => ( ( ( member_real @ X2 @ A )
% 5.82/6.12 => ( ord_less_set_real @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_real @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_real @ A @ B ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % psubset_insert_iff
% 5.82/6.12 thf(fact_5104_psubset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_nat,X2: nat,B: set_nat] :
% 5.82/6.12 ( ( ord_less_set_nat @ A @ ( insert_nat @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_nat @ X2 @ B )
% 5.82/6.12 => ( ord_less_set_nat @ A @ B ) )
% 5.82/6.12 & ( ~ ( member_nat @ X2 @ B )
% 5.82/6.12 => ( ( ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_nat @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_nat @ A @ B ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % psubset_insert_iff
% 5.82/6.12 thf(fact_5105_psubset__insert__iff,axiom,
% 5.82/6.12 ! [A: set_int,X2: int,B: set_int] :
% 5.82/6.12 ( ( ord_less_set_int @ A @ ( insert_int @ X2 @ B ) )
% 5.82/6.12 = ( ( ( member_int @ X2 @ B )
% 5.82/6.12 => ( ord_less_set_int @ A @ B ) )
% 5.82/6.12 & ( ~ ( member_int @ X2 @ B )
% 5.82/6.12 => ( ( ( member_int @ X2 @ A )
% 5.82/6.12 => ( ord_less_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B ) )
% 5.82/6.12 & ( ~ ( member_int @ X2 @ A )
% 5.82/6.12 => ( ord_less_eq_set_int @ A @ B ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % psubset_insert_iff
% 5.82/6.12 thf(fact_5106_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.82/6.12 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) @ X2 )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 5.82/6.12 thf(fact_5107_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 5.82/6.12 ! [Uu: $o,Uv: $o] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(1)
% 5.82/6.12 thf(fact_5108_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 5.82/6.12 ! [Uv: $o,Uw: $o,N: nat] :
% 5.82/6.12 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(2)
% 5.82/6.12 thf(fact_5109_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J,axiom,
% 5.82/6.12 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(4)
% 5.82/6.12 thf(fact_5110_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 5.82/6.12 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.82/6.12 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(3)
% 5.82/6.12 thf(fact_5111_insert__swap__set__eq,axiom,
% 5.82/6.12 ! [I: nat,L: list_int,X2: int] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 5.82/6.12 => ( ( insert_int @ ( nth_int @ L @ I ) @ ( set_int2 @ ( list_update_int @ L @ I @ X2 ) ) )
% 5.82/6.12 = ( insert_int @ X2 @ ( set_int2 @ L ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_swap_set_eq
% 5.82/6.12 thf(fact_5112_insert__swap__set__eq,axiom,
% 5.82/6.12 ! [I: nat,L: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.12 => ( ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ L @ I ) @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ X2 ) ) )
% 5.82/6.12 = ( insert_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_swap_set_eq
% 5.82/6.12 thf(fact_5113_insert__swap__set__eq,axiom,
% 5.82/6.12 ! [I: nat,L: list_real,X2: real] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 5.82/6.12 => ( ( insert_real @ ( nth_real @ L @ I ) @ ( set_real2 @ ( list_update_real @ L @ I @ X2 ) ) )
% 5.82/6.12 = ( insert_real @ X2 @ ( set_real2 @ L ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_swap_set_eq
% 5.82/6.12 thf(fact_5114_insert__swap__set__eq,axiom,
% 5.82/6.12 ! [I: nat,L: list_o,X2: $o] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 5.82/6.12 => ( ( insert_o @ ( nth_o @ L @ I ) @ ( set_o2 @ ( list_update_o @ L @ I @ X2 ) ) )
% 5.82/6.12 = ( insert_o @ X2 @ ( set_o2 @ L ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_swap_set_eq
% 5.82/6.12 thf(fact_5115_insert__swap__set__eq,axiom,
% 5.82/6.12 ! [I: nat,L: list_nat,X2: nat] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 5.82/6.12 => ( ( insert_nat @ ( nth_nat @ L @ I ) @ ( set_nat2 @ ( list_update_nat @ L @ I @ X2 ) ) )
% 5.82/6.12 = ( insert_nat @ X2 @ ( set_nat2 @ L ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_swap_set_eq
% 5.82/6.12 thf(fact_5116_insert__swap__set__eq,axiom,
% 5.82/6.12 ! [I: nat,L: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 5.82/6.12 => ( ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ L @ I ) @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ X2 ) ) )
% 5.82/6.12 = ( insert_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_swap_set_eq
% 5.82/6.12 thf(fact_5117_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.82/6.12 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ X2 )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 5.82/6.12 thf(fact_5118_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J,axiom,
% 5.82/6.12 ! [A2: $o,B2: $o,Va: nat] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A2 @ B2 ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(3)
% 5.82/6.12 thf(fact_5119_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.82/6.12 ! [A2: $o,B2: $o,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A2 @ B2 ) @ X2 )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 5.82/6.12 thf(fact_5120_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 5.82/6.12 ! [V: product_prod_nat_nat,Vd3: list_VEBT_VEBT,Ve3: vEBT_VEBT,Vf2: nat] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd3 @ Ve3 ) @ Vf2 )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(5)
% 5.82/6.12 thf(fact_5121_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 5.82/6.12 ! [Uu: $o,B2: $o] :
% 5.82/6.12 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu @ B2 ) @ zero_zero_nat )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(1)
% 5.82/6.12 thf(fact_5122_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 5.82/6.12 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd3: vEBT_VEBT,Ve3: nat] :
% 5.82/6.12 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd3 ) @ Ve3 )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(4)
% 5.82/6.12 thf(fact_5123_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 5.82/6.12 ! [A2: $o,Uw: $o] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A2 @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(2)
% 5.82/6.12 thf(fact_5124_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 5.82/6.12 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(6)
% 5.82/6.12 thf(fact_5125_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 5.82/6.12 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.82/6.12 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(5)
% 5.82/6.12 thf(fact_5126_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 5.82/6.12 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 5.82/6.12 thf(fact_5127_insersimp,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,Y3: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.82/6.12 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y3 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insersimp
% 5.82/6.12 thf(fact_5128_insertsimp,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ( vEBT_VEBT_minNull @ T )
% 5.82/6.12 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insertsimp
% 5.82/6.12 thf(fact_5129_insert__bound__height,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % insert_bound_height
% 5.82/6.12 thf(fact_5130_pred__bound__height,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % pred_bound_height
% 5.82/6.12 thf(fact_5131_succ__bound__height,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.82/6.12 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.12 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % succ_bound_height
% 5.82/6.12 thf(fact_5132_listI__assn__wrap__insert,axiom,
% 5.82/6.12 ! [P: assn,Uu: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.12 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.12 => ( ( member_nat @ I @ I6 )
% 5.82/6.12 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I6 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.12 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % listI_assn_wrap_insert
% 5.82/6.12 thf(fact_5133_listI__assn__wrap__insert,axiom,
% 5.82/6.12 ! [P: assn,Uu: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F3: assn,C2: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.12 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.12 => ( ( member_nat @ I @ I6 )
% 5.82/6.12 => ( ( hoare_hoare_triple_o @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I6 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.12 => ( hoare_hoare_triple_o @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % listI_assn_wrap_insert
% 5.82/6.12 thf(fact_5134_listI__assn__wrap__insert,axiom,
% 5.82/6.12 ! [P: assn,Uu: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F3: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.12 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.12 => ( ( member_nat @ I @ I6 )
% 5.82/6.12 => ( ( hoare_7629718768684598413on_nat @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I6 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.12 => ( hoare_7629718768684598413on_nat @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % listI_assn_wrap_insert
% 5.82/6.12 thf(fact_5135_listI__assn__wrap__insert,axiom,
% 5.82/6.12 ! [P: assn,Uu: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F3: assn,C2: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.12 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.12 => ( ( member_nat @ I @ I6 )
% 5.82/6.12 => ( ( hoare_3067605981109127869le_nat @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I6 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.12 => ( hoare_3067605981109127869le_nat @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % listI_assn_wrap_insert
% 5.82/6.12 thf(fact_5136_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_i_n_s_e_r_t @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.82/6.12 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 & ~ ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( 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 @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 5.82/6.12 thf(fact_5137_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 5.82/6.12 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 & ~ ( ( X2 = Mi )
% 5.82/6.12 | ( X2 = Ma ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.12 @ one_one_nat ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 5.82/6.12 thf(fact_5138_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_i_n_s_e_r_t @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 & ~ ( ( Xa = Mi2 )
% 5.82/6.12 | ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( 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 @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.82/6.12 @ one_one_nat ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 5.82/6.12 thf(fact_5139_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_s_u_c_c @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( ? [Uu2: $o,B3: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.12 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( ? [N3: nat] :
% 5.82/6.12 ( Xa
% 5.82/6.12 = ( suc @ N3 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) )
% 5.82/6.12 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.elims
% 5.82/6.12 thf(fact_5140_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_p_r_e_d @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) )
% 5.82/6.12 => ( ( ? [A3: $o,Uw2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ? [Va3: nat] :
% 5.82/6.12 ( Xa
% 5.82/6.12 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 5.82/6.12 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.82/6.12 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.elims
% 5.82/6.12 thf(fact_5141_minNull__bound,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % minNull_bound
% 5.82/6.12 thf(fact_5142_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 5.82/6.12 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 5.82/6.12 thf(fact_5143_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 5.82/6.12 ! [Uv: $o] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 5.82/6.12 thf(fact_5144_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 5.82/6.12 ! [Uu: $o] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 5.82/6.12 thf(fact_5145_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.82/6.12 ! [A2: $o,B2: $o] :
% 5.82/6.12 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 5.82/6.12 thf(fact_5146_atLeastAtMostPlus1__int__conv,axiom,
% 5.82/6.12 ! [M: int,N: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.82/6.12 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.82/6.12 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastAtMostPlus1_int_conv
% 5.82/6.12 thf(fact_5147_simp__from__to,axiom,
% 5.82/6.12 ( set_or1266510415728281911st_int
% 5.82/6.12 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % simp_from_to
% 5.82/6.12 thf(fact_5148_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.82/6.12 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.82/6.12 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 5.82/6.12 thf(fact_5149_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.82/6.12 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 5.82/6.12 thf(fact_5150_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 5.82/6.12 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 5.82/6.12 thf(fact_5151_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 5.82/6.12 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 5.82/6.12 thf(fact_5152_maxt__bound,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % maxt_bound
% 5.82/6.12 thf(fact_5153_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.82/6.12 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.82/6.12 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 5.82/6.12 thf(fact_5154_mint__bound,axiom,
% 5.82/6.12 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % mint_bound
% 5.82/6.12 thf(fact_5155_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.82/6.12 ! [A2: $o,B2: $o] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A2 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 5.82/6.12 thf(fact_5156_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.82/6.12 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.82/6.12 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.82/6.12 = one_one_nat ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 5.82/6.12 thf(fact_5157_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X2 )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [Uv2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [Uu2: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 5.82/6.12 thf(fact_5158_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_m_a_x_t @ X2 )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.82/6.12 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 5.82/6.12 thf(fact_5159_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_m_i_n_t @ X2 )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ! [A3: $o] :
% 5.82/6.12 ( ? [B3: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.82/6.12 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 5.82/6.12 thf(fact_5160_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,
% 5.82/6.12 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ X2 @ Mi )
% 5.82/6.12 | ( ord_less_nat @ Ma @ X2 ) )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( X2 = Mi )
% 5.82/6.12 & ( X2 = Ma ) )
% 5.82/6.12 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X2 = Mi ) @ ( 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 )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( 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 @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( 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 @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( X2 = Mi )
% 5.82/6.12 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.82/6.12 = Ma ) )
% 5.82/6.12 & ( ( X2 != Mi )
% 5.82/6.12 => ( X2 = Ma ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( 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 @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( X2 = Mi )
% 5.82/6.12 => ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.82/6.12 = Ma ) )
% 5.82/6.12 & ( ( X2 != Mi )
% 5.82/6.12 => ( X2 = Ma ) ) )
% 5.82/6.12 @ ( 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 @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X2 = Mi ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(7)
% 5.82/6.12 thf(fact_5161_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,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_d_e_l_e_t_e @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) )
% 5.82/6.12 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) )
% 5.82/6.12 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ? [N3: nat] :
% 5.82/6.12 ( Xa
% 5.82/6.12 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) ) )
% 5.82/6.12 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3 != one_one_nat ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( Y3
% 5.82/6.12 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( Xa = Mi2 )
% 5.82/6.12 & ( Xa = Ma2 ) )
% 5.82/6.12 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( Xa = Mi2 )
% 5.82/6.12 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.12 = Ma2 ) )
% 5.82/6.12 & ( ( Xa != Mi2 )
% 5.82/6.12 => ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( Xa = Mi2 )
% 5.82/6.12 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.12 = Ma2 ) )
% 5.82/6.12 & ( ( Xa != Mi2 )
% 5.82/6.12 => ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.elims
% 5.82/6.12 thf(fact_5162_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 5.82/6.12 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( 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 @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.82/6.12 @ ( 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 @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(7)
% 5.82/6.12 thf(fact_5163_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 5.82/6.12 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.82/6.12 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(6)
% 5.82/6.12 thf(fact_5164_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,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_d_e_l_e_t_e @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ! [N3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.82/6.12 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ord_less_nat @ Xa @ Mi2 )
% 5.82/6.12 | ( ord_less_nat @ Ma2 @ Xa ) )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( Xa = Mi2 )
% 5.82/6.12 & ( Xa = Ma2 ) )
% 5.82/6.12 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( Xa = Mi2 )
% 5.82/6.12 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.12 = Ma2 ) )
% 5.82/6.12 & ( ( Xa != Mi2 )
% 5.82/6.12 => ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( Xa = Mi2 )
% 5.82/6.12 => ( ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.82/6.12 = Ma2 ) )
% 5.82/6.12 & ( ( Xa != Mi2 )
% 5.82/6.12 => ( Xa = Ma2 ) ) )
% 5.82/6.12 @ ( 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 @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa = Mi2 ) @ ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.pelims
% 5.82/6.12 thf(fact_5165_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_s_u_c_c @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [Uv2: $o,Uw2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.82/6.12 => ! [N3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ N3 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.82/6.12 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ one_one_nat
% 5.82/6.12 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.pelims
% 5.82/6.12 thf(fact_5166_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 5.82/6.12 ! [X2: vEBT_VEBT,Xa: nat,Y3: nat] :
% 5.82/6.12 ( ( ( vEBT_T_p_r_e_d @ X2 @ Xa )
% 5.82/6.12 = Y3 )
% 5.82/6.12 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.82/6.12 => ( ! [Uu2: $o,Uv2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.82/6.12 => ( ( Xa = zero_zero_nat )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,Uw2: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.82/6.12 => ( ( Xa
% 5.82/6.12 = ( suc @ zero_zero_nat ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.82/6.12 => ( ! [A3: $o,B3: $o] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.12 => ! [Va3: nat] :
% 5.82/6.12 ( ( Xa
% 5.82/6.12 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.82/6.12 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa ) ) ) )
% 5.82/6.12 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.82/6.12 => ( ( Y3 = one_one_nat )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa ) ) ) )
% 5.82/6.12 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.12 ( ( X2
% 5.82/6.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.82/6.12 => ( ( Y3
% 5.82/6.12 = ( plus_plus_nat @ one_one_nat
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa ) @ one_one_nat
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.82/6.12 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 != none_nat )
% 5.82/6.12 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.12 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 5.82/6.12 @ ( if_nat
% 5.82/6.12 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.12 = none_nat )
% 5.82/6.12 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.82/6.12 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.12 @ one_one_nat ) ) ) ) )
% 5.82/6.12 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.pelims
% 5.82/6.12 thf(fact_5167_big__assn__simp_H,axiom,
% 5.82/6.12 ! [H2: nat,TreeList: list_VEBT_VEBT,Xaa: vEBT_VEBT,L: nat,X2: vEBT_VEBTi,Xb: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( Xaa
% 5.82/6.12 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 5.82/6.12 => ( entails
% 5.82/6.12 @ ( times_times_assn
% 5.82/6.12 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Xaa @ X2 )
% 5.82/6.12 @ ( pure_assn
% 5.82/6.12 @ ( Xb
% 5.82/6.12 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 5.82/6.12 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X2 ) ) @ ( 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 ) ) )
% 5.82/6.12 @ ( times_times_assn
% 5.82/6.12 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 5.82/6.12 @ ( pure_assn
% 5.82/6.12 @ ( Xb
% 5.82/6.12 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 5.82/6.12 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Xaa ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X2 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % big_assn_simp'
% 5.82/6.12 thf(fact_5168_big__assn__simp,axiom,
% 5.82/6.12 ! [H2: nat,TreeList: list_VEBT_VEBT,L: nat,X2: vEBT_VEBTi,Xaa: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( entails
% 5.82/6.12 @ ( times_times_assn
% 5.82/6.12 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) @ X2 )
% 5.82/6.12 @ ( pure_assn
% 5.82/6.12 @ ( Xaa
% 5.82/6.12 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 5.82/6.12 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X2 ) ) @ ( 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 ) ) )
% 5.82/6.12 @ ( times_times_assn
% 5.82/6.12 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 5.82/6.12 @ ( pure_assn
% 5.82/6.12 @ ( Xaa
% 5.82/6.12 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 5.82/6.12 @ ( 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 @ X2 ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % big_assn_simp
% 5.82/6.12 thf(fact_5169_tcd,axiom,
% 5.82/6.12 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_VEBT_VEBT,Y3: vEBT_VEBT,X2: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.12 = ( size_s6755466524823107622T_VEBT @ TreeList4 ) )
% 5.82/6.12 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y3 @ X2 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( 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 @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % tcd
% 5.82/6.12 thf(fact_5170_tcd,axiom,
% 5.82/6.12 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_real,Y3: vEBT_VEBT,X2: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.12 = ( size_size_list_real @ TreeList4 ) )
% 5.82/6.12 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y3 @ X2 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( 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 @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % tcd
% 5.82/6.12 thf(fact_5171_tcd,axiom,
% 5.82/6.12 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_o,Y3: vEBT_VEBT,X2: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.12 = ( size_size_list_o @ TreeList4 ) )
% 5.82/6.12 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y3 @ X2 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( 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 @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % tcd
% 5.82/6.12 thf(fact_5172_tcd,axiom,
% 5.82/6.12 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_nat,Y3: vEBT_VEBT,X2: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.12 = ( size_size_list_nat @ TreeList4 ) )
% 5.82/6.12 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y3 @ X2 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( 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 @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % tcd
% 5.82/6.12 thf(fact_5173_tcd,axiom,
% 5.82/6.12 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_VEBT_VEBTi,Y3: vEBT_VEBT,X2: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.82/6.12 = ( size_s7982070591426661849_VEBTi @ TreeList4 ) )
% 5.82/6.12 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y3 @ X2 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( 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 @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y3 ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X2 ) ) ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % tcd
% 5.82/6.12 thf(fact_5174_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: real,L: real,U: real] :
% 5.82/6.12 ( ( member_real @ I @ ( set_or66887138388493659n_real @ L @ U ) )
% 5.82/6.12 = ( ( ord_less_eq_real @ L @ I )
% 5.82/6.12 & ( ord_less_real @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5175_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: set_int,L: set_int,U: set_int] :
% 5.82/6.12 ( ( member_set_int @ I @ ( set_or8585797421378605585et_int @ L @ U ) )
% 5.82/6.12 = ( ( ord_less_eq_set_int @ L @ I )
% 5.82/6.12 & ( ord_less_set_int @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5176_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: rat,L: rat,U: rat] :
% 5.82/6.12 ( ( member_rat @ I @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 5.82/6.12 = ( ( ord_less_eq_rat @ L @ I )
% 5.82/6.12 & ( ord_less_rat @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5177_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: num,L: num,U: num] :
% 5.82/6.12 ( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
% 5.82/6.12 = ( ( ord_less_eq_num @ L @ I )
% 5.82/6.12 & ( ord_less_num @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5178_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: nat,L: nat,U: nat] :
% 5.82/6.12 ( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.82/6.12 = ( ( ord_less_eq_nat @ L @ I )
% 5.82/6.12 & ( ord_less_nat @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5179_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: int,L: int,U: int] :
% 5.82/6.12 ( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.82/6.12 = ( ( ord_less_eq_int @ L @ I )
% 5.82/6.12 & ( ord_less_int @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5180_atLeastLessThan__iff,axiom,
% 5.82/6.12 ! [I: code_integer,L: code_integer,U: code_integer] :
% 5.82/6.12 ( ( member_Code_integer @ I @ ( set_or8404916559141939852nteger @ L @ U ) )
% 5.82/6.12 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 5.82/6.12 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_iff
% 5.82/6.12 thf(fact_5181_atLeastLessThan__empty,axiom,
% 5.82/6.12 ! [B2: set_int,A2: set_int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ B2 @ A2 )
% 5.82/6.12 => ( ( set_or8585797421378605585et_int @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_set_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty
% 5.82/6.12 thf(fact_5182_atLeastLessThan__empty,axiom,
% 5.82/6.12 ! [B2: rat,A2: rat] :
% 5.82/6.12 ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.12 => ( ( set_or4029947393144176647an_rat @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_rat ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty
% 5.82/6.12 thf(fact_5183_atLeastLessThan__empty,axiom,
% 5.82/6.12 ! [B2: num,A2: num] :
% 5.82/6.12 ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.12 => ( ( set_or1222409239386451017an_num @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_num ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty
% 5.82/6.12 thf(fact_5184_atLeastLessThan__empty,axiom,
% 5.82/6.12 ! [B2: nat,A2: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.12 => ( ( set_or4665077453230672383an_nat @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_nat ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty
% 5.82/6.12 thf(fact_5185_atLeastLessThan__empty,axiom,
% 5.82/6.12 ! [B2: int,A2: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.12 => ( ( set_or4662586982721622107an_int @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_int ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty
% 5.82/6.12 thf(fact_5186_atLeastLessThan__empty,axiom,
% 5.82/6.12 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.12 ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 5.82/6.12 => ( ( set_or8404916559141939852nteger @ A2 @ B2 )
% 5.82/6.12 = bot_bo3990330152332043303nteger ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty
% 5.82/6.12 thf(fact_5187_atLeastLessThan__empty__iff2,axiom,
% 5.82/6.12 ! [A2: real,B2: real] :
% 5.82/6.12 ( ( bot_bot_set_real
% 5.82/6.12 = ( set_or66887138388493659n_real @ A2 @ B2 ) )
% 5.82/6.12 = ( ~ ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff2
% 5.82/6.12 thf(fact_5188_atLeastLessThan__empty__iff2,axiom,
% 5.82/6.12 ! [A2: rat,B2: rat] :
% 5.82/6.12 ( ( bot_bot_set_rat
% 5.82/6.12 = ( set_or4029947393144176647an_rat @ A2 @ B2 ) )
% 5.82/6.12 = ( ~ ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff2
% 5.82/6.12 thf(fact_5189_atLeastLessThan__empty__iff2,axiom,
% 5.82/6.12 ! [A2: num,B2: num] :
% 5.82/6.12 ( ( bot_bot_set_num
% 5.82/6.12 = ( set_or1222409239386451017an_num @ A2 @ B2 ) )
% 5.82/6.12 = ( ~ ( ord_less_num @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff2
% 5.82/6.12 thf(fact_5190_atLeastLessThan__empty__iff2,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( bot_bot_set_nat
% 5.82/6.12 = ( set_or4665077453230672383an_nat @ A2 @ B2 ) )
% 5.82/6.12 = ( ~ ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff2
% 5.82/6.12 thf(fact_5191_atLeastLessThan__empty__iff2,axiom,
% 5.82/6.12 ! [A2: int,B2: int] :
% 5.82/6.12 ( ( bot_bot_set_int
% 5.82/6.12 = ( set_or4662586982721622107an_int @ A2 @ B2 ) )
% 5.82/6.12 = ( ~ ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff2
% 5.82/6.12 thf(fact_5192_atLeastLessThan__empty__iff2,axiom,
% 5.82/6.12 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.12 ( ( bot_bo3990330152332043303nteger
% 5.82/6.12 = ( set_or8404916559141939852nteger @ A2 @ B2 ) )
% 5.82/6.12 = ( ~ ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff2
% 5.82/6.12 thf(fact_5193_atLeastLessThan__empty__iff,axiom,
% 5.82/6.12 ! [A2: real,B2: real] :
% 5.82/6.12 ( ( ( set_or66887138388493659n_real @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_real )
% 5.82/6.12 = ( ~ ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff
% 5.82/6.12 thf(fact_5194_atLeastLessThan__empty__iff,axiom,
% 5.82/6.12 ! [A2: rat,B2: rat] :
% 5.82/6.12 ( ( ( set_or4029947393144176647an_rat @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_rat )
% 5.82/6.12 = ( ~ ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff
% 5.82/6.12 thf(fact_5195_atLeastLessThan__empty__iff,axiom,
% 5.82/6.12 ! [A2: num,B2: num] :
% 5.82/6.12 ( ( ( set_or1222409239386451017an_num @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_num )
% 5.82/6.12 = ( ~ ( ord_less_num @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff
% 5.82/6.12 thf(fact_5196_atLeastLessThan__empty__iff,axiom,
% 5.82/6.12 ! [A2: nat,B2: nat] :
% 5.82/6.12 ( ( ( set_or4665077453230672383an_nat @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_nat )
% 5.82/6.12 = ( ~ ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff
% 5.82/6.12 thf(fact_5197_atLeastLessThan__empty__iff,axiom,
% 5.82/6.12 ! [A2: int,B2: int] :
% 5.82/6.12 ( ( ( set_or4662586982721622107an_int @ A2 @ B2 )
% 5.82/6.12 = bot_bot_set_int )
% 5.82/6.12 = ( ~ ( ord_less_int @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff
% 5.82/6.12 thf(fact_5198_atLeastLessThan__empty__iff,axiom,
% 5.82/6.12 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.12 ( ( ( set_or8404916559141939852nteger @ A2 @ B2 )
% 5.82/6.12 = bot_bo3990330152332043303nteger )
% 5.82/6.12 = ( ~ ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % atLeastLessThan_empty_iff
% 5.82/6.12 thf(fact_5199_ivl__subset,axiom,
% 5.82/6.12 ! [I: rat,J: rat,M: rat,N: rat] :
% 5.82/6.12 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I @ J ) @ ( set_or4029947393144176647an_rat @ M @ N ) )
% 5.82/6.12 = ( ( ord_less_eq_rat @ J @ I )
% 5.82/6.12 | ( ( ord_less_eq_rat @ M @ I )
% 5.82/6.12 & ( ord_less_eq_rat @ J @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_subset
% 5.82/6.12 thf(fact_5200_ivl__subset,axiom,
% 5.82/6.12 ! [I: num,J: num,M: num,N: num] :
% 5.82/6.12 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I @ J ) @ ( set_or1222409239386451017an_num @ M @ N ) )
% 5.82/6.12 = ( ( ord_less_eq_num @ J @ I )
% 5.82/6.12 | ( ( ord_less_eq_num @ M @ I )
% 5.82/6.12 & ( ord_less_eq_num @ J @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_subset
% 5.82/6.12 thf(fact_5201_ivl__subset,axiom,
% 5.82/6.12 ! [I: nat,J: nat,M: nat,N: nat] :
% 5.82/6.12 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.12 = ( ( ord_less_eq_nat @ J @ I )
% 5.82/6.12 | ( ( ord_less_eq_nat @ M @ I )
% 5.82/6.12 & ( ord_less_eq_nat @ J @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_subset
% 5.82/6.12 thf(fact_5202_ivl__subset,axiom,
% 5.82/6.12 ! [I: int,J: int,M: int,N: int] :
% 5.82/6.12 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I @ J ) @ ( set_or4662586982721622107an_int @ M @ N ) )
% 5.82/6.12 = ( ( ord_less_eq_int @ J @ I )
% 5.82/6.12 | ( ( ord_less_eq_int @ M @ I )
% 5.82/6.12 & ( ord_less_eq_int @ J @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_subset
% 5.82/6.12 thf(fact_5203_ivl__subset,axiom,
% 5.82/6.12 ! [I: code_integer,J: code_integer,M: code_integer,N: code_integer] :
% 5.82/6.12 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I @ J ) @ ( set_or8404916559141939852nteger @ M @ N ) )
% 5.82/6.12 = ( ( ord_le3102999989581377725nteger @ J @ I )
% 5.82/6.12 | ( ( ord_le3102999989581377725nteger @ M @ I )
% 5.82/6.12 & ( ord_le3102999989581377725nteger @ J @ N ) ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_subset
% 5.82/6.12 thf(fact_5204_ivl__diff,axiom,
% 5.82/6.12 ! [I: rat,N: rat,M: rat] :
% 5.82/6.12 ( ( ord_less_eq_rat @ I @ N )
% 5.82/6.12 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I @ M ) @ ( set_or4029947393144176647an_rat @ I @ N ) )
% 5.82/6.12 = ( set_or4029947393144176647an_rat @ N @ M ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_diff
% 5.82/6.12 thf(fact_5205_ivl__diff,axiom,
% 5.82/6.12 ! [I: num,N: num,M: num] :
% 5.82/6.12 ( ( ord_less_eq_num @ I @ N )
% 5.82/6.12 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I @ M ) @ ( set_or1222409239386451017an_num @ I @ N ) )
% 5.82/6.12 = ( set_or1222409239386451017an_num @ N @ M ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_diff
% 5.82/6.12 thf(fact_5206_ivl__diff,axiom,
% 5.82/6.12 ! [I: nat,N: nat,M: nat] :
% 5.82/6.12 ( ( ord_less_eq_nat @ I @ N )
% 5.82/6.12 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I @ M ) @ ( set_or4665077453230672383an_nat @ I @ N ) )
% 5.82/6.12 = ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_diff
% 5.82/6.12 thf(fact_5207_ivl__diff,axiom,
% 5.82/6.12 ! [I: int,N: int,M: int] :
% 5.82/6.12 ( ( ord_less_eq_int @ I @ N )
% 5.82/6.12 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I @ M ) @ ( set_or4662586982721622107an_int @ I @ N ) )
% 5.82/6.12 = ( set_or4662586982721622107an_int @ N @ M ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_diff
% 5.82/6.12 thf(fact_5208_ivl__diff,axiom,
% 5.82/6.12 ! [I: code_integer,N: code_integer,M: code_integer] :
% 5.82/6.12 ( ( ord_le3102999989581377725nteger @ I @ N )
% 5.82/6.12 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I @ M ) @ ( set_or8404916559141939852nteger @ I @ N ) )
% 5.82/6.12 = ( set_or8404916559141939852nteger @ N @ M ) ) ) ).
% 5.82/6.12
% 5.82/6.12 % ivl_diff
% 5.82/6.12 thf(fact_5209_local_Oext,axiom,
% 5.82/6.12 ! [Y3: nat,TreeList: list_VEBT_VEBT,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.12 ( ( ord_less_nat @ Y3 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.12 => ( 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 @ Y3 ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y3 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y3 @ 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 @ Y3 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y3 ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y3 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % local.ext
% 5.82/6.13 thf(fact_5210_atLeastLessThan__singleton,axiom,
% 5.82/6.13 ! [M: nat] :
% 5.82/6.13 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.82/6.13 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_singleton
% 5.82/6.13 thf(fact_5211_recomp,axiom,
% 5.82/6.13 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.13 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.13 => ( 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 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % recomp
% 5.82/6.13 thf(fact_5212_repack,axiom,
% 5.82/6.13 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,Rest: assn,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.13 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.13 => ( 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 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % repack
% 5.82/6.13 thf(fact_5213_txe,axiom,
% 5.82/6.13 ! [Y3: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 5.82/6.13 ( ( ord_less_nat @ Y3 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.82/6.13 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y3 ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y3 ) ) @ ( 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 @ Y3 @ 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 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % txe
% 5.82/6.13 thf(fact_5214_atLeastLessThan__eq__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.13 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.13 => ( ( ( set_or66887138388493659n_real @ A2 @ B2 )
% 5.82/6.13 = ( set_or66887138388493659n_real @ C2 @ D2 ) )
% 5.82/6.13 = ( ( A2 = C2 )
% 5.82/6.13 & ( B2 = D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_iff
% 5.82/6.13 thf(fact_5215_atLeastLessThan__eq__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.13 => ( ( ( set_or4029947393144176647an_rat @ A2 @ B2 )
% 5.82/6.13 = ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 5.82/6.13 = ( ( A2 = C2 )
% 5.82/6.13 & ( B2 = D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_iff
% 5.82/6.13 thf(fact_5216_atLeastLessThan__eq__iff,axiom,
% 5.82/6.13 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.13 ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_num @ C2 @ D2 )
% 5.82/6.13 => ( ( ( set_or1222409239386451017an_num @ A2 @ B2 )
% 5.82/6.13 = ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 5.82/6.13 = ( ( A2 = C2 )
% 5.82/6.13 & ( B2 = D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_iff
% 5.82/6.13 thf(fact_5217_atLeastLessThan__eq__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.13 => ( ( ( set_or4665077453230672383an_nat @ A2 @ B2 )
% 5.82/6.13 = ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 5.82/6.13 = ( ( A2 = C2 )
% 5.82/6.13 & ( B2 = D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_iff
% 5.82/6.13 thf(fact_5218_atLeastLessThan__eq__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.13 ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.13 => ( ( ( set_or4662586982721622107an_int @ A2 @ B2 )
% 5.82/6.13 = ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 5.82/6.13 = ( ( A2 = C2 )
% 5.82/6.13 & ( B2 = D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_iff
% 5.82/6.13 thf(fact_5219_atLeastLessThan__eq__iff,axiom,
% 5.82/6.13 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.13 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 5.82/6.13 => ( ( ( set_or8404916559141939852nteger @ A2 @ B2 )
% 5.82/6.13 = ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 5.82/6.13 = ( ( A2 = C2 )
% 5.82/6.13 & ( B2 = D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_iff
% 5.82/6.13 thf(fact_5220_atLeastLessThan__inj_I1_J,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.13 ( ( ( set_or66887138388493659n_real @ A2 @ B2 )
% 5.82/6.13 = ( set_or66887138388493659n_real @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.13 => ( A2 = C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(1)
% 5.82/6.13 thf(fact_5221_atLeastLessThan__inj_I1_J,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( ( set_or4029947393144176647an_rat @ A2 @ B2 )
% 5.82/6.13 = ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.13 => ( A2 = C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(1)
% 5.82/6.13 thf(fact_5222_atLeastLessThan__inj_I1_J,axiom,
% 5.82/6.13 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.13 ( ( ( set_or1222409239386451017an_num @ A2 @ B2 )
% 5.82/6.13 = ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_num @ C2 @ D2 )
% 5.82/6.13 => ( A2 = C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(1)
% 5.82/6.13 thf(fact_5223_atLeastLessThan__inj_I1_J,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( ( set_or4665077453230672383an_nat @ A2 @ B2 )
% 5.82/6.13 = ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.13 => ( A2 = C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(1)
% 5.82/6.13 thf(fact_5224_atLeastLessThan__inj_I1_J,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.13 ( ( ( set_or4662586982721622107an_int @ A2 @ B2 )
% 5.82/6.13 = ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.13 => ( A2 = C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(1)
% 5.82/6.13 thf(fact_5225_atLeastLessThan__inj_I1_J,axiom,
% 5.82/6.13 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.13 ( ( ( set_or8404916559141939852nteger @ A2 @ B2 )
% 5.82/6.13 = ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 5.82/6.13 => ( A2 = C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(1)
% 5.82/6.13 thf(fact_5226_atLeastLessThan__inj_I2_J,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.13 ( ( ( set_or66887138388493659n_real @ A2 @ B2 )
% 5.82/6.13 = ( set_or66887138388493659n_real @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_real @ C2 @ D2 )
% 5.82/6.13 => ( B2 = D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(2)
% 5.82/6.13 thf(fact_5227_atLeastLessThan__inj_I2_J,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( ( set_or4029947393144176647an_rat @ A2 @ B2 )
% 5.82/6.13 = ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_rat @ C2 @ D2 )
% 5.82/6.13 => ( B2 = D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(2)
% 5.82/6.13 thf(fact_5228_atLeastLessThan__inj_I2_J,axiom,
% 5.82/6.13 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.13 ( ( ( set_or1222409239386451017an_num @ A2 @ B2 )
% 5.82/6.13 = ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_num @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_num @ C2 @ D2 )
% 5.82/6.13 => ( B2 = D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(2)
% 5.82/6.13 thf(fact_5229_atLeastLessThan__inj_I2_J,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( ( set_or4665077453230672383an_nat @ A2 @ B2 )
% 5.82/6.13 = ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_nat @ C2 @ D2 )
% 5.82/6.13 => ( B2 = D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(2)
% 5.82/6.13 thf(fact_5230_atLeastLessThan__inj_I2_J,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.13 ( ( ( set_or4662586982721622107an_int @ A2 @ B2 )
% 5.82/6.13 = ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_int @ C2 @ D2 )
% 5.82/6.13 => ( B2 = D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(2)
% 5.82/6.13 thf(fact_5231_atLeastLessThan__inj_I2_J,axiom,
% 5.82/6.13 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.13 ( ( ( set_or8404916559141939852nteger @ A2 @ B2 )
% 5.82/6.13 = ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 5.82/6.13 => ( B2 = D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_inj(2)
% 5.82/6.13 thf(fact_5232_atLeastLessThan__subset__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A2 @ B2 ) @ ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_eq_rat @ B2 @ A2 )
% 5.82/6.13 | ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_eq_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subset_iff
% 5.82/6.13 thf(fact_5233_atLeastLessThan__subset__iff,axiom,
% 5.82/6.13 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.13 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A2 @ B2 ) @ ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_eq_num @ B2 @ A2 )
% 5.82/6.13 | ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_eq_num @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subset_iff
% 5.82/6.13 thf(fact_5234_atLeastLessThan__subset__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 5.82/6.13 | ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_eq_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subset_iff
% 5.82/6.13 thf(fact_5235_atLeastLessThan__subset__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.13 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A2 @ B2 ) @ ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_less_eq_int @ B2 @ A2 )
% 5.82/6.13 | ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_eq_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subset_iff
% 5.82/6.13 thf(fact_5236_atLeastLessThan__subset__iff,axiom,
% 5.82/6.13 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.13 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A2 @ B2 ) @ ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 5.82/6.13 => ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 5.82/6.13 | ( ( ord_le3102999989581377725nteger @ C2 @ A2 )
% 5.82/6.13 & ( ord_le3102999989581377725nteger @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subset_iff
% 5.82/6.13 thf(fact_5237_all__nat__less__eq,axiom,
% 5.82/6.13 ! [N: nat,P: nat > $o] :
% 5.82/6.13 ( ( ! [M6: nat] :
% 5.82/6.13 ( ( ord_less_nat @ M6 @ N )
% 5.82/6.13 => ( P @ M6 ) ) )
% 5.82/6.13 = ( ! [X3: nat] :
% 5.82/6.13 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.82/6.13 => ( P @ X3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % all_nat_less_eq
% 5.82/6.13 thf(fact_5238_ex__nat__less__eq,axiom,
% 5.82/6.13 ! [N: nat,P: nat > $o] :
% 5.82/6.13 ( ( ? [M6: nat] :
% 5.82/6.13 ( ( ord_less_nat @ M6 @ N )
% 5.82/6.13 & ( P @ M6 ) ) )
% 5.82/6.13 = ( ? [X3: nat] :
% 5.82/6.13 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.82/6.13 & ( P @ X3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % ex_nat_less_eq
% 5.82/6.13 thf(fact_5239_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.82/6.13 ! [L: nat,U: nat] :
% 5.82/6.13 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.82/6.13 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThanSuc_atLeastAtMost
% 5.82/6.13 thf(fact_5240_atLeast0__lessThan__Suc,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.82/6.13 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeast0_lessThan_Suc
% 5.82/6.13 thf(fact_5241_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A2 @ B2 ) @ ( set_or633870826150836451st_rat @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_eq_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subseteq_atLeastAtMost_iff
% 5.82/6.13 thf(fact_5242_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.13 ( ( ord_less_eq_set_real @ ( set_or66887138388493659n_real @ A2 @ B2 ) @ ( set_or1222579329274155063t_real @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_real @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_eq_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_subseteq_atLeastAtMost_iff
% 5.82/6.13 thf(fact_5243_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: set_int,B2: set_int,C2: set_int,D2: set_int] :
% 5.82/6.13 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A2 @ B2 ) @ ( set_or8585797421378605585et_int @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_set_int @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_set_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5244_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A2 @ B2 ) @ ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_rat @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5245_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: num,B2: num,C2: num,D2: num] :
% 5.82/6.13 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A2 @ B2 ) @ ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_eq_num @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_num @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_num @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5246_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.13 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ ( set_or66887138388493659n_real @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_real @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5247_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_nat @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5248_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.13 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A2 @ B2 ) @ ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_less_eq_int @ C2 @ A2 )
% 5.82/6.13 & ( ord_less_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5249_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.82/6.13 ! [A2: code_integer,B2: code_integer,C2: code_integer,D2: code_integer] :
% 5.82/6.13 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A2 @ B2 ) @ ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 5.82/6.13 = ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 5.82/6.13 => ( ( ord_le3102999989581377725nteger @ C2 @ A2 )
% 5.82/6.13 & ( ord_le6747313008572928689nteger @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.82/6.13 thf(fact_5250_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 5.82/6.13 ( set_or66887138388493659n_real
% 5.82/6.13 = ( ^ [A5: real,B6: real] : ( minus_minus_set_real @ ( set_or1222579329274155063t_real @ A5 @ B6 ) @ ( insert_real @ B6 @ bot_bot_set_real ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_atLeastAtMost_diff
% 5.82/6.13 thf(fact_5251_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 5.82/6.13 ( set_or4665077453230672383an_nat
% 5.82/6.13 = ( ^ [A5: nat,B6: nat] : ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A5 @ B6 ) @ ( insert_nat @ B6 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_atLeastAtMost_diff
% 5.82/6.13 thf(fact_5252_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 5.82/6.13 ( set_or4662586982721622107an_int
% 5.82/6.13 = ( ^ [A5: int,B6: int] : ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A5 @ B6 ) @ ( insert_int @ B6 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_atLeastAtMost_diff
% 5.82/6.13 thf(fact_5253_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 5.82/6.13 ( set_or8404916559141939852nteger
% 5.82/6.13 = ( ^ [A5: code_integer,B6: code_integer] : ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A5 @ B6 ) @ ( insert_Code_integer @ B6 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThan_eq_atLeastAtMost_diff
% 5.82/6.13 thf(fact_5254_atLeastLessThanSuc,axiom,
% 5.82/6.13 ! [M: nat,N: nat] :
% 5.82/6.13 ( ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.13 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.82/6.13 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.82/6.13 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.82/6.13 = bot_bot_set_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThanSuc
% 5.82/6.13 thf(fact_5255_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L1279224858307276611T_VEBT @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1279224858307276611T_VEBT @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5256_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,Xsi: list_nat,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L8296926524756676353BT_nat @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8296926524756676353BT_nat @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5257_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > $o > assn,Xs: list_VEBT_VEBT,Xsi: list_o,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L7489408758114837031VEBT_o @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L7489408758114837031VEBT_o @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5258_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,Xsi: list_real,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L5781919052683127133T_real @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L5781919052683127133T_real @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5259_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBT > assn,Xs: list_real,Xsi: list_VEBT_VEBT,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L4595930785310033027T_VEBT @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L4595930785310033027T_VEBT @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5260_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBTi > assn,Xs: list_real,Xsi: list_VEBT_VEBTi,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L9060850011106065574_VEBTi @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L9060850011106065574_VEBTi @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5261_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: real > nat > assn,Xs: list_real,Xsi: list_nat,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L1446010312343316929al_nat @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1446010312343316929al_nat @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5262_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: real > $o > assn,Xs: list_real,Xsi: list_o,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L6234343332106409831real_o @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L6234343332106409831real_o @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5263_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: real > real > assn,Xs: list_real,Xsi: list_real,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L1930518968523514909l_real @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1930518968523514909l_real @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5264_rule__at__index,axiom,
% 5.82/6.13 ! [P: assn,A: $o > vEBT_VEBT > assn,Xs: list_o,Xsi: list_VEBT_VEBT,F3: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( vEBT_L1750719106661372127T_VEBT @ A @ Xs @ Xsi ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) @ C2 @ Q2 )
% 5.82/6.13 => ( ! [R3: vEBT_VEBTi] : ( entails @ ( Q2 @ R3 ) @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ ( F4 @ R3 ) ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1750719106661372127T_VEBT @ A @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % rule_at_index
% 5.82/6.13 thf(fact_5265_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > vEBT_VEBT > assn,X2: vEBT_VEBT,Xi: vEBT_VEBT,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5266_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > nat > assn,X2: vEBT_VEBT,Xi: nat,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_update_nat @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5267_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > $o > assn,X2: vEBT_VEBT,Xi: $o,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_o,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_update_o @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5268_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > real > assn,X2: vEBT_VEBT,Xi: real,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_real,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L4281036506115550016T_real @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_update_real @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5269_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBTi > assn,X2: real,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBTi,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5270_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBT > assn,X2: real,Xi: vEBT_VEBT,I6: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBT,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5271_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > nat > assn,X2: real,Xi: nat,I6: set_nat,I: nat,Xs: list_real,Xsi: list_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L234762979517870878al_nat @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_update_nat @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5272_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > $o > assn,X2: real,Xi: $o,I6: set_nat,I: nat,Xs: list_real,Xsi: list_o,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7980206306069228746real_o @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_update_o @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5273_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > real > assn,X2: real,Xi: real,I6: set_nat,I: nat,Xs: list_real,Xsi: list_real,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L5184575500739366650l_real @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_update_real @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5274_listI__assn__reinsert__upd_H,axiom,
% 5.82/6.13 ! [P: assn,A: $o > vEBT_VEBTi > assn,X2: $o,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBTi,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L6286945158656146733_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L6286945158656146733_VEBTi @ I6 @ A @ ( list_update_o @ Xs @ I @ X2 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd'
% 5.82/6.13 thf(fact_5275_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_VEBT_VEBT,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5276_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_nat,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5277_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > $o > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_o,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5278_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_real,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5279_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBT > assn,Xs: list_real,I: nat,Xsi: list_VEBT_VEBT,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5280_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBTi > assn,Xs: list_real,I: nat,Xsi: list_VEBT_VEBTi,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5281_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > nat > assn,Xs: list_real,I: nat,Xsi: list_nat,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5282_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > $o > assn,Xs: list_real,I: nat,Xsi: list_o,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5283_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: real > real > assn,Xs: list_real,I: nat,Xsi: list_real,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5284_listI__assn__reinsert_H,axiom,
% 5.82/6.13 ! [P: assn,A: $o > vEBT_VEBT > assn,Xs: list_o,I: nat,Xsi: list_VEBT_VEBT,I6: set_nat,F3: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L1319876754960170684T_VEBT @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ C2 @ Q )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert'
% 5.82/6.13 thf(fact_5285_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > vEBT_VEBT > assn,X2: vEBT_VEBT,Xi: vEBT_VEBT,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5286_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > nat > assn,X2: vEBT_VEBT,Xi: nat,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_update_nat @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5287_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > $o > assn,X2: vEBT_VEBT,Xi: $o,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_o,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_update_o @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5288_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > real > assn,X2: vEBT_VEBT,Xi: real,I6: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_real,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L4281036506115550016T_real @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ ( list_update_real @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5289_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBTi > assn,X2: real,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBTi,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5290_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBT > assn,X2: real,Xi: vEBT_VEBT,I6: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBT,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5291_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: real > nat > assn,X2: real,Xi: nat,I6: set_nat,I: nat,Xs: list_real,Xsi: list_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L234762979517870878al_nat @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_update_nat @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5292_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: real > $o > assn,X2: real,Xi: $o,I6: set_nat,I: nat,Xs: list_real,Xsi: list_o,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L7980206306069228746real_o @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_update_o @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5293_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: real > real > assn,X2: real,Xi: real,I6: set_nat,I: nat,Xs: list_real,Xsi: list_real,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L5184575500739366650l_real @ I6 @ A @ ( list_update_real @ Xs @ I @ X2 ) @ ( list_update_real @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5294_listI__assn__reinsert__upd,axiom,
% 5.82/6.13 ! [P: assn,A: $o > vEBT_VEBTi > assn,X2: $o,Xi: vEBT_VEBTi,I6: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBTi,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ X2 @ Xi ) @ ( vEBT_L6286945158656146733_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L6286945158656146733_VEBTi @ I6 @ A @ ( list_update_o @ Xs @ I @ X2 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert_upd
% 5.82/6.13 thf(fact_5295_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_VEBT_VEBT,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5296_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_nat,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5297_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > $o > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_o,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5298_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_real,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5299_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBT > assn,Xs: list_real,I: nat,Xsi: list_VEBT_VEBT,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5300_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: real > vEBT_VEBTi > assn,Xs: list_real,I: nat,Xsi: list_VEBT_VEBTi,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5301_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: real > nat > assn,Xs: list_real,I: nat,Xsi: list_nat,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5302_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: real > $o > assn,Xs: list_real,I: nat,Xsi: list_o,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5303_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: real > real > assn,Xs: list_real,I: nat,Xsi: list_real,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5304_listI__assn__reinsert,axiom,
% 5.82/6.13 ! [P: assn,A: $o > vEBT_VEBT > assn,Xs: list_o,I: nat,Xsi: list_VEBT_VEBT,I6: set_nat,F3: assn,Q: assn] :
% 5.82/6.13 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F3 ) )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( entails @ ( times_times_assn @ ( vEBT_L1319876754960170684T_VEBT @ I6 @ A @ Xs @ Xsi ) @ F3 ) @ Q )
% 5.82/6.13 => ( entails @ P @ Q ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_reinsert
% 5.82/6.13 thf(fact_5305_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5306_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > nat > assn,Xsi: list_nat] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5307_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > $o > assn,Xsi: list_o] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7058566406413635588VEBT_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5308_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > real > assn,Xsi: list_real] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L4281036506115550016T_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5309_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5310_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5311_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > nat > assn,Xsi: list_nat] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L234762979517870878al_nat @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5312_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > $o > assn,Xsi: list_o] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7980206306069228746real_o @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5313_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > real > assn,Xsi: list_real] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L5184575500739366650l_real @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5314_listI__assn__extract,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_o,A: $o > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 5.82/6.13 ( ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L1319876754960170684T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I6 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_extract
% 5.82/6.13 thf(fact_5315_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.82/6.13 ! [L: int,U: int] :
% 5.82/6.13 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.82/6.13 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.82/6.13
% 5.82/6.13 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.82/6.13 thf(fact_5316_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_int,Xs4: list_int,Xsi: list_int,Xsi2: list_int,A: int > int > assn,A7: int > int > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: int,Xi2: int] :
% 5.82/6.13 ( ( member_int @ X4 @ ( set_int2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_int @ Xi2 @ ( set_int2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L74593716426352029nt_int @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L74593716426352029nt_int @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5317_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A: int > vEBT_VEBT > assn,A7: int > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: int,Xi2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_int @ X4 @ ( set_int2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_VEBT_VEBT @ Xi2 @ ( set_VEBT_VEBT2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L1664421287176695555T_VEBT @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L1664421287176695555T_VEBT @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5318_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_int,Xs4: list_int,Xsi: list_real,Xsi2: list_real,A: int > real > assn,A7: int > real > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: int,Xi2: real] :
% 5.82/6.13 ( ( member_int @ X4 @ ( set_int2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_real @ Xi2 @ ( set_real2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L8288995350762215837t_real @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L8288995350762215837t_real @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5319_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_int,Xs4: list_int,Xsi: list_nat,Xsi2: list_nat,A: int > nat > assn,A7: int > nat > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: int,Xi2: nat] :
% 5.82/6.13 ( ( member_int @ X4 @ ( set_int2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_nat @ Xi2 @ ( set_nat2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L77084186935402305nt_nat @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L77084186935402305nt_nat @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5320_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_int,Xsi2: list_int,A: vEBT_VEBT > int > assn,A7: vEBT_VEBT > int > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: vEBT_VEBT,Xi2: int] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_int @ Xi2 @ ( set_int2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L8294436054247626077BT_int @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L8294436054247626077BT_int @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5321_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn,A7: vEBT_VEBT > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: vEBT_VEBT,Xi2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_VEBT_VEBT @ Xi2 @ ( set_VEBT_VEBT2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L1279224858307276611T_VEBT @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L1279224858307276611T_VEBT @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5322_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_real,Xsi2: list_real,A: vEBT_VEBT > real > assn,A7: vEBT_VEBT > real > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: vEBT_VEBT,Xi2: real] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_real @ Xi2 @ ( set_real2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L5781919052683127133T_real @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L5781919052683127133T_real @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5323_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_nat,Xsi2: list_nat,A: vEBT_VEBT > nat > assn,A7: vEBT_VEBT > nat > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: vEBT_VEBT,Xi2: nat] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_nat @ Xi2 @ ( set_nat2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L8296926524756676353BT_nat @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L8296926524756676353BT_nat @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5324_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_real,Xs4: list_real,Xsi: list_int,Xsi2: list_int,A: real > int > assn,A7: real > int > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: real,Xi2: int] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_int @ Xi2 @ ( set_int2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L1443519841834266653al_int @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L1443519841834266653al_int @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5325_list__assn__cong,axiom,
% 5.82/6.13 ! [Xs: list_real,Xs4: list_real,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A: real > vEBT_VEBT > assn,A7: real > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( Xs = Xs4 )
% 5.82/6.13 => ( ( Xsi = Xsi2 )
% 5.82/6.13 => ( ! [X4: real,Xi2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs4 ) )
% 5.82/6.13 => ( ( member_VEBT_VEBT @ Xi2 @ ( set_VEBT_VEBT2 @ Xsi2 ) )
% 5.82/6.13 => ( ( A @ X4 @ Xi2 )
% 5.82/6.13 = ( A7 @ X4 @ Xi2 ) ) ) )
% 5.82/6.13 => ( ( vEBT_L4595930785310033027T_VEBT @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L4595930785310033027T_VEBT @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_cong
% 5.82/6.13 thf(fact_5326_list__assn__mono,axiom,
% 5.82/6.13 ! [P: vEBT_VEBT > vEBT_VEBTi > assn,P5: vEBT_VEBT > vEBT_VEBTi > assn,L: list_VEBT_VEBT,L4: list_VEBT_VEBTi] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT,X9: vEBT_VEBTi] : ( entails @ ( P @ X4 @ X9 ) @ ( P5 @ X4 @ X9 ) )
% 5.82/6.13 => ( entails @ ( vEBT_L6296928887356842470_VEBTi @ P @ L @ L4 ) @ ( vEBT_L6296928887356842470_VEBTi @ P5 @ L @ L4 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_mono
% 5.82/6.13 thf(fact_5327_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L1279224858307276611T_VEBT @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5328_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: real > vEBT_VEBT > assn,Xs: list_real,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L4595930785310033027T_VEBT @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_size_list_real @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5329_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: $o > vEBT_VEBT > assn,Xs: list_o,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L1750719106661372127T_VEBT @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_size_list_o @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5330_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: nat > vEBT_VEBT > assn,Xs: list_nat,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L8158188754432654943T_VEBT @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_size_list_nat @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5331_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L7265847600308530106T_VEBT @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5332_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L5781919052683127133T_real @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5333_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: real > real > assn,Xs: list_real,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L1930518968523514909l_real @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_real @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5334_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: $o > real > assn,Xs: list_o,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L4725278957065240257o_real @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_o @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5335_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: nat > real > assn,Xs: list_nat,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L6102073776069194049t_real @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_nat @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5336_extract__pre__list__assn__lengthD,axiom,
% 5.82/6.13 ! [A: vEBT_VEBTi > real > assn,Xs: list_VEBT_VEBTi,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 5.82/6.13 ( ( rep_assn @ ( vEBT_L8937798142398754470i_real @ A @ Xs @ Xsi ) @ H2 )
% 5.82/6.13 => ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % extract_pre_list_assn_lengthD
% 5.82/6.13 thf(fact_5337_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBT,Li2: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( ( size_s6755466524823107622T_VEBT @ L )
% 5.82/6.13 != ( size_s6755466524823107622T_VEBT @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L1279224858307276611T_VEBT @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5338_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBT,Li2: list_real,A: vEBT_VEBT > real > assn] :
% 5.82/6.13 ( ( ( size_s6755466524823107622T_VEBT @ L )
% 5.82/6.13 != ( size_size_list_real @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L5781919052683127133T_real @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5339_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBT,Li2: list_o,A: vEBT_VEBT > $o > assn] :
% 5.82/6.13 ( ( ( size_s6755466524823107622T_VEBT @ L )
% 5.82/6.13 != ( size_size_list_o @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L7489408758114837031VEBT_o @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5340_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBT,Li2: list_nat,A: vEBT_VEBT > nat > assn] :
% 5.82/6.13 ( ( ( size_s6755466524823107622T_VEBT @ L )
% 5.82/6.13 != ( size_size_list_nat @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L8296926524756676353BT_nat @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5341_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_real,Li2: list_VEBT_VEBT,A: real > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( ( size_size_list_real @ L )
% 5.82/6.13 != ( size_s6755466524823107622T_VEBT @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L4595930785310033027T_VEBT @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5342_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_real,Li2: list_real,A: real > real > assn] :
% 5.82/6.13 ( ( ( size_size_list_real @ L )
% 5.82/6.13 != ( size_size_list_real @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L1930518968523514909l_real @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5343_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_real,Li2: list_o,A: real > $o > assn] :
% 5.82/6.13 ( ( ( size_size_list_real @ L )
% 5.82/6.13 != ( size_size_list_o @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L6234343332106409831real_o @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5344_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_real,Li2: list_nat,A: real > nat > assn] :
% 5.82/6.13 ( ( ( size_size_list_real @ L )
% 5.82/6.13 != ( size_size_list_nat @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L1446010312343316929al_nat @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5345_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_real,Li2: list_VEBT_VEBTi,A: real > vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( ( size_size_list_real @ L )
% 5.82/6.13 != ( size_s7982070591426661849_VEBTi @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L9060850011106065574_VEBTi @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5346_list__assn__aux__ineq__len,axiom,
% 5.82/6.13 ! [L: list_o,Li2: list_VEBT_VEBT,A: $o > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( ( size_size_list_o @ L )
% 5.82/6.13 != ( size_s6755466524823107622T_VEBT @ Li2 ) )
% 5.82/6.13 => ( ( vEBT_L1750719106661372127T_VEBT @ A @ L @ Li2 )
% 5.82/6.13 = bot_bot_assn ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_aux_ineq_len
% 5.82/6.13 thf(fact_5347_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: vEBT_VEBT > vEBT_VEBT > assn,A7: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L3204528365124325536T_VEBT @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5348_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: vEBT_VEBT > real > assn,A7: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_real,Xsi2: list_real] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_real @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_real @ Xsi @ I2 )
% 5.82/6.13 = ( nth_real @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L4281036506115550016T_real @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5349_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: vEBT_VEBT > $o > assn,A7: vEBT_VEBT > $o > assn,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_o,Xsi2: list_o] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xsi )
% 5.82/6.13 = ( size_size_list_o @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_o @ Xsi @ I2 )
% 5.82/6.13 = ( nth_o @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L7058566406413635588VEBT_o @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5350_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: vEBT_VEBT > nat > assn,A7: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_nat,Xsi2: list_nat] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_nat @ Xsi )
% 5.82/6.13 = ( size_size_list_nat @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_nat @ Xsi @ I2 )
% 5.82/6.13 = ( nth_nat @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L8650695023172932196BT_nat @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5351_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: real > vEBT_VEBT > assn,A7: real > vEBT_VEBT > assn,Xs: list_real,Xs4: list_real,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L3095048238742455910T_VEBT @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5352_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: real > real > assn,A7: real > real > assn,Xs: list_real,Xs4: list_real,Xsi: list_real,Xsi2: list_real] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_real @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_real @ Xsi @ I2 )
% 5.82/6.13 = ( nth_real @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L5184575500739366650l_real @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5353_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: real > $o > assn,A7: real > $o > assn,Xs: list_real,Xs4: list_real,Xsi: list_o,Xsi2: list_o] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xsi )
% 5.82/6.13 = ( size_size_list_o @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_o @ Xsi @ I2 )
% 5.82/6.13 = ( nth_o @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L7980206306069228746real_o @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5354_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: real > nat > assn,A7: real > nat > assn,Xs: list_real,Xs4: list_real,Xsi: list_nat,Xsi2: list_nat] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_nat @ Xsi )
% 5.82/6.13 = ( size_size_list_nat @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_nat @ Xsi @ I2 )
% 5.82/6.13 = ( nth_nat @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L234762979517870878al_nat @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5355_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: real > vEBT_VEBTi > assn,A7: real > vEBT_VEBTi > assn,Xs: list_real,Xs4: list_real,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L7851252805511451907_VEBTi @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5356_listI__assn__weak__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,A: $o > vEBT_VEBT > assn,A7: $o > vEBT_VEBT > assn,Xs: list_o,Xs4: list_o,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( A = A7 )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_o @ Xs @ I2 )
% 5.82/6.13 = ( nth_o @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L1319876754960170684T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L1319876754960170684T_VEBT @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_weak_cong
% 5.82/6.13 thf(fact_5357_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn,A7: vEBT_VEBT > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_VEBT_VEBT @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_VEBT_VEBT @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L3204528365124325536T_VEBT @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5358_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_real,Xsi2: list_real,A: vEBT_VEBT > real > assn,A7: vEBT_VEBT > real > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_real @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_real @ Xsi @ I2 )
% 5.82/6.13 = ( nth_real @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_VEBT_VEBT @ Xs @ I2 ) @ ( nth_real @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_VEBT_VEBT @ Xs4 @ I2 ) @ ( nth_real @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L4281036506115550016T_real @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5359_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_o,Xsi2: list_o,A: vEBT_VEBT > $o > assn,A7: vEBT_VEBT > $o > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xsi )
% 5.82/6.13 = ( size_size_list_o @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_o @ Xsi @ I2 )
% 5.82/6.13 = ( nth_o @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_VEBT_VEBT @ Xs @ I2 ) @ ( nth_o @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_VEBT_VEBT @ Xs4 @ I2 ) @ ( nth_o @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L7058566406413635588VEBT_o @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5360_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_nat,Xsi2: list_nat,A: vEBT_VEBT > nat > assn,A7: vEBT_VEBT > nat > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_nat @ Xsi )
% 5.82/6.13 = ( size_size_list_nat @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_nat @ Xsi @ I2 )
% 5.82/6.13 = ( nth_nat @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_VEBT_VEBT @ Xs @ I2 ) @ ( nth_nat @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_VEBT_VEBT @ Xs4 @ I2 ) @ ( nth_nat @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L8650695023172932196BT_nat @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5361_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_real,Xs4: list_real,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A: real > vEBT_VEBT > assn,A7: real > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_real @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_real @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L3095048238742455910T_VEBT @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5362_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_real,Xs4: list_real,Xsi: list_real,Xsi2: list_real,A: real > real > assn,A7: real > real > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xsi )
% 5.82/6.13 = ( size_size_list_real @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_real @ Xsi @ I2 )
% 5.82/6.13 = ( nth_real @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_real @ Xs @ I2 ) @ ( nth_real @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_real @ Xs4 @ I2 ) @ ( nth_real @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L5184575500739366650l_real @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5363_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_real,Xs4: list_real,Xsi: list_o,Xsi2: list_o,A: real > $o > assn,A7: real > $o > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xsi )
% 5.82/6.13 = ( size_size_list_o @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_o @ Xsi @ I2 )
% 5.82/6.13 = ( nth_o @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_real @ Xs @ I2 ) @ ( nth_o @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_real @ Xs4 @ I2 ) @ ( nth_o @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L7980206306069228746real_o @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5364_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_real,Xs4: list_real,Xsi: list_nat,Xsi2: list_nat,A: real > nat > assn,A7: real > nat > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_size_list_nat @ Xsi )
% 5.82/6.13 = ( size_size_list_nat @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_nat @ Xsi @ I2 )
% 5.82/6.13 = ( nth_nat @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_real @ Xs @ I2 ) @ ( nth_nat @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_real @ Xs4 @ I2 ) @ ( nth_nat @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L234762979517870878al_nat @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5365_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_real,Xs4: list_real,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi,A: real > vEBT_VEBTi > assn,A7: real > vEBT_VEBTi > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_real @ Xs )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_real @ Xs @ I2 )
% 5.82/6.13 = ( nth_real @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_real @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_real @ Xs4 @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L7851252805511451907_VEBTi @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5366_listI__assn__cong,axiom,
% 5.82/6.13 ! [I6: set_nat,I7: set_nat,Xs: list_o,Xs4: list_o,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A: $o > vEBT_VEBT > assn,A7: $o > vEBT_VEBT > assn] :
% 5.82/6.13 ( ( I6 = I7 )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Xs4 ) )
% 5.82/6.13 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( member_nat @ I2 @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( ( size_size_list_o @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 5.82/6.13 => ( ( ( nth_o @ Xs @ I2 )
% 5.82/6.13 = ( nth_o @ Xs4 @ I2 ) )
% 5.82/6.13 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 5.82/6.13 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 5.82/6.13 & ( ( A @ ( nth_o @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 5.82/6.13 = ( A7 @ ( nth_o @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 5.82/6.13 => ( ( vEBT_L1319876754960170684T_VEBT @ I6 @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L1319876754960170684T_VEBT @ I7 @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_cong
% 5.82/6.13 thf(fact_5367_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBT,X22: vEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5368_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > nat > assn,X1: vEBT_VEBT,Xsi: list_nat,X22: nat] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_update_nat @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5369_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > $o > assn,X1: vEBT_VEBT,Xsi: list_o,X22: $o] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_update_o @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5370_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > real > assn,X1: vEBT_VEBT,Xsi: list_real,X22: real] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L4281036506115550016T_real @ I6 @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_update_real @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5371_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBTi > assn,X1: real,Xsi: list_VEBT_VEBTi,X22: vEBT_VEBTi] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5372_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBT > assn,X1: real,Xsi: list_VEBT_VEBT,X22: vEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5373_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > nat > assn,X1: real,Xsi: list_nat,X22: nat] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L234762979517870878al_nat @ I6 @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_update_nat @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5374_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > $o > assn,X1: real,Xsi: list_o,X22: $o] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7980206306069228746real_o @ I6 @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_update_o @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5375_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > real > assn,X1: real,Xsi: list_real,X22: real] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L5184575500739366650l_real @ I6 @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_update_real @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5376_subst__not__in,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_o,A: $o > vEBT_VEBTi > assn,X1: $o,Xsi: list_VEBT_VEBTi,X22: vEBT_VEBTi] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L6286945158656146733_VEBTi @ I6 @ A @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( vEBT_L6286945158656146733_VEBTi @ I6 @ A @ Xs @ Xsi ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % subst_not_in
% 5.82/6.13 thf(fact_5377_listI__assn__conv,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( N
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( vEBT_L6296928887356842470_VEBTi @ A @ Xs @ Xsi ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_conv
% 5.82/6.13 thf(fact_5378_list__assn__conv__idx,axiom,
% 5.82/6.13 ( vEBT_L6296928887356842470_VEBTi
% 5.82/6.13 = ( ^ [A6: vEBT_VEBT > vEBT_VEBTi > assn,Xs2: list_VEBT_VEBT] : ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) @ A6 @ Xs2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_assn_conv_idx
% 5.82/6.13 thf(fact_5379_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3204528365124325536T_VEBT @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5380_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > nat > assn,Xsi: list_nat] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L8650695023172932196BT_nat @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5381_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > $o > assn,Xsi: list_o] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7058566406413635588VEBT_o @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5382_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > real > assn,Xsi: list_real] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L4281036506115550016T_real @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5383_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3095048238742455910T_VEBT @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5384_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7851252805511451907_VEBTi @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5385_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > nat > assn,Xsi: list_nat] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L234762979517870878al_nat @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5386_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > $o > assn,Xsi: list_o] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7980206306069228746real_o @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_o @ Xsi @ I ) ) @ ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5387_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > real > assn,Xsi: list_real] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L5184575500739366650l_real @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xsi @ I ) ) @ ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5388_listI__assn__insert,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_o,A: $o > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L1319876754960170684T_VEBT @ ( insert_nat @ I @ I6 ) @ A @ Xs @ Xsi )
% 5.82/6.13 = ( times_times_assn @ ( A @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L1319876754960170684T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_insert
% 5.82/6.13 thf(fact_5389_listI__assn__conv_H,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi,F3: assn] :
% 5.82/6.13 ( ( N
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A @ Xs @ Xsi ) @ F3 )
% 5.82/6.13 = ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ A @ Xs @ Xsi ) @ F3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_conv'
% 5.82/6.13 thf(fact_5390_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > vEBT_VEBT > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBT,X22: vEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3204528365124325536T_VEBT @ ( insert_nat @ I @ I6 ) @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L3204528365124325536T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5391_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > nat > assn,X1: vEBT_VEBT,Xsi: list_nat,X22: nat] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L8650695023172932196BT_nat @ ( insert_nat @ I @ I6 ) @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_update_nat @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L8650695023172932196BT_nat @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5392_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > $o > assn,X1: vEBT_VEBT,Xsi: list_o,X22: $o] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7058566406413635588VEBT_o @ ( insert_nat @ I @ I6 ) @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_update_o @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L7058566406413635588VEBT_o @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5393_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_VEBT_VEBT,A: vEBT_VEBT > real > assn,X1: vEBT_VEBT,Xsi: list_real,X22: real] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L4281036506115550016T_real @ ( insert_nat @ I @ I6 ) @ A @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_update_real @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L4281036506115550016T_real @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5394_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBTi > assn,X1: real,Xsi: list_VEBT_VEBTi,X22: vEBT_VEBTi] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7851252805511451907_VEBTi @ ( insert_nat @ I @ I6 ) @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L7851252805511451907_VEBTi @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5395_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > vEBT_VEBT > assn,X1: real,Xsi: list_VEBT_VEBT,X22: vEBT_VEBT] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L3095048238742455910T_VEBT @ ( insert_nat @ I @ I6 ) @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L3095048238742455910T_VEBT @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5396_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > nat > assn,X1: real,Xsi: list_nat,X22: nat] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L234762979517870878al_nat @ ( insert_nat @ I @ I6 ) @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_update_nat @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L234762979517870878al_nat @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5397_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > $o > assn,X1: real,Xsi: list_o,X22: $o] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L7980206306069228746real_o @ ( insert_nat @ I @ I6 ) @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_update_o @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L7980206306069228746real_o @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5398_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_real,A: real > real > assn,X1: real,Xsi: list_real,X22: real] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L5184575500739366650l_real @ ( insert_nat @ I @ I6 ) @ A @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_update_real @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L5184575500739366650l_real @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5399_listI__assn__subst,axiom,
% 5.82/6.13 ! [I: nat,I6: set_nat,Xs: list_o,A: $o > vEBT_VEBTi > assn,X1: $o,Xsi: list_VEBT_VEBTi,X22: vEBT_VEBTi] :
% 5.82/6.13 ( ~ ( member_nat @ I @ I6 )
% 5.82/6.13 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( ( vEBT_L6286945158656146733_VEBTi @ ( insert_nat @ I @ I6 ) @ A @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X22 ) )
% 5.82/6.13 = ( times_times_assn @ ( A @ X1 @ X22 ) @ ( vEBT_L6286945158656146733_VEBTi @ I6 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listI_assn_subst
% 5.82/6.13 thf(fact_5400_lemma__termdiff3,axiom,
% 5.82/6.13 ! [H2: real,Z: real,K6: real,N: nat] :
% 5.82/6.13 ( ( H2 != zero_zero_real )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K6 )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K6 )
% 5.82/6.13 => ( 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 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % lemma_termdiff3
% 5.82/6.13 thf(fact_5401_lemma__termdiff3,axiom,
% 5.82/6.13 ! [H2: complex,Z: complex,K6: real,N: nat] :
% 5.82/6.13 ( ( H2 != zero_zero_complex )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K6 )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K6 )
% 5.82/6.13 => ( 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 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % lemma_termdiff3
% 5.82/6.13 thf(fact_5402_foldr__zero,axiom,
% 5.82/6.13 ! [Xs: list_nat,D2: nat] :
% 5.82/6.13 ( ! [I2: nat] :
% 5.82/6.13 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.82/6.13 => ( ord_less_nat @ zero_zero_nat @ ( nth_nat @ Xs @ I2 ) ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( minus_minus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ D2 ) @ D2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_zero
% 5.82/6.13 thf(fact_5403_foldr__same,axiom,
% 5.82/6.13 ! [Xs: list_real,Y3: real] :
% 5.82/6.13 ( ! [X4: real,Y4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( ( member_real @ Y4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( X4 = Y4 ) ) )
% 5.82/6.13 => ( ! [X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( X4 = Y3 ) )
% 5.82/6.13 => ( ( foldr_real_real @ plus_plus_real @ Xs @ zero_zero_real )
% 5.82/6.13 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs ) ) @ Y3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_same
% 5.82/6.13 thf(fact_5404_lowi__hT,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] :
% 5.82/6.13 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X2 @ N )
% 5.82/6.13 @ ^ [R5: nat] :
% 5.82/6.13 ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( vEBT_VEBT_low @ X2 @ N ) ) )
% 5.82/6.13 @ one_one_nat ) ).
% 5.82/6.13
% 5.82/6.13 % lowi_hT
% 5.82/6.13 thf(fact_5405_highi__hT,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] :
% 5.82/6.13 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X2 @ N )
% 5.82/6.13 @ ^ [R5: nat] :
% 5.82/6.13 ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( vEBT_VEBT_high @ X2 @ N ) ) )
% 5.82/6.13 @ one_one_nat ) ).
% 5.82/6.13
% 5.82/6.13 % highi_hT
% 5.82/6.13 thf(fact_5406_TBOUND__lowi,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] : ( time_TBOUND_nat @ ( vEBT_VEBT_lowi @ X2 @ N ) @ one_one_nat ) ).
% 5.82/6.13
% 5.82/6.13 % TBOUND_lowi
% 5.82/6.13 thf(fact_5407_TBOUND__highi,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] : ( time_TBOUND_nat @ ( vEBT_VEBT_highi @ X2 @ N ) @ one_one_nat ) ).
% 5.82/6.13
% 5.82/6.13 % TBOUND_highi
% 5.82/6.13 thf(fact_5408_foldr0,axiom,
% 5.82/6.13 ! [Xs: list_real,C2: real,D2: real] :
% 5.82/6.13 ( ( foldr_real_real @ plus_plus_real @ Xs @ ( plus_plus_real @ C2 @ D2 ) )
% 5.82/6.13 = ( plus_plus_real @ ( foldr_real_real @ plus_plus_real @ Xs @ D2 ) @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr0
% 5.82/6.13 thf(fact_5409_foldr__one,axiom,
% 5.82/6.13 ! [D2: nat,Ys: list_nat] : ( ord_less_eq_nat @ D2 @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_one
% 5.82/6.13 thf(fact_5410_highi__h,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] :
% 5.82/6.13 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X2 @ N )
% 5.82/6.13 @ ^ [R5: nat] :
% 5.82/6.13 ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( vEBT_VEBT_high @ X2 @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % highi_h
% 5.82/6.13 thf(fact_5411_lowi__h,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] :
% 5.82/6.13 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X2 @ N )
% 5.82/6.13 @ ^ [R5: nat] :
% 5.82/6.13 ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( vEBT_VEBT_low @ X2 @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % lowi_h
% 5.82/6.13 thf(fact_5412_foldr__same__int,axiom,
% 5.82/6.13 ! [Xs: list_nat,Y3: nat] :
% 5.82/6.13 ( ! [X4: nat,Y4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( ( member_nat @ Y4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( X4 = Y4 ) ) )
% 5.82/6.13 => ( ! [X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( X4 = Y3 ) )
% 5.82/6.13 => ( ( foldr_nat_nat @ plus_plus_nat @ Xs @ zero_zero_nat )
% 5.82/6.13 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ Y3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_same_int
% 5.82/6.13 thf(fact_5413_foldr__mono,axiom,
% 5.82/6.13 ! [Xs: list_nat,Ys: list_nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( ( size_size_list_nat @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Ys ) )
% 5.82/6.13 => ( ! [I2: nat] :
% 5.82/6.13 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.82/6.13 => ( ord_less_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) )
% 5.82/6.13 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 5.82/6.13 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ C2 ) @ ( size_size_list_nat @ Ys ) ) @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_mono
% 5.82/6.13 thf(fact_5414_foldr__length,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBT] :
% 5.82/6.13 ( ( foldr_VEBT_VEBT_nat
% 5.82/6.13 @ ^ [X3: vEBT_VEBT] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ zero_zero_nat )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ L ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length
% 5.82/6.13 thf(fact_5415_foldr__length,axiom,
% 5.82/6.13 ! [L: list_real] :
% 5.82/6.13 ( ( foldr_real_nat
% 5.82/6.13 @ ^ [X3: real] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ zero_zero_nat )
% 5.82/6.13 = ( size_size_list_real @ L ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length
% 5.82/6.13 thf(fact_5416_foldr__length,axiom,
% 5.82/6.13 ! [L: list_o] :
% 5.82/6.13 ( ( foldr_o_nat
% 5.82/6.13 @ ^ [X3: $o] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ zero_zero_nat )
% 5.82/6.13 = ( size_size_list_o @ L ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length
% 5.82/6.13 thf(fact_5417_foldr__length,axiom,
% 5.82/6.13 ! [L: list_nat] :
% 5.82/6.13 ( ( foldr_nat_nat
% 5.82/6.13 @ ^ [X3: nat] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ zero_zero_nat )
% 5.82/6.13 = ( size_size_list_nat @ L ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length
% 5.82/6.13 thf(fact_5418_foldr__length,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( foldr_VEBT_VEBTi_nat
% 5.82/6.13 @ ^ [X3: vEBT_VEBTi] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ zero_zero_nat )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ L ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length
% 5.82/6.13 thf(fact_5419_foldr__cong,axiom,
% 5.82/6.13 ! [A2: real,B2: real,L: list_real,K: list_real,F: real > real > real,G: real > real > real] :
% 5.82/6.13 ( ( A2 = B2 )
% 5.82/6.13 => ( ( L = K )
% 5.82/6.13 => ( ! [A3: real,X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ L ) )
% 5.82/6.13 => ( ( F @ X4 @ A3 )
% 5.82/6.13 = ( G @ X4 @ A3 ) ) )
% 5.82/6.13 => ( ( foldr_real_real @ F @ L @ A2 )
% 5.82/6.13 = ( foldr_real_real @ G @ K @ B2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_cong
% 5.82/6.13 thf(fact_5420_foldr__cong,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,L: list_nat,K: list_nat,F: nat > nat > nat,G: nat > nat > nat] :
% 5.82/6.13 ( ( A2 = B2 )
% 5.82/6.13 => ( ( L = K )
% 5.82/6.13 => ( ! [A3: nat,X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ L ) )
% 5.82/6.13 => ( ( F @ X4 @ A3 )
% 5.82/6.13 = ( G @ X4 @ A3 ) ) )
% 5.82/6.13 => ( ( foldr_nat_nat @ F @ L @ A2 )
% 5.82/6.13 = ( foldr_nat_nat @ G @ K @ B2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_cong
% 5.82/6.13 thf(fact_5421_foldr__length__aux,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBT,A2: nat] :
% 5.82/6.13 ( ( foldr_VEBT_VEBT_nat
% 5.82/6.13 @ ^ [X3: vEBT_VEBT] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ A2 )
% 5.82/6.13 = ( plus_plus_nat @ A2 @ ( size_s6755466524823107622T_VEBT @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length_aux
% 5.82/6.13 thf(fact_5422_foldr__length__aux,axiom,
% 5.82/6.13 ! [L: list_real,A2: nat] :
% 5.82/6.13 ( ( foldr_real_nat
% 5.82/6.13 @ ^ [X3: real] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ A2 )
% 5.82/6.13 = ( plus_plus_nat @ A2 @ ( size_size_list_real @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length_aux
% 5.82/6.13 thf(fact_5423_foldr__length__aux,axiom,
% 5.82/6.13 ! [L: list_o,A2: nat] :
% 5.82/6.13 ( ( foldr_o_nat
% 5.82/6.13 @ ^ [X3: $o] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ A2 )
% 5.82/6.13 = ( plus_plus_nat @ A2 @ ( size_size_list_o @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length_aux
% 5.82/6.13 thf(fact_5424_foldr__length__aux,axiom,
% 5.82/6.13 ! [L: list_nat,A2: nat] :
% 5.82/6.13 ( ( foldr_nat_nat
% 5.82/6.13 @ ^ [X3: nat] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ A2 )
% 5.82/6.13 = ( plus_plus_nat @ A2 @ ( size_size_list_nat @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length_aux
% 5.82/6.13 thf(fact_5425_foldr__length__aux,axiom,
% 5.82/6.13 ! [L: list_VEBT_VEBTi,A2: nat] :
% 5.82/6.13 ( ( foldr_VEBT_VEBTi_nat
% 5.82/6.13 @ ^ [X3: vEBT_VEBTi] : suc
% 5.82/6.13 @ L
% 5.82/6.13 @ A2 )
% 5.82/6.13 = ( plus_plus_nat @ A2 @ ( size_s7982070591426661849_VEBTi @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % foldr_length_aux
% 5.82/6.13 thf(fact_5426_norm__divide__numeral,axiom,
% 5.82/6.13 ! [A2: real,W: num] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A2 @ ( numeral_numeral_real @ W ) ) )
% 5.82/6.13 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_divide_numeral
% 5.82/6.13 thf(fact_5427_norm__divide__numeral,axiom,
% 5.82/6.13 ! [A2: complex,W: num] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A2 @ ( numera6690914467698888265omplex @ W ) ) )
% 5.82/6.13 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_divide_numeral
% 5.82/6.13 thf(fact_5428_norm__mult__numeral1,axiom,
% 5.82/6.13 ! [W: num,A2: real] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A2 ) )
% 5.82/6.13 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_numeral1
% 5.82/6.13 thf(fact_5429_norm__mult__numeral1,axiom,
% 5.82/6.13 ! [W: num,A2: complex] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A2 ) )
% 5.82/6.13 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_numeral1
% 5.82/6.13 thf(fact_5430_norm__mult__numeral2,axiom,
% 5.82/6.13 ! [A2: real,W: num] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W ) ) )
% 5.82/6.13 = ( times_times_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_numeral2
% 5.82/6.13 thf(fact_5431_norm__mult__numeral2,axiom,
% 5.82/6.13 ! [A2: complex,W: num] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ W ) ) )
% 5.82/6.13 = ( times_times_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_numeral2
% 5.82/6.13 thf(fact_5432_norm__le__zero__iff,axiom,
% 5.82/6.13 ! [X2: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ zero_zero_real )
% 5.82/6.13 = ( X2 = zero_zero_real ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_le_zero_iff
% 5.82/6.13 thf(fact_5433_norm__le__zero__iff,axiom,
% 5.82/6.13 ! [X2: complex] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real )
% 5.82/6.13 = ( X2 = zero_zero_complex ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_le_zero_iff
% 5.82/6.13 thf(fact_5434_norm__numeral,axiom,
% 5.82/6.13 ! [W: num] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.82/6.13 = ( numeral_numeral_real @ W ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_numeral
% 5.82/6.13 thf(fact_5435_norm__numeral,axiom,
% 5.82/6.13 ! [W: num] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.82/6.13 = ( numeral_numeral_real @ W ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_numeral
% 5.82/6.13 thf(fact_5436_norm__one,axiom,
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.82/6.13 = one_one_real ) ).
% 5.82/6.13
% 5.82/6.13 % norm_one
% 5.82/6.13 thf(fact_5437_norm__one,axiom,
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.82/6.13 = one_one_real ) ).
% 5.82/6.13
% 5.82/6.13 % norm_one
% 5.82/6.13 thf(fact_5438_norm__minus__commute,axiom,
% 5.82/6.13 ! [A2: real,B2: real] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.13 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_minus_commute
% 5.82/6.13 thf(fact_5439_norm__minus__commute,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ B2 ) )
% 5.82/6.13 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_minus_commute
% 5.82/6.13 thf(fact_5440_norm__mult,axiom,
% 5.82/6.13 ! [X2: real,Y3: real] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y3 ) )
% 5.82/6.13 = ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult
% 5.82/6.13 thf(fact_5441_norm__mult,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y3 ) )
% 5.82/6.13 = ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult
% 5.82/6.13 thf(fact_5442_norm__ge__zero,axiom,
% 5.82/6.13 ! [X2: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_ge_zero
% 5.82/6.13 thf(fact_5443_norm__divide,axiom,
% 5.82/6.13 ! [A2: real,B2: real] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A2 @ B2 ) )
% 5.82/6.13 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_divide
% 5.82/6.13 thf(fact_5444_norm__divide,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A2 @ B2 ) )
% 5.82/6.13 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_divide
% 5.82/6.13 thf(fact_5445_norm__power,axiom,
% 5.82/6.13 ! [X2: real,N: nat] :
% 5.82/6.13 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) )
% 5.82/6.13 = ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_power
% 5.82/6.13 thf(fact_5446_norm__power,axiom,
% 5.82/6.13 ! [X2: complex,N: nat] :
% 5.82/6.13 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) )
% 5.82/6.13 = ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_power
% 5.82/6.13 thf(fact_5447_power__eq__imp__eq__norm,axiom,
% 5.82/6.13 ! [W: real,N: nat,Z: real] :
% 5.82/6.13 ( ( ( power_power_real @ W @ N )
% 5.82/6.13 = ( power_power_real @ Z @ N ) )
% 5.82/6.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.13 => ( ( real_V7735802525324610683m_real @ W )
% 5.82/6.13 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_eq_imp_eq_norm
% 5.82/6.13 thf(fact_5448_power__eq__imp__eq__norm,axiom,
% 5.82/6.13 ! [W: complex,N: nat,Z: complex] :
% 5.82/6.13 ( ( ( power_power_complex @ W @ N )
% 5.82/6.13 = ( power_power_complex @ Z @ N ) )
% 5.82/6.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.13 => ( ( real_V1022390504157884413omplex @ W )
% 5.82/6.13 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_eq_imp_eq_norm
% 5.82/6.13 thf(fact_5449_nonzero__norm__divide,axiom,
% 5.82/6.13 ! [B2: real,A2: real] :
% 5.82/6.13 ( ( B2 != zero_zero_real )
% 5.82/6.13 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A2 @ B2 ) )
% 5.82/6.13 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nonzero_norm_divide
% 5.82/6.13 thf(fact_5450_nonzero__norm__divide,axiom,
% 5.82/6.13 ! [B2: complex,A2: complex] :
% 5.82/6.13 ( ( B2 != zero_zero_complex )
% 5.82/6.13 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A2 @ B2 ) )
% 5.82/6.13 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nonzero_norm_divide
% 5.82/6.13 thf(fact_5451_norm__mult__less,axiom,
% 5.82/6.13 ! [X2: real,R2: real,Y3: real,S2: real] :
% 5.82/6.13 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.82/6.13 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S2 )
% 5.82/6.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y3 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_less
% 5.82/6.13 thf(fact_5452_norm__mult__less,axiom,
% 5.82/6.13 ! [X2: complex,R2: real,Y3: complex,S2: real] :
% 5.82/6.13 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.82/6.13 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S2 )
% 5.82/6.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y3 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_less
% 5.82/6.13 thf(fact_5453_norm__mult__ineq,axiom,
% 5.82/6.13 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y3 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_ineq
% 5.82/6.13 thf(fact_5454_norm__mult__ineq,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y3 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_mult_ineq
% 5.82/6.13 thf(fact_5455_norm__add__less,axiom,
% 5.82/6.13 ! [X2: real,R2: real,Y3: real,S2: real] :
% 5.82/6.13 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.82/6.13 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S2 )
% 5.82/6.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_add_less
% 5.82/6.13 thf(fact_5456_norm__add__less,axiom,
% 5.82/6.13 ! [X2: complex,R2: real,Y3: complex,S2: real] :
% 5.82/6.13 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.82/6.13 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S2 )
% 5.82/6.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_add_less
% 5.82/6.13 thf(fact_5457_norm__triangle__lt,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,E: real] :
% 5.82/6.13 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E )
% 5.82/6.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ E ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_lt
% 5.82/6.13 thf(fact_5458_norm__triangle__lt,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex,E: real] :
% 5.82/6.13 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E )
% 5.82/6.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ E ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_lt
% 5.82/6.13 thf(fact_5459_norm__triangle__le,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,E: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ E ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_le
% 5.82/6.13 thf(fact_5460_norm__triangle__le,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex,E: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ E ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_le
% 5.82/6.13 thf(fact_5461_norm__triangle__mono,axiom,
% 5.82/6.13 ! [A2: real,R2: real,B2: real,S2: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A2 ) @ R2 )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B2 ) @ S2 )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A2 @ B2 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_mono
% 5.82/6.13 thf(fact_5462_norm__triangle__mono,axiom,
% 5.82/6.13 ! [A2: complex,R2: real,B2: complex,S2: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A2 ) @ R2 )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B2 ) @ S2 )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A2 @ B2 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_mono
% 5.82/6.13 thf(fact_5463_norm__triangle__ineq,axiom,
% 5.82/6.13 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_ineq
% 5.82/6.13 thf(fact_5464_norm__triangle__ineq,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_ineq
% 5.82/6.13 thf(fact_5465_norm__add__leD,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A2 @ B2 ) ) @ C2 )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B2 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A2 ) @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_add_leD
% 5.82/6.13 thf(fact_5466_norm__add__leD,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex,C2: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A2 @ B2 ) ) @ C2 )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A2 ) @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_add_leD
% 5.82/6.13 thf(fact_5467_norm__diff__triangle__less,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,E1: real,Z: real,E22: real] :
% 5.82/6.13 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ E1 )
% 5.82/6.13 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 5.82/6.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_triangle_less
% 5.82/6.13 thf(fact_5468_norm__diff__triangle__less,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 5.82/6.13 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) @ E1 )
% 5.82/6.13 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 5.82/6.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_triangle_less
% 5.82/6.13 thf(fact_5469_norm__power__ineq,axiom,
% 5.82/6.13 ! [X2: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_power_ineq
% 5.82/6.13 thf(fact_5470_norm__power__ineq,axiom,
% 5.82/6.13 ! [X2: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_power_ineq
% 5.82/6.13 thf(fact_5471_norm__triangle__le__diff,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,E: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ E ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_le_diff
% 5.82/6.13 thf(fact_5472_norm__triangle__le__diff,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex,E: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) @ E ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_le_diff
% 5.82/6.13 thf(fact_5473_norm__diff__triangle__le,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,E1: real,Z: real,E22: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ E1 )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_triangle_le
% 5.82/6.13 thf(fact_5474_norm__diff__triangle__le,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) @ E1 )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_triangle_le
% 5.82/6.13 thf(fact_5475_norm__triangle__ineq4,axiom,
% 5.82/6.13 ! [A2: real,B2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ B2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_ineq4
% 5.82/6.13 thf(fact_5476_norm__triangle__ineq4,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ B2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_ineq4
% 5.82/6.13 thf(fact_5477_norm__triangle__sub,axiom,
% 5.82/6.13 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y3 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_sub
% 5.82/6.13 thf(fact_5478_norm__triangle__sub,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y3 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_sub
% 5.82/6.13 thf(fact_5479_norm__diff__ineq,axiom,
% 5.82/6.13 ! [A2: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B2 ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_ineq
% 5.82/6.13 thf(fact_5480_norm__diff__ineq,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_ineq
% 5.82/6.13 thf(fact_5481_norm__triangle__ineq2,axiom,
% 5.82/6.13 ! [A2: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B2 ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_ineq2
% 5.82/6.13 thf(fact_5482_norm__triangle__ineq2,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_triangle_ineq2
% 5.82/6.13 thf(fact_5483_power__eq__1__iff,axiom,
% 5.82/6.13 ! [W: real,N: nat] :
% 5.82/6.13 ( ( ( power_power_real @ W @ N )
% 5.82/6.13 = one_one_real )
% 5.82/6.13 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.82/6.13 = one_one_real )
% 5.82/6.13 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_eq_1_iff
% 5.82/6.13 thf(fact_5484_power__eq__1__iff,axiom,
% 5.82/6.13 ! [W: complex,N: nat] :
% 5.82/6.13 ( ( ( power_power_complex @ W @ N )
% 5.82/6.13 = one_one_complex )
% 5.82/6.13 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.82/6.13 = one_one_real )
% 5.82/6.13 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_eq_1_iff
% 5.82/6.13 thf(fact_5485_norm__diff__triangle__ineq,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A2 @ B2 ) @ ( plus_plus_real @ C2 @ D2 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ C2 ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_triangle_ineq
% 5.82/6.13 thf(fact_5486_norm__diff__triangle__ineq,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex,C2: complex,D2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A2 @ B2 ) @ ( plus_plus_complex @ C2 @ D2 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ C2 ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_diff_triangle_ineq
% 5.82/6.13 thf(fact_5487_square__norm__one,axiom,
% 5.82/6.13 ! [X2: real] :
% 5.82/6.13 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = one_one_real )
% 5.82/6.13 => ( ( real_V7735802525324610683m_real @ X2 )
% 5.82/6.13 = one_one_real ) ) ).
% 5.82/6.13
% 5.82/6.13 % square_norm_one
% 5.82/6.13 thf(fact_5488_square__norm__one,axiom,
% 5.82/6.13 ! [X2: complex] :
% 5.82/6.13 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = one_one_complex )
% 5.82/6.13 => ( ( real_V1022390504157884413omplex @ X2 )
% 5.82/6.13 = one_one_real ) ) ).
% 5.82/6.13
% 5.82/6.13 % square_norm_one
% 5.82/6.13 thf(fact_5489_norm__power__diff,axiom,
% 5.82/6.13 ! [Z: real,W: real,M: nat] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_power_diff
% 5.82/6.13 thf(fact_5490_norm__power__diff,axiom,
% 5.82/6.13 ! [Z: complex,W: complex,M: nat] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.82/6.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % norm_power_diff
% 5.82/6.13 thf(fact_5491_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,Bound: real,I: real] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound_real
% 5.82/6.13 thf(fact_5492_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.82/6.13 ! [Xs: list_real,F: real > real,Bound: real,I: real] :
% 5.82/6.13 ( ! [X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound_real
% 5.82/6.13 thf(fact_5493_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.82/6.13 ! [Xs: list_o,F: $o > real,Bound: real,I: real] :
% 5.82/6.13 ( ! [X4: $o] :
% 5.82/6.13 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_o_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_o @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound_real
% 5.82/6.13 thf(fact_5494_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.82/6.13 ! [Xs: list_nat,F: nat > real,Bound: real,I: real] :
% 5.82/6.13 ( ! [X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_nat @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound_real
% 5.82/6.13 thf(fact_5495_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBTi,F: vEBT_VEBTi > real,Bound: real,I: real] :
% 5.82/6.13 ( ! [X4: vEBT_VEBTi] :
% 5.82/6.13 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBTi_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound_real
% 5.82/6.13 thf(fact_5496_f__g__map__foldr__bound,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,C2: real,G: vEBT_VEBT > real,D2: real] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ ( times_times_real @ C2 @ ( G @ X4 ) ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C2 @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ G @ Xs ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % f_g_map_foldr_bound
% 5.82/6.13 thf(fact_5497_f__g__map__foldr__bound,axiom,
% 5.82/6.13 ! [Xs: list_real,F: real > real,C2: real,G: real > real,D2: real] :
% 5.82/6.13 ( ! [X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ ( times_times_real @ C2 @ ( G @ X4 ) ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C2 @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ G @ Xs ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % f_g_map_foldr_bound
% 5.82/6.13 thf(fact_5498_f__g__map__foldr__bound,axiom,
% 5.82/6.13 ! [Xs: list_nat,F: nat > real,C2: real,G: nat > real,D2: real] :
% 5.82/6.13 ( ! [X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( F @ X4 ) @ ( times_times_real @ C2 @ ( G @ X4 ) ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C2 @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ G @ Xs ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % f_g_map_foldr_bound
% 5.82/6.13 thf(fact_5499_list__every__elemnt__bound__sum__bound,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > nat,Bound: nat,I: nat] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound
% 5.82/6.13 thf(fact_5500_list__every__elemnt__bound__sum__bound,axiom,
% 5.82/6.13 ! [Xs: list_real,F: real > nat,Bound: nat,I: nat] :
% 5.82/6.13 ( ! [X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_real_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_real @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound
% 5.82/6.13 thf(fact_5501_list__every__elemnt__bound__sum__bound,axiom,
% 5.82/6.13 ! [Xs: list_o,F: $o > nat,Bound: nat,I: nat] :
% 5.82/6.13 ( ! [X4: $o] :
% 5.82/6.13 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_o_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound
% 5.82/6.13 thf(fact_5502_list__every__elemnt__bound__sum__bound,axiom,
% 5.82/6.13 ! [Xs: list_nat,F: nat > nat,Bound: nat,I: nat] :
% 5.82/6.13 ( ! [X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_nat_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound
% 5.82/6.13 thf(fact_5503_list__every__elemnt__bound__sum__bound,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBTi,F: vEBT_VEBTi > nat,Bound: nat,I: nat] :
% 5.82/6.13 ( ! [X4: vEBT_VEBTi] :
% 5.82/6.13 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.82/6.13 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBTi_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list_every_elemnt_bound_sum_bound
% 5.82/6.13 thf(fact_5504_vebt__memberi__refines,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,X2: nat,T: vEBT_VEBT] : ( refine_Imp_refines_o @ ( vEBT_vebt_memberi @ Ti @ X2 ) @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % vebt_memberi_refines
% 5.82/6.13 thf(fact_5505_refines__replicate,axiom,
% 5.82/6.13 ! [F: heap_Time_Heap_o,F5: heap_Time_Heap_o,N: nat] :
% 5.82/6.13 ( ( refine_Imp_refines_o @ F @ F5 )
% 5.82/6.13 => ( refine5896690332125372649list_o @ ( vEBT_V2326993469660664182atei_o @ N @ F ) @ ( vEBT_V2326993469660664182atei_o @ N @ F5 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % refines_replicate
% 5.82/6.13 thf(fact_5506_refines__replicate,axiom,
% 5.82/6.13 ! [F: heap_T2636463487746394924on_nat,F5: heap_T2636463487746394924on_nat,N: nat] :
% 5.82/6.13 ( ( refine7594492741263601813on_nat @ F @ F5 )
% 5.82/6.13 => ( refine1935026298455697829on_nat @ ( vEBT_V792416675989592002on_nat @ N @ F ) @ ( vEBT_V792416675989592002on_nat @ N @ F5 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % refines_replicate
% 5.82/6.13 thf(fact_5507_refines__replicate,axiom,
% 5.82/6.13 ! [F: heap_T8145700208782473153_VEBTi,F5: heap_T8145700208782473153_VEBTi,N: nat] :
% 5.82/6.13 ( ( refine5565527176597971370_VEBTi @ F @ F5 )
% 5.82/6.13 => ( refine3700189196150522554_VEBTi @ ( vEBT_V1859673955506687831_VEBTi @ N @ F ) @ ( vEBT_V1859673955506687831_VEBTi @ N @ F5 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % refines_replicate
% 5.82/6.13 thf(fact_5508_listsum__bound,axiom,
% 5.82/6.13 ! [Xs: list_int,F: int > real,Y3: real] :
% 5.82/6.13 ( ! [X4: int] :
% 5.82/6.13 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ Y3 @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs ) @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listsum_bound
% 5.82/6.13 thf(fact_5509_listsum__bound,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,Y3: real] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ Y3 @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listsum_bound
% 5.82/6.13 thf(fact_5510_listsum__bound,axiom,
% 5.82/6.13 ! [Xs: list_real,F: real > real,Y3: real] :
% 5.82/6.13 ( ! [X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ Y3 @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs ) @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listsum_bound
% 5.82/6.13 thf(fact_5511_listsum__bound,axiom,
% 5.82/6.13 ! [Xs: list_nat,F: nat > real,Y3: real] :
% 5.82/6.13 ( ! [X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.13 => ( ord_less_eq_real @ Y3 @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs ) @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % listsum_bound
% 5.82/6.13 thf(fact_5512_length__map,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.82/6.13 ( ( size_s6755466524823107622T_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs ) )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5513_length__map,axiom,
% 5.82/6.13 ! [F: real > vEBT_VEBT,Xs: list_real] :
% 5.82/6.13 ( ( size_s6755466524823107622T_VEBT @ ( map_real_VEBT_VEBT @ F @ Xs ) )
% 5.82/6.13 = ( size_size_list_real @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5514_length__map,axiom,
% 5.82/6.13 ! [F: $o > vEBT_VEBT,Xs: list_o] :
% 5.82/6.13 ( ( size_s6755466524823107622T_VEBT @ ( map_o_VEBT_VEBT @ F @ Xs ) )
% 5.82/6.13 = ( size_size_list_o @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5515_length__map,axiom,
% 5.82/6.13 ! [F: nat > vEBT_VEBT,Xs: list_nat] :
% 5.82/6.13 ( ( size_s6755466524823107622T_VEBT @ ( map_nat_VEBT_VEBT @ F @ Xs ) )
% 5.82/6.13 = ( size_size_list_nat @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5516_length__map,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > vEBT_VEBT,Xs: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( size_s6755466524823107622T_VEBT @ ( map_VE7998069337340375161T_VEBT @ F @ Xs ) )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5517_length__map,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT] :
% 5.82/6.13 ( ( size_size_list_real @ ( map_VEBT_VEBT_real @ F @ Xs ) )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5518_length__map,axiom,
% 5.82/6.13 ! [F: real > real,Xs: list_real] :
% 5.82/6.13 ( ( size_size_list_real @ ( map_real_real @ F @ Xs ) )
% 5.82/6.13 = ( size_size_list_real @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5519_length__map,axiom,
% 5.82/6.13 ! [F: $o > real,Xs: list_o] :
% 5.82/6.13 ( ( size_size_list_real @ ( map_o_real @ F @ Xs ) )
% 5.82/6.13 = ( size_size_list_o @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5520_length__map,axiom,
% 5.82/6.13 ! [F: nat > real,Xs: list_nat] :
% 5.82/6.13 ( ( size_size_list_real @ ( map_nat_real @ F @ Xs ) )
% 5.82/6.13 = ( size_size_list_nat @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5521_length__map,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > real,Xs: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( size_size_list_real @ ( map_VEBT_VEBTi_real @ F @ Xs ) )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % length_map
% 5.82/6.13 thf(fact_5522_map__eq__conv,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ G @ Xs ) )
% 5.82/6.13 = ( ! [X3: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X3 )
% 5.82/6.13 = ( G @ X3 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_conv
% 5.82/6.13 thf(fact_5523_map__eq__conv,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ G @ Xs ) )
% 5.82/6.13 = ( ! [X3: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X3 )
% 5.82/6.13 = ( G @ X3 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_conv
% 5.82/6.13 thf(fact_5524_real__nat__list,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,C2: nat] :
% 5.82/6.13 ( ( semiri5074537144036343181t_real @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ C2 ) )
% 5.82/6.13 = ( foldr_real_real @ plus_plus_real
% 5.82/6.13 @ ( map_VEBT_VEBT_real
% 5.82/6.13 @ ^ [X3: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( F @ X3 ) )
% 5.82/6.13 @ Xs )
% 5.82/6.13 @ ( semiri5074537144036343181t_real @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % real_nat_list
% 5.82/6.13 thf(fact_5525_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( nth_VEBT_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5526_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBTi] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( nth_VEBT_VEBTi @ ( map_VE7029150624388687525_VEBTi @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5527_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > $o] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( nth_o @ ( map_VEBT_VEBT_o @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5528_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( nth_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5529_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.82/6.13 => ( ( nth_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5530_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_real,F: real > vEBT_VEBT] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( nth_VEBT_VEBT @ ( map_real_VEBT_VEBT @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5531_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_real,F: real > vEBT_VEBTi] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( nth_VEBT_VEBTi @ ( map_real_VEBT_VEBTi @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5532_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_real,F: real > nat] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( nth_nat @ ( map_real_nat @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5533_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_real,F: real > $o] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( nth_o @ ( map_real_o @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5534_nth__map,axiom,
% 5.82/6.13 ! [N: nat,Xs: list_real,F: real > real] :
% 5.82/6.13 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.82/6.13 => ( ( nth_real @ ( map_real_real @ F @ Xs ) @ N )
% 5.82/6.13 = ( F @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_map
% 5.82/6.13 thf(fact_5535_refines__case__VEBTi,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,Ti2: vEBT_VEBTi,F1: $o > $o > heap_Time_Heap_o,F12: $o > $o > heap_Time_Heap_o,F22: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_Time_Heap_o,F23: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_Time_Heap_o] :
% 5.82/6.13 ( ( Ti = Ti2 )
% 5.82/6.13 => ( ! [A3: $o,B3: $o] : ( refine_Imp_refines_o @ ( F1 @ A3 @ B3 ) @ ( F12 @ A3 @ B3 ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] : ( refine_Imp_refines_o @ ( F22 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( F23 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( refine_Imp_refines_o @ ( vEBT_c6104975476656191286Heap_o @ F22 @ F1 @ Ti ) @ ( vEBT_c6104975476656191286Heap_o @ F23 @ F12 @ Ti2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % refines_case_VEBTi
% 5.82/6.13 thf(fact_5536_refines__case__VEBTi,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,Ti2: vEBT_VEBTi,F1: $o > $o > heap_T2636463487746394924on_nat,F12: $o > $o > heap_T2636463487746394924on_nat,F22: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T2636463487746394924on_nat,F23: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T2636463487746394924on_nat] :
% 5.82/6.13 ( ( Ti = Ti2 )
% 5.82/6.13 => ( ! [A3: $o,B3: $o] : ( refine7594492741263601813on_nat @ ( F1 @ A3 @ B3 ) @ ( F12 @ A3 @ B3 ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] : ( refine7594492741263601813on_nat @ ( F22 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( F23 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( refine7594492741263601813on_nat @ ( vEBT_c6250501799366334488on_nat @ F22 @ F1 @ Ti ) @ ( vEBT_c6250501799366334488on_nat @ F23 @ F12 @ Ti2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % refines_case_VEBTi
% 5.82/6.13 thf(fact_5537_refines__case__VEBTi,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,Ti2: vEBT_VEBTi,F1: $o > $o > heap_T8145700208782473153_VEBTi,F12: $o > $o > heap_T8145700208782473153_VEBTi,F22: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T8145700208782473153_VEBTi,F23: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T8145700208782473153_VEBTi] :
% 5.82/6.13 ( ( Ti = Ti2 )
% 5.82/6.13 => ( ! [A3: $o,B3: $o] : ( refine5565527176597971370_VEBTi @ ( F1 @ A3 @ B3 ) @ ( F12 @ A3 @ B3 ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] : ( refine5565527176597971370_VEBTi @ ( F22 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( F23 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( refine5565527176597971370_VEBTi @ ( vEBT_c6028912655521741485_VEBTi @ F22 @ F1 @ Ti ) @ ( vEBT_c6028912655521741485_VEBTi @ F23 @ F12 @ Ti2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % refines_case_VEBTi
% 5.82/6.13 thf(fact_5538_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: vEBT_VEBT > nat,Ys: list_VEBT_VEBT] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5539_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: vEBT_VEBT > real,Ys: list_VEBT_VEBT] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5540_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: real > nat,Ys: list_real] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_real_nat @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5541_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: real > real,Ys: list_real] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_real_real @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_real @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5542_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: $o > nat,Ys: list_o] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_o_nat @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5543_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: $o > real,Ys: list_o] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_o_real @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_o @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5544_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: nat > nat,Ys: list_nat] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_nat_nat @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5545_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: nat > real,Ys: list_nat] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_nat_real @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_size_list_nat @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5546_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: vEBT_VEBTi > nat,Ys: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBTi_nat @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5547_map__eq__imp__length__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: vEBT_VEBTi > real,Ys: list_VEBT_VEBTi] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBTi_real @ G @ Ys ) )
% 5.82/6.13 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.13 = ( size_s7982070591426661849_VEBTi @ Ys ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_imp_length_eq
% 5.82/6.13 thf(fact_5548_list_Omap__cong,axiom,
% 5.82/6.13 ! [X2: list_VEBT_VEBT,Ya: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.13 ( ( X2 = Ya )
% 5.82/6.13 => ( ! [Z2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ Z2 @ ( set_VEBT_VEBT2 @ Ya ) )
% 5.82/6.13 => ( ( F @ Z2 )
% 5.82/6.13 = ( G @ Z2 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_nat @ F @ X2 )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ G @ Ya ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list.map_cong
% 5.82/6.13 thf(fact_5549_list_Omap__cong,axiom,
% 5.82/6.13 ! [X2: list_VEBT_VEBT,Ya: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.13 ( ( X2 = Ya )
% 5.82/6.13 => ( ! [Z2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ Z2 @ ( set_VEBT_VEBT2 @ Ya ) )
% 5.82/6.13 => ( ( F @ Z2 )
% 5.82/6.13 = ( G @ Z2 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_real @ F @ X2 )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ G @ Ya ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list.map_cong
% 5.82/6.13 thf(fact_5550_list_Omap__cong0,axiom,
% 5.82/6.13 ! [X2: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.13 ( ! [Z2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ Z2 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.82/6.13 => ( ( F @ Z2 )
% 5.82/6.13 = ( G @ Z2 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_nat @ F @ X2 )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ G @ X2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list.map_cong0
% 5.82/6.13 thf(fact_5551_list_Omap__cong0,axiom,
% 5.82/6.13 ! [X2: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.13 ( ! [Z2: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ Z2 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.82/6.13 => ( ( F @ Z2 )
% 5.82/6.13 = ( G @ Z2 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_real @ F @ X2 )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ G @ X2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list.map_cong0
% 5.82/6.13 thf(fact_5552_list_Oinj__map__strong,axiom,
% 5.82/6.13 ! [X2: list_VEBT_VEBT,Xa: list_VEBT_VEBT,F: vEBT_VEBT > nat,Fa: vEBT_VEBT > nat] :
% 5.82/6.13 ( ! [Z2: vEBT_VEBT,Za: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ Z2 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.82/6.13 => ( ( member_VEBT_VEBT @ Za @ ( set_VEBT_VEBT2 @ Xa ) )
% 5.82/6.13 => ( ( ( F @ Z2 )
% 5.82/6.13 = ( Fa @ Za ) )
% 5.82/6.13 => ( Z2 = Za ) ) ) )
% 5.82/6.13 => ( ( ( map_VEBT_VEBT_nat @ F @ X2 )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ Fa @ Xa ) )
% 5.82/6.13 => ( X2 = Xa ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list.inj_map_strong
% 5.82/6.13 thf(fact_5553_list_Oinj__map__strong,axiom,
% 5.82/6.13 ! [X2: list_VEBT_VEBT,Xa: list_VEBT_VEBT,F: vEBT_VEBT > real,Fa: vEBT_VEBT > real] :
% 5.82/6.13 ( ! [Z2: vEBT_VEBT,Za: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ Z2 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.82/6.13 => ( ( member_VEBT_VEBT @ Za @ ( set_VEBT_VEBT2 @ Xa ) )
% 5.82/6.13 => ( ( ( F @ Z2 )
% 5.82/6.13 = ( Fa @ Za ) )
% 5.82/6.13 => ( Z2 = Za ) ) ) )
% 5.82/6.13 => ( ( ( map_VEBT_VEBT_real @ F @ X2 )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ Fa @ Xa ) )
% 5.82/6.13 => ( X2 = Xa ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % list.inj_map_strong
% 5.82/6.13 thf(fact_5554_map__ext,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = ( G @ X4 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ G @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_ext
% 5.82/6.13 thf(fact_5555_map__ext,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = ( G @ X4 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ G @ Xs ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_ext
% 5.82/6.13 thf(fact_5556_map__idI,axiom,
% 5.82/6.13 ! [Xs: list_int,F: int > int] :
% 5.82/6.13 ( ! [X4: int] :
% 5.82/6.13 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = X4 ) )
% 5.82/6.13 => ( ( map_int_int @ F @ Xs )
% 5.82/6.13 = Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_idI
% 5.82/6.13 thf(fact_5557_map__idI,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 5.82/6.13 ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = X4 ) )
% 5.82/6.13 => ( ( map_VE8901447254227204932T_VEBT @ F @ Xs )
% 5.82/6.13 = Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_idI
% 5.82/6.13 thf(fact_5558_map__idI,axiom,
% 5.82/6.13 ! [Xs: list_real,F: real > real] :
% 5.82/6.13 ( ! [X4: real] :
% 5.82/6.13 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = X4 ) )
% 5.82/6.13 => ( ( map_real_real @ F @ Xs )
% 5.82/6.13 = Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_idI
% 5.82/6.13 thf(fact_5559_map__idI,axiom,
% 5.82/6.13 ! [Xs: list_nat,F: nat > nat] :
% 5.82/6.13 ( ! [X4: nat] :
% 5.82/6.13 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = X4 ) )
% 5.82/6.13 => ( ( map_nat_nat @ F @ Xs )
% 5.82/6.13 = Xs ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_idI
% 5.82/6.13 thf(fact_5560_map__cong,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.13 ( ( Xs = Ys )
% 5.82/6.13 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Ys ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = ( G @ X4 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ G @ Ys ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_cong
% 5.82/6.13 thf(fact_5561_map__cong,axiom,
% 5.82/6.13 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.13 ( ( Xs = Ys )
% 5.82/6.13 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Ys ) )
% 5.82/6.13 => ( ( F @ X4 )
% 5.82/6.13 = ( G @ X4 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ G @ Ys ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_cong
% 5.82/6.13 thf(fact_5562_ex__map__conv,axiom,
% 5.82/6.13 ! [Ys: list_real,F: vEBT_VEBT > real] :
% 5.82/6.13 ( ( ? [Xs2: list_VEBT_VEBT] :
% 5.82/6.13 ( Ys
% 5.82/6.13 = ( map_VEBT_VEBT_real @ F @ Xs2 ) ) )
% 5.82/6.13 = ( ! [X3: real] :
% 5.82/6.13 ( ( member_real @ X3 @ ( set_real2 @ Ys ) )
% 5.82/6.13 => ? [Y: vEBT_VEBT] :
% 5.82/6.13 ( X3
% 5.82/6.13 = ( F @ Y ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % ex_map_conv
% 5.82/6.13 thf(fact_5563_ex__map__conv,axiom,
% 5.82/6.13 ! [Ys: list_nat,F: vEBT_VEBT > nat] :
% 5.82/6.13 ( ( ? [Xs2: list_VEBT_VEBT] :
% 5.82/6.13 ( Ys
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ F @ Xs2 ) ) )
% 5.82/6.13 = ( ! [X3: nat] :
% 5.82/6.13 ( ( member_nat @ X3 @ ( set_nat2 @ Ys ) )
% 5.82/6.13 => ? [Y: vEBT_VEBT] :
% 5.82/6.13 ( X3
% 5.82/6.13 = ( F @ Y ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % ex_map_conv
% 5.82/6.13 thf(fact_5564_map__eq__nth__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,L: list_VEBT_VEBT,L4: list_VEBT_VEBT,I: nat] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_nat @ F @ L )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ F @ L4 ) )
% 5.82/6.13 => ( ( F @ ( nth_VEBT_VEBT @ L @ I ) )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ L4 @ I ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_nth_eq
% 5.82/6.13 thf(fact_5565_map__eq__nth__eq,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,L: list_VEBT_VEBT,L4: list_VEBT_VEBT,I: nat] :
% 5.82/6.13 ( ( ( map_VEBT_VEBT_real @ F @ L )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ F @ L4 ) )
% 5.82/6.13 => ( ( F @ ( nth_VEBT_VEBT @ L @ I ) )
% 5.82/6.13 = ( F @ ( nth_VEBT_VEBT @ L4 @ I ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_eq_nth_eq
% 5.82/6.13 thf(fact_5566_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > vEBT_VEBTi,Xs: list_VEBT_VEBTi,K: nat,Y3: vEBT_VEBTi] :
% 5.82/6.13 ( ( map_VE483055756984248624_VEBTi @ F @ ( list_u6098035379799741383_VEBTi @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_u6098035379799741383_VEBTi @ ( map_VE483055756984248624_VEBTi @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5567_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > vEBT_VEBT,Xs: list_VEBT_VEBTi,K: nat,Y3: vEBT_VEBTi] :
% 5.82/6.13 ( ( map_VE7998069337340375161T_VEBT @ F @ ( list_u6098035379799741383_VEBTi @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_u1324408373059187874T_VEBT @ ( map_VE7998069337340375161T_VEBT @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5568_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > nat,Xs: list_VEBT_VEBTi,K: nat,Y3: vEBT_VEBTi] :
% 5.82/6.13 ( ( map_VEBT_VEBTi_nat @ F @ ( list_u6098035379799741383_VEBTi @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_update_nat @ ( map_VEBT_VEBTi_nat @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5569_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > $o,Xs: list_VEBT_VEBTi,K: nat,Y3: vEBT_VEBTi] :
% 5.82/6.13 ( ( map_VEBT_VEBTi_o @ F @ ( list_u6098035379799741383_VEBTi @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_update_o @ ( map_VEBT_VEBTi_o @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5570_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBTi > real,Xs: list_VEBT_VEBTi,K: nat,Y3: vEBT_VEBTi] :
% 5.82/6.13 ( ( map_VEBT_VEBTi_real @ F @ ( list_u6098035379799741383_VEBTi @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_update_real @ ( map_VEBT_VEBTi_real @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5571_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > vEBT_VEBTi,Xs: list_VEBT_VEBT,K: nat,Y3: vEBT_VEBT] :
% 5.82/6.13 ( ( map_VE7029150624388687525_VEBTi @ F @ ( list_u1324408373059187874T_VEBT @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_u6098035379799741383_VEBTi @ ( map_VE7029150624388687525_VEBTi @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5572_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > vEBT_VEBT,Xs: list_VEBT_VEBT,K: nat,Y3: vEBT_VEBT] :
% 5.82/6.13 ( ( map_VE8901447254227204932T_VEBT @ F @ ( list_u1324408373059187874T_VEBT @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_u1324408373059187874T_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5573_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,K: nat,Y3: vEBT_VEBT] :
% 5.82/6.13 ( ( map_VEBT_VEBT_nat @ F @ ( list_u1324408373059187874T_VEBT @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_update_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5574_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > $o,Xs: list_VEBT_VEBT,K: nat,Y3: vEBT_VEBT] :
% 5.82/6.13 ( ( map_VEBT_VEBT_o @ F @ ( list_u1324408373059187874T_VEBT @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_update_o @ ( map_VEBT_VEBT_o @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5575_map__update,axiom,
% 5.82/6.13 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,K: nat,Y3: vEBT_VEBT] :
% 5.82/6.13 ( ( map_VEBT_VEBT_real @ F @ ( list_u1324408373059187874T_VEBT @ Xs @ K @ Y3 ) )
% 5.82/6.13 = ( list_update_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ K @ ( F @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_update
% 5.82/6.13 thf(fact_5576_map__upd__eq,axiom,
% 5.82/6.13 ! [I: nat,L: list_VEBT_VEBT,F: vEBT_VEBT > nat,X2: vEBT_VEBT] :
% 5.82/6.13 ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.13 => ( ( F @ ( nth_VEBT_VEBT @ L @ I ) )
% 5.82/6.13 = ( F @ X2 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_nat @ F @ ( list_u1324408373059187874T_VEBT @ L @ I @ X2 ) )
% 5.82/6.13 = ( map_VEBT_VEBT_nat @ F @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_upd_eq
% 5.82/6.13 thf(fact_5577_map__upd__eq,axiom,
% 5.82/6.13 ! [I: nat,L: list_VEBT_VEBT,F: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.82/6.13 ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 5.82/6.13 => ( ( F @ ( nth_VEBT_VEBT @ L @ I ) )
% 5.82/6.13 = ( F @ X2 ) ) )
% 5.82/6.13 => ( ( map_VEBT_VEBT_real @ F @ ( list_u1324408373059187874T_VEBT @ L @ I @ X2 ) )
% 5.82/6.13 = ( map_VEBT_VEBT_real @ F @ L ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % map_upd_eq
% 5.82/6.13 thf(fact_5578_VEBT__internal_Ocnt_H_Osimps_I2_J,axiom,
% 5.82/6.13 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.13 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.82/6.13 = ( 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 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.cnt'.simps(2)
% 5.82/6.13 thf(fact_5579_VEBT__internal_Ocnt_Osimps_I2_J,axiom,
% 5.82/6.13 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.13 ( ( vEBT_VEBT_cnt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.82/6.13 = ( 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 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.cnt.simps(2)
% 5.82/6.13 thf(fact_5580_VEBT__internal_Ocnt_H_Oelims,axiom,
% 5.82/6.13 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.13 ( ( ( vEBT_VEBT_cnt2 @ X2 )
% 5.82/6.13 = Y3 )
% 5.82/6.13 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.13 ( X2
% 5.82/6.13 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.13 => ( Y3 != one_one_nat ) )
% 5.82/6.13 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.13 ( ( X2
% 5.82/6.13 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.13 => ( Y3
% 5.82/6.13 != ( 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 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.cnt'.elims
% 5.82/6.13 thf(fact_5581_VEBT__internal_Ocnt_Oelims,axiom,
% 5.82/6.13 ! [X2: vEBT_VEBT,Y3: real] :
% 5.82/6.13 ( ( ( vEBT_VEBT_cnt @ X2 )
% 5.82/6.13 = Y3 )
% 5.82/6.13 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.13 ( X2
% 5.82/6.13 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.13 => ( Y3 != one_one_real ) )
% 5.82/6.13 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.13 ( ( X2
% 5.82/6.13 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.13 => ( Y3
% 5.82/6.13 != ( 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 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.cnt.elims
% 5.82/6.13 thf(fact_5582_VEBT__internal_Ospace_H_Osimps_I2_J,axiom,
% 5.82/6.13 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.13 ( ( vEBT_VEBT_space2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.82/6.13 = ( 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 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.space'.simps(2)
% 5.82/6.13 thf(fact_5583_VEBT__internal_Ospace_H_Oelims,axiom,
% 5.82/6.13 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.13 ( ( ( vEBT_VEBT_space2 @ X2 )
% 5.82/6.13 = Y3 )
% 5.82/6.13 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.13 ( X2
% 5.82/6.13 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.13 => ( Y3
% 5.82/6.13 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.13 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.13 ( ( X2
% 5.82/6.13 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.13 => ( Y3
% 5.82/6.13 != ( 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 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.space'.elims
% 5.82/6.13 thf(fact_5584_VEBT__internal_Ospace_Osimps_I2_J,axiom,
% 5.82/6.13 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.13 ( ( vEBT_VEBT_space @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.82/6.13 = ( 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 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.space.simps(2)
% 5.82/6.13 thf(fact_5585_VEBT__internal_Ospace_Oelims,axiom,
% 5.82/6.13 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.13 ( ( ( vEBT_VEBT_space @ X2 )
% 5.82/6.13 = Y3 )
% 5.82/6.13 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.13 ( X2
% 5.82/6.13 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.13 => ( Y3
% 5.82/6.13 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.82/6.13 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.13 ( ( X2
% 5.82/6.13 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.13 => ( Y3
% 5.82/6.13 != ( 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 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.space.elims
% 5.82/6.13 thf(fact_5586_round__unique,axiom,
% 5.82/6.13 ! [X2: real,Y3: int] :
% 5.82/6.13 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y3 ) )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.13 => ( ( archim8280529875227126926d_real @ X2 )
% 5.82/6.13 = Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % round_unique
% 5.82/6.13 thf(fact_5587_round__unique,axiom,
% 5.82/6.13 ! [X2: rat,Y3: int] :
% 5.82/6.13 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y3 ) )
% 5.82/6.13 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.13 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.82/6.13 = Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % round_unique
% 5.82/6.13 thf(fact_5588_mult__le__cancel__iff1,axiom,
% 5.82/6.13 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.13 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 5.82/6.13 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_le_cancel_iff1
% 5.82/6.13 thf(fact_5589_mult__le__cancel__iff1,axiom,
% 5.82/6.13 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.13 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.82/6.13 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 5.82/6.13 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_le_cancel_iff1
% 5.82/6.13 thf(fact_5590_mult__le__cancel__iff1,axiom,
% 5.82/6.13 ! [Z: int,X2: int,Y3: int] :
% 5.82/6.13 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.13 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 5.82/6.13 = ( ord_less_eq_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_le_cancel_iff1
% 5.82/6.13 thf(fact_5591_mult__le__cancel__iff2,axiom,
% 5.82/6.13 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.13 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.82/6.13 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y3 ) )
% 5.82/6.13 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_le_cancel_iff2
% 5.82/6.13 thf(fact_5592_mult__le__cancel__iff2,axiom,
% 5.82/6.13 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.13 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.82/6.13 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y3 ) )
% 5.82/6.13 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_le_cancel_iff2
% 5.82/6.13 thf(fact_5593_mult__le__cancel__iff2,axiom,
% 5.82/6.13 ! [Z: int,X2: int,Y3: int] :
% 5.82/6.13 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.13 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y3 ) )
% 5.82/6.13 = ( ord_less_eq_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_le_cancel_iff2
% 5.82/6.13 thf(fact_5594_vebt__succi__refines,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,X2: nat,T: vEBT_VEBT] : ( refine7594492741263601813on_nat @ ( vEBT_vebt_succi @ Ti @ X2 ) @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % vebt_succi_refines
% 5.82/6.13 thf(fact_5595_vebt__predi__refines,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,X2: nat,T: vEBT_VEBT] : ( refine7594492741263601813on_nat @ ( vEBT_vebt_predi @ Ti @ X2 ) @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % vebt_predi_refines
% 5.82/6.13 thf(fact_5596_divmod__algorithm__code_I7_J,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( ( ord_less_eq_num @ M @ N )
% 5.82/6.13 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.82/6.13 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(7)
% 5.82/6.13 thf(fact_5597_divmod__algorithm__code_I7_J,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( ( ord_less_eq_num @ M @ N )
% 5.82/6.13 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.82/6.13 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(7)
% 5.82/6.13 thf(fact_5598_divmod__algorithm__code_I7_J,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( ( ord_less_eq_num @ M @ N )
% 5.82/6.13 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.82/6.13 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(7)
% 5.82/6.13 thf(fact_5599_vebt__buildupi__refines,axiom,
% 5.82/6.13 ! [N: nat] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_V739175172307565963ildupi @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % vebt_buildupi_refines
% 5.82/6.13 thf(fact_5600_vebt__inserti__refines,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,X2: nat,T: vEBT_VEBT] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_inserti @ Ti @ X2 ) @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % vebt_inserti_refines
% 5.82/6.13 thf(fact_5601_round__numeral,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.82/6.13 = ( numeral_numeral_int @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % round_numeral
% 5.82/6.13 thf(fact_5602_round__numeral,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.82/6.13 = ( numeral_numeral_int @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % round_numeral
% 5.82/6.13 thf(fact_5603_round__1,axiom,
% 5.82/6.13 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.82/6.13 = one_one_int ) ).
% 5.82/6.13
% 5.82/6.13 % round_1
% 5.82/6.13 thf(fact_5604_round__1,axiom,
% 5.82/6.13 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.82/6.13 = one_one_int ) ).
% 5.82/6.13
% 5.82/6.13 % round_1
% 5.82/6.13 thf(fact_5605_divmod__algorithm__code_I2_J,axiom,
% 5.82/6.13 ! [M: num] :
% 5.82/6.13 ( ( unique3479559517661332726nteger @ M @ one )
% 5.82/6.13 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(2)
% 5.82/6.13 thf(fact_5606_divmod__algorithm__code_I2_J,axiom,
% 5.82/6.13 ! [M: num] :
% 5.82/6.13 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.82/6.13 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(2)
% 5.82/6.13 thf(fact_5607_divmod__algorithm__code_I2_J,axiom,
% 5.82/6.13 ! [M: num] :
% 5.82/6.13 ( ( unique5052692396658037445od_int @ M @ one )
% 5.82/6.13 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(2)
% 5.82/6.13 thf(fact_5608_divmod__algorithm__code_I3_J,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.82/6.13 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(3)
% 5.82/6.13 thf(fact_5609_divmod__algorithm__code_I3_J,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.82/6.13 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(3)
% 5.82/6.13 thf(fact_5610_divmod__algorithm__code_I3_J,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.82/6.13 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(3)
% 5.82/6.13 thf(fact_5611_divmod__algorithm__code_I4_J,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.82/6.13 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(4)
% 5.82/6.13 thf(fact_5612_divmod__algorithm__code_I4_J,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.82/6.13 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(4)
% 5.82/6.13 thf(fact_5613_divmod__algorithm__code_I4_J,axiom,
% 5.82/6.13 ! [N: num] :
% 5.82/6.13 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.82/6.13 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(4)
% 5.82/6.13 thf(fact_5614_divmod__algorithm__code_I8_J,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( ( ord_less_num @ M @ N )
% 5.82/6.13 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_num @ M @ N )
% 5.82/6.13 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(8)
% 5.82/6.13 thf(fact_5615_divmod__algorithm__code_I8_J,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( ( ord_less_num @ M @ N )
% 5.82/6.13 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_num @ M @ N )
% 5.82/6.13 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(8)
% 5.82/6.13 thf(fact_5616_divmod__algorithm__code_I8_J,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( ( ord_less_num @ M @ N )
% 5.82/6.13 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.82/6.13 & ( ~ ( ord_less_num @ M @ N )
% 5.82/6.13 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.82/6.13 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_algorithm_code(8)
% 5.82/6.13 thf(fact_5617_TBOUND__VEBT__case,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,F: $o > $o > heap_T8145700208782473153_VEBTi,Bnd: $o > $o > nat,F5: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T8145700208782473153_VEBTi,Bnd2: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > nat] :
% 5.82/6.13 ( ! [A3: $o,B3: $o] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.13 => ( time_T5737551269749752165_VEBTi @ ( F @ A3 @ B3 ) @ ( Bnd @ A3 @ B3 ) ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Nodei @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( time_T5737551269749752165_VEBTi @ ( F5 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( Bnd2 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) ) )
% 5.82/6.13 => ( time_T5737551269749752165_VEBTi @ ( vEBT_c6028912655521741485_VEBTi @ F5 @ F @ Ti ) @ ( vEBT_case_VEBTi_nat @ Bnd2 @ Bnd @ Ti ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % TBOUND_VEBT_case
% 5.82/6.13 thf(fact_5618_TBOUND__VEBT__case,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,F: $o > $o > heap_Time_Heap_o,Bnd: $o > $o > nat,F5: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_Time_Heap_o,Bnd2: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > nat] :
% 5.82/6.13 ( ! [A3: $o,B3: $o] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.13 => ( time_TBOUND_o @ ( F @ A3 @ B3 ) @ ( Bnd @ A3 @ B3 ) ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Nodei @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( time_TBOUND_o @ ( F5 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( Bnd2 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) ) )
% 5.82/6.13 => ( time_TBOUND_o @ ( vEBT_c6104975476656191286Heap_o @ F5 @ F @ Ti ) @ ( vEBT_case_VEBTi_nat @ Bnd2 @ Bnd @ Ti ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % TBOUND_VEBT_case
% 5.82/6.13 thf(fact_5619_TBOUND__VEBT__case,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,F: $o > $o > heap_T2636463487746394924on_nat,Bnd: $o > $o > nat,F5: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_T2636463487746394924on_nat,Bnd2: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > nat] :
% 5.82/6.13 ( ! [A3: $o,B3: $o] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.13 => ( time_T8353473612707095248on_nat @ ( F @ A3 @ B3 ) @ ( Bnd @ A3 @ B3 ) ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Nodei @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( time_T8353473612707095248on_nat @ ( F5 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( Bnd2 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) ) )
% 5.82/6.13 => ( time_T8353473612707095248on_nat @ ( vEBT_c6250501799366334488on_nat @ F5 @ F @ Ti ) @ ( vEBT_case_VEBTi_nat @ Bnd2 @ Bnd @ Ti ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % TBOUND_VEBT_case
% 5.82/6.13 thf(fact_5620_TBOUND__VEBT__case,axiom,
% 5.82/6.13 ! [Ti: vEBT_VEBTi,F: $o > $o > heap_Time_Heap_nat,Bnd: $o > $o > nat,F5: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > heap_Time_Heap_nat,Bnd2: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > nat] :
% 5.82/6.13 ( ! [A3: $o,B3: $o] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.13 => ( time_TBOUND_nat @ ( F @ A3 @ B3 ) @ ( Bnd @ A3 @ B3 ) ) )
% 5.82/6.13 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeArray: array_VEBT_VEBTi,Summary2: vEBT_VEBTi] :
% 5.82/6.13 ( ( Ti
% 5.82/6.13 = ( vEBT_Nodei @ Info2 @ Deg2 @ TreeArray @ Summary2 ) )
% 5.82/6.13 => ( time_TBOUND_nat @ ( F5 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) @ ( Bnd2 @ Info2 @ Deg2 @ TreeArray @ Summary2 ) ) )
% 5.82/6.13 => ( time_TBOUND_nat @ ( vEBT_c1335663792808957512ap_nat @ F5 @ F @ Ti ) @ ( vEBT_case_VEBTi_nat @ Bnd2 @ Bnd @ Ti ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % TBOUND_VEBT_case
% 5.82/6.13 thf(fact_5621_round__mono,axiom,
% 5.82/6.13 ! [X2: rat,Y3: rat] :
% 5.82/6.13 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.13 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % round_mono
% 5.82/6.13 thf(fact_5622_ceiling__ge__round,axiom,
% 5.82/6.13 ! [X2: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % ceiling_ge_round
% 5.82/6.13 thf(fact_5623_divmod__divmod__step,axiom,
% 5.82/6.13 ( unique5055182867167087721od_nat
% 5.82/6.13 = ( ^ [M6: num,N4: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N4 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N4 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_divmod_step
% 5.82/6.13 thf(fact_5624_divmod__divmod__step,axiom,
% 5.82/6.13 ( unique5052692396658037445od_int
% 5.82/6.13 = ( ^ [M6: num,N4: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N4 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N4 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_divmod_step
% 5.82/6.13 thf(fact_5625_divmod__divmod__step,axiom,
% 5.82/6.13 ( unique3479559517661332726nteger
% 5.82/6.13 = ( ^ [M6: num,N4: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N4 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N4 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % divmod_divmod_step
% 5.82/6.13 thf(fact_5626_mult__less__iff1,axiom,
% 5.82/6.13 ! [Z: real,X2: real,Y3: real] :
% 5.82/6.13 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.82/6.13 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 5.82/6.13 = ( ord_less_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_less_iff1
% 5.82/6.13 thf(fact_5627_mult__less__iff1,axiom,
% 5.82/6.13 ! [Z: rat,X2: rat,Y3: rat] :
% 5.82/6.13 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.82/6.13 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 5.82/6.13 = ( ord_less_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_less_iff1
% 5.82/6.13 thf(fact_5628_mult__less__iff1,axiom,
% 5.82/6.13 ! [Z: int,X2: int,Y3: int] :
% 5.82/6.13 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.82/6.13 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 5.82/6.13 = ( ord_less_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_less_iff1
% 5.82/6.13 thf(fact_5629_of__int__round__le,axiom,
% 5.82/6.13 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_int_round_le
% 5.82/6.13 thf(fact_5630_of__int__round__le,axiom,
% 5.82/6.13 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_int_round_le
% 5.82/6.13 thf(fact_5631_of__int__round__ge,axiom,
% 5.82/6.13 ! [X2: real] : ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_int_round_ge
% 5.82/6.13 thf(fact_5632_of__int__round__ge,axiom,
% 5.82/6.13 ! [X2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_int_round_ge
% 5.82/6.13 thf(fact_5633_of__int__round__gt,axiom,
% 5.82/6.13 ! [X2: real] : ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_int_round_gt
% 5.82/6.13 thf(fact_5634_of__int__round__gt,axiom,
% 5.82/6.13 ! [X2: rat] : ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_int_round_gt
% 5.82/6.13 thf(fact_5635_divides__aux__eq,axiom,
% 5.82/6.13 ! [Q3: code_integer,R2: code_integer] :
% 5.82/6.13 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.82/6.13 = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.13
% 5.82/6.13 % divides_aux_eq
% 5.82/6.13 thf(fact_5636_divides__aux__eq,axiom,
% 5.82/6.13 ! [Q3: nat,R2: nat] :
% 5.82/6.13 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.82/6.13 = ( R2 = zero_zero_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % divides_aux_eq
% 5.82/6.13 thf(fact_5637_divides__aux__eq,axiom,
% 5.82/6.13 ! [Q3: int,R2: int] :
% 5.82/6.13 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.13 = ( R2 = zero_zero_int ) ) ).
% 5.82/6.13
% 5.82/6.13 % divides_aux_eq
% 5.82/6.13 thf(fact_5638_VEBT__internal_OT__vebt__buildupi_H_Oelims,axiom,
% 5.82/6.13 ! [X2: nat,Y3: int] :
% 5.82/6.13 ( ( ( vEBT_V9176841429113362141ildupi @ X2 )
% 5.82/6.13 = Y3 )
% 5.82/6.13 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.13 => ( Y3 != one_one_int ) )
% 5.82/6.13 => ( ( ( X2
% 5.82/6.13 = ( suc @ zero_zero_nat ) )
% 5.82/6.13 => ( Y3 != one_one_int ) )
% 5.82/6.13 => ~ ! [N3: nat] :
% 5.82/6.13 ( ( X2
% 5.82/6.13 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.13 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.13 => ( Y3
% 5.82/6.13 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.13 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.13 => ( Y3
% 5.82/6.13 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % VEBT_internal.T_vebt_buildupi'.elims
% 5.82/6.13 thf(fact_5639_highi__def,axiom,
% 5.82/6.13 ( vEBT_VEBT_highi
% 5.82/6.13 = ( ^ [X3: nat,N4: nat] : ( heap_Time_return_nat @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % highi_def
% 5.82/6.13 thf(fact_5640_nth__rule,axiom,
% 5.82/6.13 ! [I: nat,Xs: list_VEBT_VEBTi,A2: array_VEBT_VEBTi] :
% 5.82/6.13 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs ) @ ( array_nth_VEBT_VEBTi @ A2 @ I )
% 5.82/6.13 @ ^ [R5: vEBT_VEBTi] :
% 5.82/6.13 ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs )
% 5.82/6.13 @ ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( nth_VEBT_VEBTi @ Xs @ I ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_rule
% 5.82/6.13 thf(fact_5641_nth__rule,axiom,
% 5.82/6.13 ! [I: nat,Xs: list_o,A2: array_o] :
% 5.82/6.13 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.13 => ( hoare_hoare_triple_o @ ( snga_assn_o @ A2 @ Xs ) @ ( array_nth_o @ A2 @ I )
% 5.82/6.13 @ ^ [R5: $o] :
% 5.82/6.13 ( times_times_assn @ ( snga_assn_o @ A2 @ Xs )
% 5.82/6.13 @ ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( nth_o @ Xs @ I ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_rule
% 5.82/6.13 thf(fact_5642_nth__rule,axiom,
% 5.82/6.13 ! [I: nat,Xs: list_option_nat,A2: array_option_nat] :
% 5.82/6.13 ( ( ord_less_nat @ I @ ( size_s6086282163384603972on_nat @ Xs ) )
% 5.82/6.13 => ( hoare_7629718768684598413on_nat @ ( snga_assn_option_nat @ A2 @ Xs ) @ ( array_nth_option_nat @ A2 @ I )
% 5.82/6.13 @ ^ [R5: option_nat] :
% 5.82/6.13 ( times_times_assn @ ( snga_assn_option_nat @ A2 @ Xs )
% 5.82/6.13 @ ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( nth_option_nat @ Xs @ I ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_rule
% 5.82/6.13 thf(fact_5643_nth__rule,axiom,
% 5.82/6.13 ! [I: nat,Xs: list_nat,A2: array_nat] :
% 5.82/6.13 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.82/6.13 => ( hoare_3067605981109127869le_nat @ ( snga_assn_nat @ A2 @ Xs ) @ ( array_nth_nat @ A2 @ I )
% 5.82/6.13 @ ^ [R5: nat] :
% 5.82/6.13 ( times_times_assn @ ( snga_assn_nat @ A2 @ Xs )
% 5.82/6.13 @ ( pure_assn
% 5.82/6.13 @ ( R5
% 5.82/6.13 = ( nth_nat @ Xs @ I ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nth_rule
% 5.82/6.13 thf(fact_5644_unset__bit__0,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A2 )
% 5.82/6.13 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unset_bit_0
% 5.82/6.13 thf(fact_5645_unset__bit__0,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A2 )
% 5.82/6.13 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unset_bit_0
% 5.82/6.13 thf(fact_5646_fi__rule,axiom,
% 5.82/6.13 ! [P: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,Ps: assn,F3: assn] :
% 5.82/6.13 ( ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q )
% 5.82/6.13 => ( ( entails @ Ps @ ( times_times_assn @ P @ F3 ) )
% 5.82/6.13 => ( hoare_1429296392585015714_VEBTi @ Ps @ C2
% 5.82/6.13 @ ^ [X3: vEBT_VEBTi] : ( times_times_assn @ ( Q @ X3 ) @ F3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % fi_rule
% 5.82/6.13 thf(fact_5647_fi__rule,axiom,
% 5.82/6.13 ! [P: assn,C2: heap_Time_Heap_o,Q: $o > assn,Ps: assn,F3: assn] :
% 5.82/6.13 ( ( hoare_hoare_triple_o @ P @ C2 @ Q )
% 5.82/6.13 => ( ( entails @ Ps @ ( times_times_assn @ P @ F3 ) )
% 5.82/6.13 => ( hoare_hoare_triple_o @ Ps @ C2
% 5.82/6.13 @ ^ [X3: $o] : ( times_times_assn @ ( Q @ X3 ) @ F3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % fi_rule
% 5.82/6.13 thf(fact_5648_fi__rule,axiom,
% 5.82/6.13 ! [P: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn,Ps: assn,F3: assn] :
% 5.82/6.13 ( ( hoare_7629718768684598413on_nat @ P @ C2 @ Q )
% 5.82/6.13 => ( ( entails @ Ps @ ( times_times_assn @ P @ F3 ) )
% 5.82/6.13 => ( hoare_7629718768684598413on_nat @ Ps @ C2
% 5.82/6.13 @ ^ [X3: option_nat] : ( times_times_assn @ ( Q @ X3 ) @ F3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % fi_rule
% 5.82/6.13 thf(fact_5649_fi__rule,axiom,
% 5.82/6.13 ! [P: assn,C2: heap_Time_Heap_nat,Q: nat > assn,Ps: assn,F3: assn] :
% 5.82/6.13 ( ( hoare_3067605981109127869le_nat @ P @ C2 @ Q )
% 5.82/6.13 => ( ( entails @ Ps @ ( times_times_assn @ P @ F3 ) )
% 5.82/6.13 => ( hoare_3067605981109127869le_nat @ Ps @ C2
% 5.82/6.13 @ ^ [X3: nat] : ( times_times_assn @ ( Q @ X3 ) @ F3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % fi_rule
% 5.82/6.13 thf(fact_5650_highsimp,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] :
% 5.82/6.13 ( ( heap_Time_return_nat @ ( vEBT_VEBT_high @ X2 @ N ) )
% 5.82/6.13 = ( vEBT_VEBT_highi @ X2 @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % highsimp
% 5.82/6.13 thf(fact_5651_lowsimp,axiom,
% 5.82/6.13 ! [X2: nat,N: nat] :
% 5.82/6.13 ( ( heap_Time_return_nat @ ( vEBT_VEBT_low @ X2 @ N ) )
% 5.82/6.13 = ( vEBT_VEBT_lowi @ X2 @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % lowsimp
% 5.82/6.13 thf(fact_5652_dvd__add__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ ( plus_plus_real @ B2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_real @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_right_iff
% 5.82/6.13 thf(fact_5653_dvd__add__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ B2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_rat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_right_iff
% 5.82/6.13 thf(fact_5654_dvd__add__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ B2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_right_iff
% 5.82/6.13 thf(fact_5655_dvd__add__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ B2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_right_iff
% 5.82/6.13 thf(fact_5656_dvd__add__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_real @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_left_iff
% 5.82/6.13 thf(fact_5657_dvd__add__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_rat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_left_iff
% 5.82/6.13 thf(fact_5658_dvd__add__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_left_iff
% 5.82/6.13 thf(fact_5659_dvd__add__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_triv_left_iff
% 5.82/6.13 thf(fact_5660_div__dvd__div,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ A2 @ C2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B2 @ A2 ) @ ( divide_divide_nat @ C2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_dvd_div
% 5.82/6.13 thf(fact_5661_div__dvd__div,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ A2 @ C2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ ( divide_divide_int @ B2 @ A2 ) @ ( divide_divide_int @ C2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_dvd_div
% 5.82/6.13 thf(fact_5662_unset__bit__nonnegative__int__iff,axiom,
% 5.82/6.13 ! [N: nat,K: int] :
% 5.82/6.13 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.82/6.13 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.13
% 5.82/6.13 % unset_bit_nonnegative_int_iff
% 5.82/6.13 thf(fact_5663_nat__dvd__1__iff__1,axiom,
% 5.82/6.13 ! [M: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.82/6.13 = ( M = one_one_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % nat_dvd_1_iff_1
% 5.82/6.13 thf(fact_5664_dvd__times__right__cancel__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( A2 != zero_zero_nat )
% 5.82/6.13 => ( ( dvd_dvd_nat @ ( times_times_nat @ B2 @ A2 ) @ ( times_times_nat @ C2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_times_right_cancel_iff
% 5.82/6.13 thf(fact_5665_dvd__times__right__cancel__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( A2 != zero_zero_int )
% 5.82/6.13 => ( ( dvd_dvd_int @ ( times_times_int @ B2 @ A2 ) @ ( times_times_int @ C2 @ A2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_times_right_cancel_iff
% 5.82/6.13 thf(fact_5666_dvd__times__left__cancel__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( A2 != zero_zero_nat )
% 5.82/6.13 => ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ ( times_times_nat @ A2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_times_left_cancel_iff
% 5.82/6.13 thf(fact_5667_dvd__times__left__cancel__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( A2 != zero_zero_int )
% 5.82/6.13 => ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_times_left_cancel_iff
% 5.82/6.13 thf(fact_5668_dvd__mult__cancel__right,axiom,
% 5.82/6.13 ! [A2: complex,C2: complex,B2: complex] :
% 5.82/6.13 ( ( dvd_dvd_complex @ ( times_times_complex @ A2 @ C2 ) @ ( times_times_complex @ B2 @ C2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_complex )
% 5.82/6.13 | ( dvd_dvd_complex @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_right
% 5.82/6.13 thf(fact_5669_dvd__mult__cancel__right,axiom,
% 5.82/6.13 ! [A2: real,C2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ C2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_real )
% 5.82/6.13 | ( dvd_dvd_real @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_right
% 5.82/6.13 thf(fact_5670_dvd__mult__cancel__right,axiom,
% 5.82/6.13 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ C2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_rat )
% 5.82/6.13 | ( dvd_dvd_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_right
% 5.82/6.13 thf(fact_5671_dvd__mult__cancel__right,axiom,
% 5.82/6.13 ! [A2: int,C2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_int )
% 5.82/6.13 | ( dvd_dvd_int @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_right
% 5.82/6.13 thf(fact_5672_dvd__mult__cancel__left,axiom,
% 5.82/6.13 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.13 ( ( dvd_dvd_complex @ ( times_times_complex @ C2 @ A2 ) @ ( times_times_complex @ C2 @ B2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_complex )
% 5.82/6.13 | ( dvd_dvd_complex @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_left
% 5.82/6.13 thf(fact_5673_dvd__mult__cancel__left,axiom,
% 5.82/6.13 ! [C2: real,A2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ ( times_times_real @ C2 @ A2 ) @ ( times_times_real @ C2 @ B2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_real )
% 5.82/6.13 | ( dvd_dvd_real @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_left
% 5.82/6.13 thf(fact_5674_dvd__mult__cancel__left,axiom,
% 5.82/6.13 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ ( times_times_rat @ C2 @ A2 ) @ ( times_times_rat @ C2 @ B2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_rat )
% 5.82/6.13 | ( dvd_dvd_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_left
% 5.82/6.13 thf(fact_5675_dvd__mult__cancel__left,axiom,
% 5.82/6.13 ! [C2: int,A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.13 = ( ( C2 = zero_zero_int )
% 5.82/6.13 | ( dvd_dvd_int @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_cancel_left
% 5.82/6.13 thf(fact_5676_dvd__add__times__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ ( plus_plus_real @ B2 @ ( times_times_real @ C2 @ A2 ) ) )
% 5.82/6.13 = ( dvd_dvd_real @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_right_iff
% 5.82/6.13 thf(fact_5677_dvd__add__times__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ B2 @ ( times_times_rat @ C2 @ A2 ) ) )
% 5.82/6.13 = ( dvd_dvd_rat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_right_iff
% 5.82/6.13 thf(fact_5678_dvd__add__times__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ B2 @ ( times_times_nat @ C2 @ A2 ) ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_right_iff
% 5.82/6.13 thf(fact_5679_dvd__add__times__triv__right__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ B2 @ ( times_times_int @ C2 @ A2 ) ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_right_iff
% 5.82/6.13 thf(fact_5680_dvd__add__times__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: real,C2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ ( plus_plus_real @ ( times_times_real @ C2 @ A2 ) @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_real @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_left_iff
% 5.82/6.13 thf(fact_5681_dvd__add__times__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ ( times_times_rat @ C2 @ A2 ) @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_rat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_left_iff
% 5.82/6.13 thf(fact_5682_dvd__add__times__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ ( times_times_nat @ C2 @ A2 ) @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_left_iff
% 5.82/6.13 thf(fact_5683_dvd__add__times__triv__left__iff,axiom,
% 5.82/6.13 ! [A2: int,C2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ ( times_times_int @ C2 @ A2 ) @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_times_triv_left_iff
% 5.82/6.13 thf(fact_5684_unit__prod,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.13 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.13 => ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ one_one_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_prod
% 5.82/6.13 thf(fact_5685_unit__prod,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.13 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.13 => ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ one_one_int ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_prod
% 5.82/6.13 thf(fact_5686_div__add,axiom,
% 5.82/6.13 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.13 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.13 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ C2 ) @ ( divide_divide_nat @ B2 @ C2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_add
% 5.82/6.13 thf(fact_5687_div__add,axiom,
% 5.82/6.13 ! [C2: int,A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.13 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.13 = ( plus_plus_int @ ( divide_divide_int @ A2 @ C2 ) @ ( divide_divide_int @ B2 @ C2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_add
% 5.82/6.13 thf(fact_5688_unit__div,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.13 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.13 => ( dvd_dvd_nat @ ( divide_divide_nat @ A2 @ B2 ) @ one_one_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div
% 5.82/6.13 thf(fact_5689_unit__div,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.13 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.13 => ( dvd_dvd_int @ ( divide_divide_int @ A2 @ B2 ) @ one_one_int ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div
% 5.82/6.13 thf(fact_5690_unit__div__1__unit,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.13 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A2 ) @ one_one_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div_1_unit
% 5.82/6.13 thf(fact_5691_unit__div__1__unit,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.13 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A2 ) @ one_one_int ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div_1_unit
% 5.82/6.13 thf(fact_5692_unit__div__1__div__1,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.13 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A2 ) )
% 5.82/6.13 = A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div_1_div_1
% 5.82/6.13 thf(fact_5693_unit__div__1__div__1,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.13 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A2 ) )
% 5.82/6.13 = A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div_1_div_1
% 5.82/6.13 thf(fact_5694_dvd__div__mult__self,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ A2 ) @ A2 )
% 5.82/6.13 = B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_mult_self
% 5.82/6.13 thf(fact_5695_dvd__div__mult__self,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( times_times_int @ ( divide_divide_int @ B2 @ A2 ) @ A2 )
% 5.82/6.13 = B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_mult_self
% 5.82/6.13 thf(fact_5696_dvd__mult__div__cancel,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( times_times_nat @ A2 @ ( divide_divide_nat @ B2 @ A2 ) )
% 5.82/6.13 = B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_div_cancel
% 5.82/6.13 thf(fact_5697_dvd__mult__div__cancel,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( times_times_int @ A2 @ ( divide_divide_int @ B2 @ A2 ) )
% 5.82/6.13 = B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_div_cancel
% 5.82/6.13 thf(fact_5698_div__diff,axiom,
% 5.82/6.13 ! [C2: int,A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.13 => ( ( divide_divide_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.13 = ( minus_minus_int @ ( divide_divide_int @ A2 @ C2 ) @ ( divide_divide_int @ B2 @ C2 ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_diff
% 5.82/6.13 thf(fact_5699_dvd__1__iff__1,axiom,
% 5.82/6.13 ! [M: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.82/6.13 = ( M
% 5.82/6.13 = ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_1_iff_1
% 5.82/6.13 thf(fact_5700_dvd__1__left,axiom,
% 5.82/6.13 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_1_left
% 5.82/6.13 thf(fact_5701_nat__mult__dvd__cancel__disj,axiom,
% 5.82/6.13 ! [K: nat,M: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.13 = ( ( K = zero_zero_nat )
% 5.82/6.13 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % nat_mult_dvd_cancel_disj
% 5.82/6.13 thf(fact_5702_unit__mult__div__div,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.13 => ( ( times_times_nat @ B2 @ ( divide_divide_nat @ one_one_nat @ A2 ) )
% 5.82/6.13 = ( divide_divide_nat @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_mult_div_div
% 5.82/6.13 thf(fact_5703_unit__mult__div__div,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.13 => ( ( times_times_int @ B2 @ ( divide_divide_int @ one_one_int @ A2 ) )
% 5.82/6.13 = ( divide_divide_int @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_mult_div_div
% 5.82/6.13 thf(fact_5704_unit__div__mult__self,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.13 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ A2 ) @ A2 )
% 5.82/6.13 = B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div_mult_self
% 5.82/6.13 thf(fact_5705_unit__div__mult__self,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.13 => ( ( times_times_int @ ( divide_divide_int @ B2 @ A2 ) @ A2 )
% 5.82/6.13 = B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_div_mult_self
% 5.82/6.13 thf(fact_5706_odd__add,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A2 @ B2 ) ) )
% 5.82/6.13 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.13 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_add
% 5.82/6.13 thf(fact_5707_odd__add,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A2 @ B2 ) ) )
% 5.82/6.13 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.13 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_add
% 5.82/6.13 thf(fact_5708_even__add,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_add
% 5.82/6.13 thf(fact_5709_even__add,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.13 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_add
% 5.82/6.13 thf(fact_5710_even__mult__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A2 @ B2 ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_mult_iff
% 5.82/6.13 thf(fact_5711_even__mult__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.13 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_mult_iff
% 5.82/6.13 thf(fact_5712_even__Suc,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_Suc
% 5.82/6.13 thf(fact_5713_even__Suc__Suc__iff,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.82/6.13 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_Suc_Suc_iff
% 5.82/6.13 thf(fact_5714_dvd__numeral__simp,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.13 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_numeral_simp
% 5.82/6.13 thf(fact_5715_dvd__numeral__simp,axiom,
% 5.82/6.13 ! [M: num,N: num] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.82/6.13 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_numeral_simp
% 5.82/6.13 thf(fact_5716_even__plus__one__iff,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A2 @ one_one_nat ) )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_plus_one_iff
% 5.82/6.13 thf(fact_5717_even__plus__one__iff,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A2 @ one_one_int ) )
% 5.82/6.13 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_plus_one_iff
% 5.82/6.13 thf(fact_5718_even__diff,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_diff
% 5.82/6.13 thf(fact_5719_odd__Suc__div__two,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_Suc_div_two
% 5.82/6.13 thf(fact_5720_even__Suc__div__two,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_Suc_div_two
% 5.82/6.13 thf(fact_5721_even__succ__div__2,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_2
% 5.82/6.13 thf(fact_5722_even__succ__div__2,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_2
% 5.82/6.13 thf(fact_5723_odd__succ__div__two,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_succ_div_two
% 5.82/6.13 thf(fact_5724_odd__succ__div__two,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( plus_plus_int @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_succ_div_two
% 5.82/6.13 thf(fact_5725_even__succ__div__two,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_two
% 5.82/6.13 thf(fact_5726_even__succ__div__two,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.13 = ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_two
% 5.82/6.13 thf(fact_5727_even__power,axiom,
% 5.82/6.13 ! [A2: code_integer,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.13 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_power
% 5.82/6.13 thf(fact_5728_even__power,axiom,
% 5.82/6.13 ! [A2: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A2 @ N ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_power
% 5.82/6.13 thf(fact_5729_even__power,axiom,
% 5.82/6.13 ! [A2: int,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A2 @ N ) )
% 5.82/6.13 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_power
% 5.82/6.13 thf(fact_5730_zero__le__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: real,W: num] :
% 5.82/6.13 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_le_power_eq_numeral
% 5.82/6.13 thf(fact_5731_zero__le__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: code_integer,W: num] :
% 5.82/6.13 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_le_power_eq_numeral
% 5.82/6.13 thf(fact_5732_zero__le__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: rat,W: num] :
% 5.82/6.13 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_le_power_eq_numeral
% 5.82/6.13 thf(fact_5733_zero__le__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: int,W: num] :
% 5.82/6.13 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_le_power_eq_numeral
% 5.82/6.13 thf(fact_5734_power__less__zero__eq,axiom,
% 5.82/6.13 ! [A2: code_integer,N: nat] :
% 5.82/6.13 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ zero_z3403309356797280102nteger )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 & ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq
% 5.82/6.13 thf(fact_5735_power__less__zero__eq,axiom,
% 5.82/6.13 ! [A2: real,N: nat] :
% 5.82/6.13 ( ( ord_less_real @ ( power_power_real @ A2 @ N ) @ zero_zero_real )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 & ( ord_less_real @ A2 @ zero_zero_real ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq
% 5.82/6.13 thf(fact_5736_power__less__zero__eq,axiom,
% 5.82/6.13 ! [A2: rat,N: nat] :
% 5.82/6.13 ( ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ zero_zero_rat )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 & ( ord_less_rat @ A2 @ zero_zero_rat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq
% 5.82/6.13 thf(fact_5737_power__less__zero__eq,axiom,
% 5.82/6.13 ! [A2: int,N: nat] :
% 5.82/6.13 ( ( ord_less_int @ ( power_power_int @ A2 @ N ) @ zero_zero_int )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 & ( ord_less_int @ A2 @ zero_zero_int ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq
% 5.82/6.13 thf(fact_5738_power__less__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: code_integer,W: num] :
% 5.82/6.13 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_z3403309356797280102nteger )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq_numeral
% 5.82/6.13 thf(fact_5739_power__less__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: real,W: num] :
% 5.82/6.13 ( ( ord_less_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_real @ A2 @ zero_zero_real ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq_numeral
% 5.82/6.13 thf(fact_5740_power__less__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: rat,W: num] :
% 5.82/6.13 ( ( ord_less_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_rat @ A2 @ zero_zero_rat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq_numeral
% 5.82/6.13 thf(fact_5741_power__less__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: int,W: num] :
% 5.82/6.13 ( ( ord_less_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.82/6.13 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_int @ A2 @ zero_zero_int ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_less_zero_eq_numeral
% 5.82/6.13 thf(fact_5742_even__of__nat,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.13 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_of_nat
% 5.82/6.13 thf(fact_5743_even__of__nat,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.13 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_of_nat
% 5.82/6.13 thf(fact_5744_odd__Suc__minus__one,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.82/6.13 = N ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_Suc_minus_one
% 5.82/6.13 thf(fact_5745_even__diff__nat,axiom,
% 5.82/6.13 ! [M: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.13 = ( ( ord_less_nat @ M @ N )
% 5.82/6.13 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_diff_nat
% 5.82/6.13 thf(fact_5746_odd__two__times__div__two__succ,axiom,
% 5.82/6.13 ! [A2: nat] :
% 5.82/6.13 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.82/6.13 = A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_two_times_div_two_succ
% 5.82/6.13 thf(fact_5747_odd__two__times__div__two__succ,axiom,
% 5.82/6.13 ! [A2: int] :
% 5.82/6.13 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.82/6.13 = A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_two_times_div_two_succ
% 5.82/6.13 thf(fact_5748_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.82/6.13 = ( N = zero_zero_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % semiring_parity_class.even_mask_iff
% 5.82/6.13 thf(fact_5749_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.82/6.13 = ( N = zero_zero_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % semiring_parity_class.even_mask_iff
% 5.82/6.13 thf(fact_5750_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.82/6.13 = ( N = zero_zero_nat ) ) ).
% 5.82/6.13
% 5.82/6.13 % semiring_parity_class.even_mask_iff
% 5.82/6.13 thf(fact_5751_zero__less__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: code_integer,W: num] :
% 5.82/6.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( ( numeral_numeral_nat @ W )
% 5.82/6.13 = zero_zero_nat )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 != zero_z3403309356797280102nteger ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_less_power_eq_numeral
% 5.82/6.13 thf(fact_5752_zero__less__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: real,W: num] :
% 5.82/6.13 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( ( numeral_numeral_nat @ W )
% 5.82/6.13 = zero_zero_nat )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 != zero_zero_real ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_real @ zero_zero_real @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_less_power_eq_numeral
% 5.82/6.13 thf(fact_5753_zero__less__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: rat,W: num] :
% 5.82/6.13 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( ( numeral_numeral_nat @ W )
% 5.82/6.13 = zero_zero_nat )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 != zero_zero_rat ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_rat @ zero_zero_rat @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_less_power_eq_numeral
% 5.82/6.13 thf(fact_5754_zero__less__power__eq__numeral,axiom,
% 5.82/6.13 ! [A2: int,W: num] :
% 5.82/6.13 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ W ) ) )
% 5.82/6.13 = ( ( ( numeral_numeral_nat @ W )
% 5.82/6.13 = zero_zero_nat )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 != zero_zero_int ) )
% 5.82/6.13 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_int @ zero_zero_int @ A2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % zero_less_power_eq_numeral
% 5.82/6.13 thf(fact_5755_odd__two__times__div__two__nat,axiom,
% 5.82/6.13 ! [N: nat] :
% 5.82/6.13 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.13 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.13 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % odd_two_times_div_two_nat
% 5.82/6.13 thf(fact_5756_power__le__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: real,W: num] :
% 5.82/6.13 ( ( ord_less_eq_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.82/6.13 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_eq_real @ A2 @ zero_zero_real ) )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_le_zero_eq_numeral
% 5.82/6.13 thf(fact_5757_power__le__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: code_integer,W: num] :
% 5.82/6.13 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_z3403309356797280102nteger )
% 5.82/6.13 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_le_zero_eq_numeral
% 5.82/6.13 thf(fact_5758_power__le__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: rat,W: num] :
% 5.82/6.13 ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.82/6.13 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_eq_rat @ A2 @ zero_zero_rat ) )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_le_zero_eq_numeral
% 5.82/6.13 thf(fact_5759_power__le__zero__eq__numeral,axiom,
% 5.82/6.13 ! [A2: int,W: num] :
% 5.82/6.13 ( ( ord_less_eq_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.82/6.13 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( ord_less_eq_int @ A2 @ zero_zero_int ) )
% 5.82/6.13 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.82/6.13 & ( A2 = zero_zero_int ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % power_le_zero_eq_numeral
% 5.82/6.13 thf(fact_5760_even__succ__div__exp,axiom,
% 5.82/6.13 ! [A2: code_integer,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.13 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.13 = ( divide6298287555418463151nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_exp
% 5.82/6.13 thf(fact_5761_even__succ__div__exp,axiom,
% 5.82/6.13 ! [A2: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.13 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.13 = ( divide_divide_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_exp
% 5.82/6.13 thf(fact_5762_even__succ__div__exp,axiom,
% 5.82/6.13 ! [A2: int,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.13 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.13 = ( divide_divide_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % even_succ_div_exp
% 5.82/6.13 thf(fact_5763_dvd__antisym,axiom,
% 5.82/6.13 ! [M: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ M @ N )
% 5.82/6.13 => ( ( dvd_dvd_nat @ N @ M )
% 5.82/6.13 => ( M = N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_antisym
% 5.82/6.13 thf(fact_5764_of__nat__dvd__iff,axiom,
% 5.82/6.13 ! [M: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.13 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_nat_dvd_iff
% 5.82/6.13 thf(fact_5765_of__nat__dvd__iff,axiom,
% 5.82/6.13 ! [M: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.82/6.13 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.82/6.13
% 5.82/6.13 % of_nat_dvd_iff
% 5.82/6.13 thf(fact_5766_dvd__add__right__iff,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_real @ A2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_right_iff
% 5.82/6.13 thf(fact_5767_dvd__add__right__iff,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_rat @ A2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_right_iff
% 5.82/6.13 thf(fact_5768_dvd__add__right__iff,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_right_iff
% 5.82/6.13 thf(fact_5769_dvd__add__right__iff,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_right_iff
% 5.82/6.13 thf(fact_5770_dvd__add__left__iff,axiom,
% 5.82/6.13 ! [A2: real,C2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ C2 )
% 5.82/6.13 => ( ( dvd_dvd_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_real @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_left_iff
% 5.82/6.13 thf(fact_5771_dvd__add__left__iff,axiom,
% 5.82/6.13 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ C2 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_left_iff
% 5.82/6.13 thf(fact_5772_dvd__add__left__iff,axiom,
% 5.82/6.13 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ C2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_left_iff
% 5.82/6.13 thf(fact_5773_dvd__add__left__iff,axiom,
% 5.82/6.13 ! [A2: int,C2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ C2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ B2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add_left_iff
% 5.82/6.13 thf(fact_5774_dvd__add,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_real @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_real @ A2 @ ( plus_plus_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add
% 5.82/6.13 thf(fact_5775_dvd__add,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add
% 5.82/6.13 thf(fact_5776_dvd__add,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add
% 5.82/6.13 thf(fact_5777_dvd__add,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_int @ A2 @ ( plus_plus_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_add
% 5.82/6.13 thf(fact_5778_dvd__unit__imp__unit,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.13 => ( dvd_dvd_nat @ A2 @ one_one_nat ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_unit_imp_unit
% 5.82/6.13 thf(fact_5779_dvd__unit__imp__unit,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.13 => ( dvd_dvd_int @ A2 @ one_one_int ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_unit_imp_unit
% 5.82/6.13 thf(fact_5780_unit__imp__dvd,axiom,
% 5.82/6.13 ! [B2: nat,A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.13 => ( dvd_dvd_nat @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_imp_dvd
% 5.82/6.13 thf(fact_5781_unit__imp__dvd,axiom,
% 5.82/6.13 ! [B2: int,A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.13 => ( dvd_dvd_int @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % unit_imp_dvd
% 5.82/6.13 thf(fact_5782_one__dvd,axiom,
% 5.82/6.13 ! [A2: assn] : ( dvd_dvd_assn @ one_one_assn @ A2 ) ).
% 5.82/6.13
% 5.82/6.13 % one_dvd
% 5.82/6.13 thf(fact_5783_one__dvd,axiom,
% 5.82/6.13 ! [A2: real] : ( dvd_dvd_real @ one_one_real @ A2 ) ).
% 5.82/6.13
% 5.82/6.13 % one_dvd
% 5.82/6.13 thf(fact_5784_one__dvd,axiom,
% 5.82/6.13 ! [A2: rat] : ( dvd_dvd_rat @ one_one_rat @ A2 ) ).
% 5.82/6.13
% 5.82/6.13 % one_dvd
% 5.82/6.13 thf(fact_5785_one__dvd,axiom,
% 5.82/6.13 ! [A2: nat] : ( dvd_dvd_nat @ one_one_nat @ A2 ) ).
% 5.82/6.13
% 5.82/6.13 % one_dvd
% 5.82/6.13 thf(fact_5786_one__dvd,axiom,
% 5.82/6.13 ! [A2: int] : ( dvd_dvd_int @ one_one_int @ A2 ) ).
% 5.82/6.13
% 5.82/6.13 % one_dvd
% 5.82/6.13 thf(fact_5787_dvdE,axiom,
% 5.82/6.13 ! [B2: real,A2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ B2 @ A2 )
% 5.82/6.13 => ~ ! [K2: real] :
% 5.82/6.13 ( A2
% 5.82/6.13 != ( times_times_real @ B2 @ K2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdE
% 5.82/6.13 thf(fact_5788_dvdE,axiom,
% 5.82/6.13 ! [B2: rat,A2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ B2 @ A2 )
% 5.82/6.13 => ~ ! [K2: rat] :
% 5.82/6.13 ( A2
% 5.82/6.13 != ( times_times_rat @ B2 @ K2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdE
% 5.82/6.13 thf(fact_5789_dvdE,axiom,
% 5.82/6.13 ! [B2: nat,A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.13 => ~ ! [K2: nat] :
% 5.82/6.13 ( A2
% 5.82/6.13 != ( times_times_nat @ B2 @ K2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdE
% 5.82/6.13 thf(fact_5790_dvdE,axiom,
% 5.82/6.13 ! [B2: int,A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.13 => ~ ! [K2: int] :
% 5.82/6.13 ( A2
% 5.82/6.13 != ( times_times_int @ B2 @ K2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdE
% 5.82/6.13 thf(fact_5791_dvdI,axiom,
% 5.82/6.13 ! [A2: real,B2: real,K: real] :
% 5.82/6.13 ( ( A2
% 5.82/6.13 = ( times_times_real @ B2 @ K ) )
% 5.82/6.13 => ( dvd_dvd_real @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdI
% 5.82/6.13 thf(fact_5792_dvdI,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,K: rat] :
% 5.82/6.13 ( ( A2
% 5.82/6.13 = ( times_times_rat @ B2 @ K ) )
% 5.82/6.13 => ( dvd_dvd_rat @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdI
% 5.82/6.13 thf(fact_5793_dvdI,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,K: nat] :
% 5.82/6.13 ( ( A2
% 5.82/6.13 = ( times_times_nat @ B2 @ K ) )
% 5.82/6.13 => ( dvd_dvd_nat @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdI
% 5.82/6.13 thf(fact_5794_dvdI,axiom,
% 5.82/6.13 ! [A2: int,B2: int,K: int] :
% 5.82/6.13 ( ( A2
% 5.82/6.13 = ( times_times_int @ B2 @ K ) )
% 5.82/6.13 => ( dvd_dvd_int @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvdI
% 5.82/6.13 thf(fact_5795_dvd__def,axiom,
% 5.82/6.13 ( dvd_dvd_real
% 5.82/6.13 = ( ^ [B6: real,A5: real] :
% 5.82/6.13 ? [K3: real] :
% 5.82/6.13 ( A5
% 5.82/6.13 = ( times_times_real @ B6 @ K3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_def
% 5.82/6.13 thf(fact_5796_dvd__def,axiom,
% 5.82/6.13 ( dvd_dvd_rat
% 5.82/6.13 = ( ^ [B6: rat,A5: rat] :
% 5.82/6.13 ? [K3: rat] :
% 5.82/6.13 ( A5
% 5.82/6.13 = ( times_times_rat @ B6 @ K3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_def
% 5.82/6.13 thf(fact_5797_dvd__def,axiom,
% 5.82/6.13 ( dvd_dvd_nat
% 5.82/6.13 = ( ^ [B6: nat,A5: nat] :
% 5.82/6.13 ? [K3: nat] :
% 5.82/6.13 ( A5
% 5.82/6.13 = ( times_times_nat @ B6 @ K3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_def
% 5.82/6.13 thf(fact_5798_dvd__def,axiom,
% 5.82/6.13 ( dvd_dvd_int
% 5.82/6.13 = ( ^ [B6: int,A5: int] :
% 5.82/6.13 ? [K3: int] :
% 5.82/6.13 ( A5
% 5.82/6.13 = ( times_times_int @ B6 @ K3 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_def
% 5.82/6.13 thf(fact_5799_dvd__mult,axiom,
% 5.82/6.13 ! [A2: real,C2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_real @ A2 @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult
% 5.82/6.13 thf(fact_5800_dvd__mult,axiom,
% 5.82/6.13 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_rat @ A2 @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult
% 5.82/6.13 thf(fact_5801_dvd__mult,axiom,
% 5.82/6.13 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult
% 5.82/6.13 thf(fact_5802_dvd__mult,axiom,
% 5.82/6.13 ! [A2: int,C2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ C2 )
% 5.82/6.13 => ( dvd_dvd_int @ A2 @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult
% 5.82/6.13 thf(fact_5803_dvd__mult2,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ B2 )
% 5.82/6.13 => ( dvd_dvd_real @ A2 @ ( times_times_real @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult2
% 5.82/6.13 thf(fact_5804_dvd__mult2,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ B2 )
% 5.82/6.13 => ( dvd_dvd_rat @ A2 @ ( times_times_rat @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult2
% 5.82/6.13 thf(fact_5805_dvd__mult2,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult2
% 5.82/6.13 thf(fact_5806_dvd__mult2,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( dvd_dvd_int @ A2 @ ( times_times_int @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult2
% 5.82/6.13 thf(fact_5807_dvd__mult__left,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ ( times_times_real @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_real @ A2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_left
% 5.82/6.13 thf(fact_5808_dvd__mult__left,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ ( times_times_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_rat @ A2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_left
% 5.82/6.13 thf(fact_5809_dvd__mult__left,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_nat @ A2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_left
% 5.82/6.13 thf(fact_5810_dvd__mult__left,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_int @ A2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_left
% 5.82/6.13 thf(fact_5811_dvd__triv__left,axiom,
% 5.82/6.13 ! [A2: real,B2: real] : ( dvd_dvd_real @ A2 @ ( times_times_real @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_left
% 5.82/6.13 thf(fact_5812_dvd__triv__left,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat] : ( dvd_dvd_rat @ A2 @ ( times_times_rat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_left
% 5.82/6.13 thf(fact_5813_dvd__triv__left,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] : ( dvd_dvd_nat @ A2 @ ( times_times_nat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_left
% 5.82/6.13 thf(fact_5814_dvd__triv__left,axiom,
% 5.82/6.13 ! [A2: int,B2: int] : ( dvd_dvd_int @ A2 @ ( times_times_int @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_left
% 5.82/6.13 thf(fact_5815_mult__dvd__mono,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_real @ C2 @ D2 )
% 5.82/6.13 => ( dvd_dvd_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_dvd_mono
% 5.82/6.13 thf(fact_5816_mult__dvd__mono,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat,D2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ C2 @ D2 )
% 5.82/6.13 => ( dvd_dvd_rat @ ( times_times_rat @ A2 @ C2 ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_dvd_mono
% 5.82/6.13 thf(fact_5817_mult__dvd__mono,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat,D2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ C2 @ D2 )
% 5.82/6.13 => ( dvd_dvd_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_dvd_mono
% 5.82/6.13 thf(fact_5818_mult__dvd__mono,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int,D2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ C2 @ D2 )
% 5.82/6.13 => ( dvd_dvd_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % mult_dvd_mono
% 5.82/6.13 thf(fact_5819_dvd__mult__right,axiom,
% 5.82/6.13 ! [A2: real,B2: real,C2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ ( times_times_real @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_real @ B2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_right
% 5.82/6.13 thf(fact_5820_dvd__mult__right,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat,C2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ ( times_times_rat @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_rat @ B2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_right
% 5.82/6.13 thf(fact_5821_dvd__mult__right,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_nat @ B2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_right
% 5.82/6.13 thf(fact_5822_dvd__mult__right,axiom,
% 5.82/6.13 ! [A2: int,B2: int,C2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.13 => ( dvd_dvd_int @ B2 @ C2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_mult_right
% 5.82/6.13 thf(fact_5823_dvd__triv__right,axiom,
% 5.82/6.13 ! [A2: real,B2: real] : ( dvd_dvd_real @ A2 @ ( times_times_real @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_right
% 5.82/6.13 thf(fact_5824_dvd__triv__right,axiom,
% 5.82/6.13 ! [A2: rat,B2: rat] : ( dvd_dvd_rat @ A2 @ ( times_times_rat @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_right
% 5.82/6.13 thf(fact_5825_dvd__triv__right,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] : ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_right
% 5.82/6.13 thf(fact_5826_dvd__triv__right,axiom,
% 5.82/6.13 ! [A2: int,B2: int] : ( dvd_dvd_int @ A2 @ ( times_times_int @ B2 @ A2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_triv_right
% 5.82/6.13 thf(fact_5827_dvd__diff__commute,axiom,
% 5.82/6.13 ! [A2: int,C2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ A2 @ ( minus_minus_int @ C2 @ B2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ ( minus_minus_int @ B2 @ C2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_diff_commute
% 5.82/6.13 thf(fact_5828_dvd__diff,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ X2 @ Y3 )
% 5.82/6.13 => ( ( dvd_dvd_real @ X2 @ Z )
% 5.82/6.13 => ( dvd_dvd_real @ X2 @ ( minus_minus_real @ Y3 @ Z ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_diff
% 5.82/6.13 thf(fact_5829_dvd__diff,axiom,
% 5.82/6.13 ! [X2: rat,Y3: rat,Z: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ X2 @ Y3 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ X2 @ Z )
% 5.82/6.13 => ( dvd_dvd_rat @ X2 @ ( minus_minus_rat @ Y3 @ Z ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_diff
% 5.82/6.13 thf(fact_5830_dvd__diff,axiom,
% 5.82/6.13 ! [X2: int,Y3: int,Z: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ X2 @ Y3 )
% 5.82/6.13 => ( ( dvd_dvd_int @ X2 @ Z )
% 5.82/6.13 => ( dvd_dvd_int @ X2 @ ( minus_minus_int @ Y3 @ Z ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_diff
% 5.82/6.13 thf(fact_5831_dvd__div__eq__iff,axiom,
% 5.82/6.13 ! [C2: complex,A2: complex,B2: complex] :
% 5.82/6.13 ( ( dvd_dvd_complex @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_complex @ C2 @ B2 )
% 5.82/6.13 => ( ( ( divide1717551699836669952omplex @ A2 @ C2 )
% 5.82/6.13 = ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.13 = ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_iff
% 5.82/6.13 thf(fact_5832_dvd__div__eq__iff,axiom,
% 5.82/6.13 ! [C2: real,A2: real,B2: real] :
% 5.82/6.13 ( ( dvd_dvd_real @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_real @ C2 @ B2 )
% 5.82/6.13 => ( ( ( divide_divide_real @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.13 = ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_iff
% 5.82/6.13 thf(fact_5833_dvd__div__eq__iff,axiom,
% 5.82/6.13 ! [C2: rat,A2: rat,B2: rat] :
% 5.82/6.13 ( ( dvd_dvd_rat @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ C2 @ B2 )
% 5.82/6.13 => ( ( ( divide_divide_rat @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.13 = ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_iff
% 5.82/6.13 thf(fact_5834_dvd__div__eq__iff,axiom,
% 5.82/6.13 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.13 => ( ( ( divide_divide_nat @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_nat @ B2 @ C2 ) )
% 5.82/6.13 = ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_iff
% 5.82/6.13 thf(fact_5835_dvd__div__eq__iff,axiom,
% 5.82/6.13 ! [C2: int,A2: int,B2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.13 => ( ( ( divide_divide_int @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_int @ B2 @ C2 ) )
% 5.82/6.13 = ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_iff
% 5.82/6.13 thf(fact_5836_dvd__div__eq__cancel,axiom,
% 5.82/6.13 ! [A2: complex,C2: complex,B2: complex] :
% 5.82/6.13 ( ( ( divide1717551699836669952omplex @ A2 @ C2 )
% 5.82/6.13 = ( divide1717551699836669952omplex @ B2 @ C2 ) )
% 5.82/6.13 => ( ( dvd_dvd_complex @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_complex @ C2 @ B2 )
% 5.82/6.13 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_cancel
% 5.82/6.13 thf(fact_5837_dvd__div__eq__cancel,axiom,
% 5.82/6.13 ! [A2: real,C2: real,B2: real] :
% 5.82/6.13 ( ( ( divide_divide_real @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_real @ B2 @ C2 ) )
% 5.82/6.13 => ( ( dvd_dvd_real @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_real @ C2 @ B2 )
% 5.82/6.13 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_cancel
% 5.82/6.13 thf(fact_5838_dvd__div__eq__cancel,axiom,
% 5.82/6.13 ! [A2: rat,C2: rat,B2: rat] :
% 5.82/6.13 ( ( ( divide_divide_rat @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_rat @ B2 @ C2 ) )
% 5.82/6.13 => ( ( dvd_dvd_rat @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ C2 @ B2 )
% 5.82/6.13 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_cancel
% 5.82/6.13 thf(fact_5839_dvd__div__eq__cancel,axiom,
% 5.82/6.13 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.13 ( ( ( divide_divide_nat @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_nat @ B2 @ C2 ) )
% 5.82/6.13 => ( ( dvd_dvd_nat @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.13 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_cancel
% 5.82/6.13 thf(fact_5840_dvd__div__eq__cancel,axiom,
% 5.82/6.13 ! [A2: int,C2: int,B2: int] :
% 5.82/6.13 ( ( ( divide_divide_int @ A2 @ C2 )
% 5.82/6.13 = ( divide_divide_int @ B2 @ C2 ) )
% 5.82/6.13 => ( ( dvd_dvd_int @ C2 @ A2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.13 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_div_eq_cancel
% 5.82/6.13 thf(fact_5841_div__div__div__same,axiom,
% 5.82/6.13 ! [D2: nat,B2: nat,A2: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ D2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.13 => ( ( divide_divide_nat @ ( divide_divide_nat @ A2 @ D2 ) @ ( divide_divide_nat @ B2 @ D2 ) )
% 5.82/6.13 = ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_div_div_same
% 5.82/6.13 thf(fact_5842_div__div__div__same,axiom,
% 5.82/6.13 ! [D2: int,B2: int,A2: int] :
% 5.82/6.13 ( ( dvd_dvd_int @ D2 @ B2 )
% 5.82/6.13 => ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.13 => ( ( divide_divide_int @ ( divide_divide_int @ A2 @ D2 ) @ ( divide_divide_int @ B2 @ D2 ) )
% 5.82/6.13 = ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % div_div_div_same
% 5.82/6.13 thf(fact_5843_dvd__power__same,axiom,
% 5.82/6.13 ! [X2: nat,Y3: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ X2 @ Y3 )
% 5.82/6.13 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y3 @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_power_same
% 5.82/6.13 thf(fact_5844_dvd__power__same,axiom,
% 5.82/6.13 ! [X2: real,Y3: real,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_real @ X2 @ Y3 )
% 5.82/6.13 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y3 @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_power_same
% 5.82/6.13 thf(fact_5845_dvd__power__same,axiom,
% 5.82/6.13 ! [X2: int,Y3: int,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_int @ X2 @ Y3 )
% 5.82/6.13 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y3 @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_power_same
% 5.82/6.13 thf(fact_5846_dvd__power__same,axiom,
% 5.82/6.13 ! [X2: complex,Y3: complex,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_complex @ X2 @ Y3 )
% 5.82/6.13 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y3 @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_power_same
% 5.82/6.13 thf(fact_5847_dvd__power__same,axiom,
% 5.82/6.13 ! [X2: code_integer,Y3: code_integer,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_Code_integer @ X2 @ Y3 )
% 5.82/6.13 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ N ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_power_same
% 5.82/6.13 thf(fact_5848_dvd__diff__nat,axiom,
% 5.82/6.13 ! [K: nat,M: nat,N: nat] :
% 5.82/6.13 ( ( dvd_dvd_nat @ K @ M )
% 5.82/6.13 => ( ( dvd_dvd_nat @ K @ N )
% 5.82/6.13 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % dvd_diff_nat
% 5.82/6.13 thf(fact_5849_unset__bit__less__eq,axiom,
% 5.82/6.13 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.82/6.13
% 5.82/6.13 % unset_bit_less_eq
% 5.82/6.13 thf(fact_5850_subset__divisors__dvd,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] :
% 5.82/6.13 ( ( ord_le211207098394363844omplex
% 5.82/6.13 @ ( collect_complex
% 5.82/6.13 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ A2 ) )
% 5.82/6.13 @ ( collect_complex
% 5.82/6.13 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ B2 ) ) )
% 5.82/6.13 = ( dvd_dvd_complex @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % subset_divisors_dvd
% 5.82/6.13 thf(fact_5851_subset__divisors__dvd,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( ord_less_eq_set_nat
% 5.82/6.13 @ ( collect_nat
% 5.82/6.13 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A2 ) )
% 5.82/6.13 @ ( collect_nat
% 5.82/6.13 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B2 ) ) )
% 5.82/6.13 = ( dvd_dvd_nat @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % subset_divisors_dvd
% 5.82/6.13 thf(fact_5852_subset__divisors__dvd,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( ord_less_eq_set_int
% 5.82/6.13 @ ( collect_int
% 5.82/6.13 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A2 ) )
% 5.82/6.13 @ ( collect_int
% 5.82/6.13 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B2 ) ) )
% 5.82/6.13 = ( dvd_dvd_int @ A2 @ B2 ) ) ).
% 5.82/6.13
% 5.82/6.13 % subset_divisors_dvd
% 5.82/6.13 thf(fact_5853_strict__subset__divisors__dvd,axiom,
% 5.82/6.13 ! [A2: complex,B2: complex] :
% 5.82/6.13 ( ( ord_less_set_complex
% 5.82/6.13 @ ( collect_complex
% 5.82/6.13 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ A2 ) )
% 5.82/6.13 @ ( collect_complex
% 5.82/6.13 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ B2 ) ) )
% 5.82/6.13 = ( ( dvd_dvd_complex @ A2 @ B2 )
% 5.82/6.13 & ~ ( dvd_dvd_complex @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % strict_subset_divisors_dvd
% 5.82/6.13 thf(fact_5854_strict__subset__divisors__dvd,axiom,
% 5.82/6.13 ! [A2: nat,B2: nat] :
% 5.82/6.13 ( ( ord_less_set_nat
% 5.82/6.13 @ ( collect_nat
% 5.82/6.13 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A2 ) )
% 5.82/6.13 @ ( collect_nat
% 5.82/6.13 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B2 ) ) )
% 5.82/6.13 = ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.13 & ~ ( dvd_dvd_nat @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % strict_subset_divisors_dvd
% 5.82/6.13 thf(fact_5855_strict__subset__divisors__dvd,axiom,
% 5.82/6.13 ! [A2: int,B2: int] :
% 5.82/6.13 ( ( ord_less_set_int
% 5.82/6.13 @ ( collect_int
% 5.82/6.13 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A2 ) )
% 5.82/6.13 @ ( collect_int
% 5.82/6.13 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B2 ) ) )
% 5.82/6.13 = ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.13 & ~ ( dvd_dvd_int @ B2 @ A2 ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % strict_subset_divisors_dvd
% 5.82/6.13 thf(fact_5856_not__is__unit__0,axiom,
% 5.82/6.13 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.82/6.13
% 5.82/6.13 % not_is_unit_0
% 5.82/6.13 thf(fact_5857_not__is__unit__0,axiom,
% 5.82/6.13 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.82/6.13
% 5.82/6.13 % not_is_unit_0
% 5.82/6.13 thf(fact_5858_pinf_I9_J,axiom,
% 5.82/6.13 ! [D2: real,S2: real] :
% 5.82/6.13 ? [Z2: real] :
% 5.82/6.13 ! [X8: real] :
% 5.82/6.13 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.13 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) )
% 5.82/6.13 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % pinf(9)
% 5.82/6.13 thf(fact_5859_pinf_I9_J,axiom,
% 5.82/6.13 ! [D2: rat,S2: rat] :
% 5.82/6.13 ? [Z2: rat] :
% 5.82/6.13 ! [X8: rat] :
% 5.82/6.13 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.13 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) )
% 5.82/6.13 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % pinf(9)
% 5.82/6.13 thf(fact_5860_pinf_I9_J,axiom,
% 5.82/6.13 ! [D2: nat,S2: nat] :
% 5.82/6.13 ? [Z2: nat] :
% 5.82/6.13 ! [X8: nat] :
% 5.82/6.13 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.13 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) )
% 5.82/6.13 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % pinf(9)
% 5.82/6.13 thf(fact_5861_pinf_I9_J,axiom,
% 5.82/6.13 ! [D2: int,S2: int] :
% 5.82/6.13 ? [Z2: int] :
% 5.82/6.13 ! [X8: int] :
% 5.82/6.13 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.13 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) )
% 5.82/6.13 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) ) ) ) ).
% 5.82/6.13
% 5.82/6.13 % pinf(9)
% 5.82/6.14 thf(fact_5862_pinf_I10_J,axiom,
% 5.82/6.14 ! [D2: real,S2: real] :
% 5.82/6.14 ? [Z2: real] :
% 5.82/6.14 ! [X8: real] :
% 5.82/6.14 ( ( ord_less_real @ Z2 @ X8 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pinf(10)
% 5.82/6.14 thf(fact_5863_pinf_I10_J,axiom,
% 5.82/6.14 ! [D2: rat,S2: rat] :
% 5.82/6.14 ? [Z2: rat] :
% 5.82/6.14 ! [X8: rat] :
% 5.82/6.14 ( ( ord_less_rat @ Z2 @ X8 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pinf(10)
% 5.82/6.14 thf(fact_5864_pinf_I10_J,axiom,
% 5.82/6.14 ! [D2: nat,S2: nat] :
% 5.82/6.14 ? [Z2: nat] :
% 5.82/6.14 ! [X8: nat] :
% 5.82/6.14 ( ( ord_less_nat @ Z2 @ X8 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pinf(10)
% 5.82/6.14 thf(fact_5865_pinf_I10_J,axiom,
% 5.82/6.14 ! [D2: int,S2: int] :
% 5.82/6.14 ? [Z2: int] :
% 5.82/6.14 ! [X8: int] :
% 5.82/6.14 ( ( ord_less_int @ Z2 @ X8 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pinf(10)
% 5.82/6.14 thf(fact_5866_minf_I9_J,axiom,
% 5.82/6.14 ! [D2: real,S2: real] :
% 5.82/6.14 ? [Z2: real] :
% 5.82/6.14 ! [X8: real] :
% 5.82/6.14 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.14 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) )
% 5.82/6.14 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(9)
% 5.82/6.14 thf(fact_5867_minf_I9_J,axiom,
% 5.82/6.14 ! [D2: rat,S2: rat] :
% 5.82/6.14 ? [Z2: rat] :
% 5.82/6.14 ! [X8: rat] :
% 5.82/6.14 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.14 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) )
% 5.82/6.14 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(9)
% 5.82/6.14 thf(fact_5868_minf_I9_J,axiom,
% 5.82/6.14 ! [D2: nat,S2: nat] :
% 5.82/6.14 ? [Z2: nat] :
% 5.82/6.14 ! [X8: nat] :
% 5.82/6.14 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(9)
% 5.82/6.14 thf(fact_5869_minf_I9_J,axiom,
% 5.82/6.14 ! [D2: int,S2: int] :
% 5.82/6.14 ? [Z2: int] :
% 5.82/6.14 ! [X8: int] :
% 5.82/6.14 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) )
% 5.82/6.14 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(9)
% 5.82/6.14 thf(fact_5870_minf_I10_J,axiom,
% 5.82/6.14 ! [D2: real,S2: real] :
% 5.82/6.14 ? [Z2: real] :
% 5.82/6.14 ! [X8: real] :
% 5.82/6.14 ( ( ord_less_real @ X8 @ Z2 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(10)
% 5.82/6.14 thf(fact_5871_minf_I10_J,axiom,
% 5.82/6.14 ! [D2: rat,S2: rat] :
% 5.82/6.14 ? [Z2: rat] :
% 5.82/6.14 ! [X8: rat] :
% 5.82/6.14 ( ( ord_less_rat @ X8 @ Z2 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(10)
% 5.82/6.14 thf(fact_5872_minf_I10_J,axiom,
% 5.82/6.14 ! [D2: nat,S2: nat] :
% 5.82/6.14 ? [Z2: nat] :
% 5.82/6.14 ! [X8: nat] :
% 5.82/6.14 ( ( ord_less_nat @ X8 @ Z2 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(10)
% 5.82/6.14 thf(fact_5873_minf_I10_J,axiom,
% 5.82/6.14 ! [D2: int,S2: int] :
% 5.82/6.14 ? [Z2: int] :
% 5.82/6.14 ! [X8: int] :
% 5.82/6.14 ( ( ord_less_int @ X8 @ Z2 )
% 5.82/6.14 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ S2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minf(10)
% 5.82/6.14 thf(fact_5874_dvd__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: complex,A2: complex] :
% 5.82/6.14 ( ( dvd_dvd_complex @ B2 @ A2 )
% 5.82/6.14 => ( ( ( divide1717551699836669952omplex @ A2 @ B2 )
% 5.82/6.14 = zero_zero_complex )
% 5.82/6.14 = ( A2 = zero_zero_complex ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_0_iff
% 5.82/6.14 thf(fact_5875_dvd__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: real,A2: real] :
% 5.82/6.14 ( ( dvd_dvd_real @ B2 @ A2 )
% 5.82/6.14 => ( ( ( divide_divide_real @ A2 @ B2 )
% 5.82/6.14 = zero_zero_real )
% 5.82/6.14 = ( A2 = zero_zero_real ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_0_iff
% 5.82/6.14 thf(fact_5876_dvd__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: rat,A2: rat] :
% 5.82/6.14 ( ( dvd_dvd_rat @ B2 @ A2 )
% 5.82/6.14 => ( ( ( divide_divide_rat @ A2 @ B2 )
% 5.82/6.14 = zero_zero_rat )
% 5.82/6.14 = ( A2 = zero_zero_rat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_0_iff
% 5.82/6.14 thf(fact_5877_dvd__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.14 => ( ( ( divide_divide_nat @ A2 @ B2 )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 = ( A2 = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_0_iff
% 5.82/6.14 thf(fact_5878_dvd__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.14 => ( ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.14 = zero_zero_int )
% 5.82/6.14 = ( A2 = zero_zero_int ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_0_iff
% 5.82/6.14 thf(fact_5879_unit__mult__right__cancel,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 => ( ( ( times_times_nat @ B2 @ A2 )
% 5.82/6.14 = ( times_times_nat @ C2 @ A2 ) )
% 5.82/6.14 = ( B2 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_mult_right_cancel
% 5.82/6.14 thf(fact_5880_unit__mult__right__cancel,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 => ( ( ( times_times_int @ B2 @ A2 )
% 5.82/6.14 = ( times_times_int @ C2 @ A2 ) )
% 5.82/6.14 = ( B2 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_mult_right_cancel
% 5.82/6.14 thf(fact_5881_unit__mult__left__cancel,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 => ( ( ( times_times_nat @ A2 @ B2 )
% 5.82/6.14 = ( times_times_nat @ A2 @ C2 ) )
% 5.82/6.14 = ( B2 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_mult_left_cancel
% 5.82/6.14 thf(fact_5882_unit__mult__left__cancel,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 => ( ( ( times_times_int @ A2 @ B2 )
% 5.82/6.14 = ( times_times_int @ A2 @ C2 ) )
% 5.82/6.14 = ( B2 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_mult_left_cancel
% 5.82/6.14 thf(fact_5883_mult__unit__dvd__iff_H,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_unit_dvd_iff'
% 5.82/6.14 thf(fact_5884_mult__unit__dvd__iff_H,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_int @ B2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_unit_dvd_iff'
% 5.82/6.14 thf(fact_5885_dvd__mult__unit__iff_H,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_unit_iff'
% 5.82/6.14 thf(fact_5886_dvd__mult__unit__iff_H,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_unit_iff'
% 5.82/6.14 thf(fact_5887_mult__unit__dvd__iff,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_unit_dvd_iff
% 5.82/6.14 thf(fact_5888_mult__unit__dvd__iff,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_unit_dvd_iff
% 5.82/6.14 thf(fact_5889_dvd__mult__unit__iff,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ A2 @ ( times_times_nat @ C2 @ B2 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_unit_iff
% 5.82/6.14 thf(fact_5890_dvd__mult__unit__iff,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ ( times_times_int @ C2 @ B2 ) )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_unit_iff
% 5.82/6.14 thf(fact_5891_is__unit__mult__iff,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B2 ) @ one_one_nat )
% 5.82/6.14 = ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 & ( dvd_dvd_nat @ B2 @ one_one_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_mult_iff
% 5.82/6.14 thf(fact_5892_is__unit__mult__iff,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B2 ) @ one_one_int )
% 5.82/6.14 = ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 & ( dvd_dvd_int @ B2 @ one_one_int ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_mult_iff
% 5.82/6.14 thf(fact_5893_div__plus__div__distrib__dvd__right,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.14 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ C2 ) @ ( divide_divide_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_plus_div_distrib_dvd_right
% 5.82/6.14 thf(fact_5894_div__plus__div__distrib__dvd__right,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.14 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_int @ ( divide_divide_int @ A2 @ C2 ) @ ( divide_divide_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_plus_div_distrib_dvd_right
% 5.82/6.14 thf(fact_5895_div__plus__div__distrib__dvd__left,axiom,
% 5.82/6.14 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ A2 )
% 5.82/6.14 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ C2 ) @ ( divide_divide_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_plus_div_distrib_dvd_left
% 5.82/6.14 thf(fact_5896_div__plus__div__distrib__dvd__left,axiom,
% 5.82/6.14 ! [C2: int,A2: int,B2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ A2 )
% 5.82/6.14 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_int @ ( divide_divide_int @ A2 @ C2 ) @ ( divide_divide_int @ B2 @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_plus_div_distrib_dvd_left
% 5.82/6.14 thf(fact_5897_unit__div__cancel,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 => ( ( ( divide_divide_nat @ B2 @ A2 )
% 5.82/6.14 = ( divide_divide_nat @ C2 @ A2 ) )
% 5.82/6.14 = ( B2 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_cancel
% 5.82/6.14 thf(fact_5898_unit__div__cancel,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 => ( ( ( divide_divide_int @ B2 @ A2 )
% 5.82/6.14 = ( divide_divide_int @ C2 @ A2 ) )
% 5.82/6.14 = ( B2 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_cancel
% 5.82/6.14 thf(fact_5899_div__unit__dvd__iff,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_unit_dvd_iff
% 5.82/6.14 thf(fact_5900_div__unit__dvd__iff,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_unit_dvd_iff
% 5.82/6.14 thf(fact_5901_dvd__div__unit__iff,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ A2 @ ( divide_divide_nat @ C2 @ B2 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_unit_iff
% 5.82/6.14 thf(fact_5902_dvd__div__unit__iff,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ ( divide_divide_int @ C2 @ B2 ) )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_unit_iff
% 5.82/6.14 thf(fact_5903_dvd__div__mult,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.14 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.14 = ( divide_divide_nat @ ( times_times_nat @ B2 @ A2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_mult
% 5.82/6.14 thf(fact_5904_dvd__div__mult,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.14 => ( ( times_times_int @ ( divide_divide_int @ B2 @ C2 ) @ A2 )
% 5.82/6.14 = ( divide_divide_int @ ( times_times_int @ B2 @ A2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_mult
% 5.82/6.14 thf(fact_5905_div__mult__swap,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.14 => ( ( times_times_nat @ A2 @ ( divide_divide_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_swap
% 5.82/6.14 thf(fact_5906_div__mult__swap,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.14 => ( ( times_times_int @ A2 @ ( divide_divide_int @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_swap
% 5.82/6.14 thf(fact_5907_div__div__eq__right,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.14 => ( ( divide_divide_nat @ A2 @ ( divide_divide_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_div_eq_right
% 5.82/6.14 thf(fact_5908_div__div__eq__right,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.14 => ( ( divide_divide_int @ A2 @ ( divide_divide_int @ B2 @ C2 ) )
% 5.82/6.14 = ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_div_eq_right
% 5.82/6.14 thf(fact_5909_dvd__div__mult2__eq,axiom,
% 5.82/6.14 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( times_times_nat @ B2 @ C2 ) @ A2 )
% 5.82/6.14 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_mult2_eq
% 5.82/6.14 thf(fact_5910_dvd__div__mult2__eq,axiom,
% 5.82/6.14 ! [B2: int,C2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( times_times_int @ B2 @ C2 ) @ A2 )
% 5.82/6.14 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_mult2_eq
% 5.82/6.14 thf(fact_5911_dvd__mult__imp__div,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ C2 ) @ B2 )
% 5.82/6.14 => ( dvd_dvd_nat @ A2 @ ( divide_divide_nat @ B2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_imp_div
% 5.82/6.14 thf(fact_5912_dvd__mult__imp__div,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ C2 ) @ B2 )
% 5.82/6.14 => ( dvd_dvd_int @ A2 @ ( divide_divide_int @ B2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_imp_div
% 5.82/6.14 thf(fact_5913_div__mult__div__if__dvd,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,D2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ D2 @ C2 )
% 5.82/6.14 => ( ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ ( divide_divide_nat @ C2 @ D2 ) )
% 5.82/6.14 = ( divide_divide_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_div_if_dvd
% 5.82/6.14 thf(fact_5914_div__mult__div__if__dvd,axiom,
% 5.82/6.14 ! [B2: int,A2: int,D2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ D2 @ C2 )
% 5.82/6.14 => ( ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ ( divide_divide_int @ C2 @ D2 ) )
% 5.82/6.14 = ( divide_divide_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_div_if_dvd
% 5.82/6.14 thf(fact_5915_div__power,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ B2 @ A2 )
% 5.82/6.14 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ N )
% 5.82/6.14 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_power
% 5.82/6.14 thf(fact_5916_div__power,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.14 => ( ( power_power_nat @ ( divide_divide_nat @ A2 @ B2 ) @ N )
% 5.82/6.14 = ( divide_divide_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_power
% 5.82/6.14 thf(fact_5917_div__power,axiom,
% 5.82/6.14 ! [B2: int,A2: int,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.14 => ( ( power_power_int @ ( divide_divide_int @ A2 @ B2 ) @ N )
% 5.82/6.14 = ( divide_divide_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_power
% 5.82/6.14 thf(fact_5918_le__imp__power__dvd,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % le_imp_power_dvd
% 5.82/6.14 thf(fact_5919_le__imp__power__dvd,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: real] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % le_imp_power_dvd
% 5.82/6.14 thf(fact_5920_le__imp__power__dvd,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: int] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % le_imp_power_dvd
% 5.82/6.14 thf(fact_5921_le__imp__power__dvd,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: complex] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_complex @ ( power_power_complex @ A2 @ M ) @ ( power_power_complex @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % le_imp_power_dvd
% 5.82/6.14 thf(fact_5922_le__imp__power__dvd,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: code_integer] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A2 @ M ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % le_imp_power_dvd
% 5.82/6.14 thf(fact_5923_power__le__dvd,axiom,
% 5.82/6.14 ! [A2: nat,N: nat,B2: nat,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( power_power_nat @ A2 @ N ) @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_nat @ ( power_power_nat @ A2 @ M ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_dvd
% 5.82/6.14 thf(fact_5924_power__le__dvd,axiom,
% 5.82/6.14 ! [A2: real,N: nat,B2: real,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_real @ ( power_power_real @ A2 @ N ) @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_real @ ( power_power_real @ A2 @ M ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_dvd
% 5.82/6.14 thf(fact_5925_power__le__dvd,axiom,
% 5.82/6.14 ! [A2: int,N: nat,B2: int,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( power_power_int @ A2 @ N ) @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_int @ ( power_power_int @ A2 @ M ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_dvd
% 5.82/6.14 thf(fact_5926_power__le__dvd,axiom,
% 5.82/6.14 ! [A2: complex,N: nat,B2: complex,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_complex @ ( power_power_complex @ A2 @ N ) @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_complex @ ( power_power_complex @ A2 @ M ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_dvd
% 5.82/6.14 thf(fact_5927_power__le__dvd,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat,B2: code_integer,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N ) @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A2 @ M ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_dvd
% 5.82/6.14 thf(fact_5928_dvd__power__le,axiom,
% 5.82/6.14 ! [X2: nat,Y3: nat,N: nat,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ X2 @ Y3 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y3 @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_le
% 5.82/6.14 thf(fact_5929_dvd__power__le,axiom,
% 5.82/6.14 ! [X2: real,Y3: real,N: nat,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_real @ X2 @ Y3 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y3 @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_le
% 5.82/6.14 thf(fact_5930_dvd__power__le,axiom,
% 5.82/6.14 ! [X2: int,Y3: int,N: nat,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ X2 @ Y3 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y3 @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_le
% 5.82/6.14 thf(fact_5931_dvd__power__le,axiom,
% 5.82/6.14 ! [X2: complex,Y3: complex,N: nat,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_complex @ X2 @ Y3 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y3 @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_le
% 5.82/6.14 thf(fact_5932_dvd__power__le,axiom,
% 5.82/6.14 ! [X2: code_integer,Y3: code_integer,N: nat,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ X2 @ Y3 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_le
% 5.82/6.14 thf(fact_5933_nat__dvd__not__less,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.14 => ( ( ord_less_nat @ M @ N )
% 5.82/6.14 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_dvd_not_less
% 5.82/6.14 thf(fact_5934_dvd__minus__self,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.82/6.14 = ( ( ord_less_nat @ N @ M )
% 5.82/6.14 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_minus_self
% 5.82/6.14 thf(fact_5935_less__eq__dvd__minus,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( ( dvd_dvd_nat @ M @ N )
% 5.82/6.14 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % less_eq_dvd_minus
% 5.82/6.14 thf(fact_5936_dvd__diffD1,axiom,
% 5.82/6.14 ! [K: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.14 => ( ( dvd_dvd_nat @ K @ M )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_diffD1
% 5.82/6.14 thf(fact_5937_dvd__diffD,axiom,
% 5.82/6.14 ! [K: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.82/6.14 => ( ( dvd_dvd_nat @ K @ N )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_diffD
% 5.82/6.14 thf(fact_5938_return__cons__rule,axiom,
% 5.82/6.14 ! [P: assn,Q: vEBT_VEBTi > assn,X2: vEBT_VEBTi] :
% 5.82/6.14 ( ( entails @ P @ ( Q @ X2 ) )
% 5.82/6.14 => ( hoare_1429296392585015714_VEBTi @ P @ ( heap_T3630416162098727440_VEBTi @ X2 ) @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_cons_rule
% 5.82/6.14 thf(fact_5939_return__cons__rule,axiom,
% 5.82/6.14 ! [P: assn,Q: $o > assn,X2: $o] :
% 5.82/6.14 ( ( entails @ P @ ( Q @ X2 ) )
% 5.82/6.14 => ( hoare_hoare_triple_o @ P @ ( heap_Time_return_o @ X2 ) @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_cons_rule
% 5.82/6.14 thf(fact_5940_return__cons__rule,axiom,
% 5.82/6.14 ! [P: assn,Q: option_nat > assn,X2: option_nat] :
% 5.82/6.14 ( ( entails @ P @ ( Q @ X2 ) )
% 5.82/6.14 => ( hoare_7629718768684598413on_nat @ P @ ( heap_T3487192422709364219on_nat @ X2 ) @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_cons_rule
% 5.82/6.14 thf(fact_5941_return__cons__rule,axiom,
% 5.82/6.14 ! [P: assn,Q: nat > assn,X2: nat] :
% 5.82/6.14 ( ( entails @ P @ ( Q @ X2 ) )
% 5.82/6.14 => ( hoare_3067605981109127869le_nat @ P @ ( heap_Time_return_nat @ X2 ) @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_cons_rule
% 5.82/6.14 thf(fact_5942_even__unset__bit__iff,axiom,
% 5.82/6.14 ! [M: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A2 ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 | ( M = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_unset_bit_iff
% 5.82/6.14 thf(fact_5943_even__unset__bit__iff,axiom,
% 5.82/6.14 ! [M: nat,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A2 ) )
% 5.82/6.14 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 | ( M = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_unset_bit_iff
% 5.82/6.14 thf(fact_5944_even__of__int__iff,axiom,
% 5.82/6.14 ! [K: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.82/6.14 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_of_int_iff
% 5.82/6.14 thf(fact_5945_even__numeral,axiom,
% 5.82/6.14 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_numeral
% 5.82/6.14 thf(fact_5946_even__numeral,axiom,
% 5.82/6.14 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_numeral
% 5.82/6.14 thf(fact_5947_unity__coeff__ex,axiom,
% 5.82/6.14 ! [P: complex > $o,L: complex] :
% 5.82/6.14 ( ( ? [X3: complex] : ( P @ ( times_times_complex @ L @ X3 ) ) )
% 5.82/6.14 = ( ? [X3: complex] :
% 5.82/6.14 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X3 @ zero_zero_complex ) )
% 5.82/6.14 & ( P @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unity_coeff_ex
% 5.82/6.14 thf(fact_5948_unity__coeff__ex,axiom,
% 5.82/6.14 ! [P: real > $o,L: real] :
% 5.82/6.14 ( ( ? [X3: real] : ( P @ ( times_times_real @ L @ X3 ) ) )
% 5.82/6.14 = ( ? [X3: real] :
% 5.82/6.14 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X3 @ zero_zero_real ) )
% 5.82/6.14 & ( P @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unity_coeff_ex
% 5.82/6.14 thf(fact_5949_unity__coeff__ex,axiom,
% 5.82/6.14 ! [P: rat > $o,L: rat] :
% 5.82/6.14 ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 5.82/6.14 = ( ? [X3: rat] :
% 5.82/6.14 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 5.82/6.14 & ( P @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unity_coeff_ex
% 5.82/6.14 thf(fact_5950_unity__coeff__ex,axiom,
% 5.82/6.14 ! [P: nat > $o,L: nat] :
% 5.82/6.14 ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 5.82/6.14 = ( ? [X3: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 5.82/6.14 & ( P @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unity_coeff_ex
% 5.82/6.14 thf(fact_5951_unity__coeff__ex,axiom,
% 5.82/6.14 ! [P: int > $o,L: int] :
% 5.82/6.14 ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 5.82/6.14 = ( ? [X3: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 5.82/6.14 & ( P @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unity_coeff_ex
% 5.82/6.14 thf(fact_5952_unit__dvdE,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 => ~ ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ! [C3: nat] :
% 5.82/6.14 ( B2
% 5.82/6.14 != ( times_times_nat @ A2 @ C3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_dvdE
% 5.82/6.14 thf(fact_5953_unit__dvdE,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 => ~ ( ( A2 != zero_zero_int )
% 5.82/6.14 => ! [C3: int] :
% 5.82/6.14 ( B2
% 5.82/6.14 != ( times_times_int @ A2 @ C3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_dvdE
% 5.82/6.14 thf(fact_5954_unit__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( ( divide_divide_nat @ A2 @ B2 )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 = ( A2 = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_eq_0_iff
% 5.82/6.14 thf(fact_5955_unit__div__eq__0__iff,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.14 = zero_zero_int )
% 5.82/6.14 = ( A2 = zero_zero_int ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_eq_0_iff
% 5.82/6.14 thf(fact_5956_dvd__div__eq__mult,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.14 => ( ( ( divide_divide_nat @ B2 @ A2 )
% 5.82/6.14 = C2 )
% 5.82/6.14 = ( B2
% 5.82/6.14 = ( times_times_nat @ C2 @ A2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_mult
% 5.82/6.14 thf(fact_5957_dvd__div__eq__mult,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( A2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.14 => ( ( ( divide_divide_int @ B2 @ A2 )
% 5.82/6.14 = C2 )
% 5.82/6.14 = ( B2
% 5.82/6.14 = ( times_times_int @ C2 @ A2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_eq_mult
% 5.82/6.14 thf(fact_5958_div__dvd__iff__mult,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( B2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ ( times_times_nat @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_dvd_iff_mult
% 5.82/6.14 thf(fact_5959_div__dvd__iff__mult,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( B2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ ( times_times_int @ C2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_dvd_iff_mult
% 5.82/6.14 thf(fact_5960_dvd__div__iff__mult,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( C2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ A2 @ ( divide_divide_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ ( times_times_nat @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_iff_mult
% 5.82/6.14 thf(fact_5961_dvd__div__iff__mult,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( C2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ ( divide_divide_int @ B2 @ C2 ) )
% 5.82/6.14 = ( dvd_dvd_int @ ( times_times_int @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_iff_mult
% 5.82/6.14 thf(fact_5962_dvd__div__div__eq__mult,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat,D2: nat] :
% 5.82/6.14 ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ( ( C2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ A2 @ B2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ C2 @ D2 )
% 5.82/6.14 => ( ( ( divide_divide_nat @ B2 @ A2 )
% 5.82/6.14 = ( divide_divide_nat @ D2 @ C2 ) )
% 5.82/6.14 = ( ( times_times_nat @ B2 @ C2 )
% 5.82/6.14 = ( times_times_nat @ A2 @ D2 ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_div_eq_mult
% 5.82/6.14 thf(fact_5963_dvd__div__div__eq__mult,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int,D2: int] :
% 5.82/6.14 ( ( A2 != zero_zero_int )
% 5.82/6.14 => ( ( C2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ B2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ C2 @ D2 )
% 5.82/6.14 => ( ( ( divide_divide_int @ B2 @ A2 )
% 5.82/6.14 = ( divide_divide_int @ D2 @ C2 ) )
% 5.82/6.14 = ( ( times_times_int @ B2 @ C2 )
% 5.82/6.14 = ( times_times_int @ A2 @ D2 ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_div_div_eq_mult
% 5.82/6.14 thf(fact_5964_inf__period_I3_J,axiom,
% 5.82/6.14 ! [D2: real,D: real,T: real] :
% 5.82/6.14 ( ( dvd_dvd_real @ D2 @ D )
% 5.82/6.14 => ! [X8: real,K5: real] :
% 5.82/6.14 ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ T ) )
% 5.82/6.14 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X8 @ ( times_times_real @ K5 @ D ) ) @ T ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % inf_period(3)
% 5.82/6.14 thf(fact_5965_inf__period_I3_J,axiom,
% 5.82/6.14 ! [D2: rat,D: rat,T: rat] :
% 5.82/6.14 ( ( dvd_dvd_rat @ D2 @ D )
% 5.82/6.14 => ! [X8: rat,K5: rat] :
% 5.82/6.14 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ T ) )
% 5.82/6.14 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K5 @ D ) ) @ T ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % inf_period(3)
% 5.82/6.14 thf(fact_5966_inf__period_I3_J,axiom,
% 5.82/6.14 ! [D2: int,D: int,T: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ D )
% 5.82/6.14 => ! [X8: int,K5: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 5.82/6.14 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ ( times_times_int @ K5 @ D ) ) @ T ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % inf_period(3)
% 5.82/6.14 thf(fact_5967_inf__period_I4_J,axiom,
% 5.82/6.14 ! [D2: real,D: real,T: real] :
% 5.82/6.14 ( ( dvd_dvd_real @ D2 @ D )
% 5.82/6.14 => ! [X8: real,K5: real] :
% 5.82/6.14 ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X8 @ T ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X8 @ ( times_times_real @ K5 @ D ) ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % inf_period(4)
% 5.82/6.14 thf(fact_5968_inf__period_I4_J,axiom,
% 5.82/6.14 ! [D2: rat,D: rat,T: rat] :
% 5.82/6.14 ( ( dvd_dvd_rat @ D2 @ D )
% 5.82/6.14 => ! [X8: rat,K5: rat] :
% 5.82/6.14 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X8 @ T ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X8 @ ( times_times_rat @ K5 @ D ) ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % inf_period(4)
% 5.82/6.14 thf(fact_5969_inf__period_I4_J,axiom,
% 5.82/6.14 ! [D2: int,D: int,T: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ D )
% 5.82/6.14 => ! [X8: int,K5: int] :
% 5.82/6.14 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ ( times_times_int @ K5 @ D ) ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % inf_period(4)
% 5.82/6.14 thf(fact_5970_unit__eq__div1,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( ( divide_divide_nat @ A2 @ B2 )
% 5.82/6.14 = C2 )
% 5.82/6.14 = ( A2
% 5.82/6.14 = ( times_times_nat @ C2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_eq_div1
% 5.82/6.14 thf(fact_5971_unit__eq__div1,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.14 = C2 )
% 5.82/6.14 = ( A2
% 5.82/6.14 = ( times_times_int @ C2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_eq_div1
% 5.82/6.14 thf(fact_5972_unit__eq__div2,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( A2
% 5.82/6.14 = ( divide_divide_nat @ C2 @ B2 ) )
% 5.82/6.14 = ( ( times_times_nat @ A2 @ B2 )
% 5.82/6.14 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_eq_div2
% 5.82/6.14 thf(fact_5973_unit__eq__div2,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( A2
% 5.82/6.14 = ( divide_divide_int @ C2 @ B2 ) )
% 5.82/6.14 = ( ( times_times_int @ A2 @ B2 )
% 5.82/6.14 = C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_eq_div2
% 5.82/6.14 thf(fact_5974_div__mult__unit2,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B2 @ A2 )
% 5.82/6.14 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_unit2
% 5.82/6.14 thf(fact_5975_div__mult__unit2,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ B2 @ A2 )
% 5.82/6.14 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_unit2
% 5.82/6.14 thf(fact_5976_unit__div__commute,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( divide_divide_nat @ ( times_times_nat @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_commute
% 5.82/6.14 thf(fact_5977_unit__div__commute,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( divide_divide_int @ ( times_times_int @ A2 @ C2 ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_commute
% 5.82/6.14 thf(fact_5978_unit__div__mult__swap,axiom,
% 5.82/6.14 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 5.82/6.14 => ( ( times_times_nat @ A2 @ ( divide_divide_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_mult_swap
% 5.82/6.14 thf(fact_5979_unit__div__mult__swap,axiom,
% 5.82/6.14 ! [C2: int,A2: int,B2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 5.82/6.14 => ( ( times_times_int @ A2 @ ( divide_divide_int @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_div_mult_swap
% 5.82/6.14 thf(fact_5980_is__unit__div__mult2__eq,axiom,
% 5.82/6.14 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 5.82/6.14 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_div_mult2_eq
% 5.82/6.14 thf(fact_5981_is__unit__div__mult2__eq,axiom,
% 5.82/6.14 ! [B2: int,C2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ C2 @ one_one_int )
% 5.82/6.14 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_div_mult2_eq
% 5.82/6.14 thf(fact_5982_is__unit__power__iff,axiom,
% 5.82/6.14 ! [A2: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( power_power_nat @ A2 @ N ) @ one_one_nat )
% 5.82/6.14 = ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_power_iff
% 5.82/6.14 thf(fact_5983_is__unit__power__iff,axiom,
% 5.82/6.14 ! [A2: int,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( power_power_int @ A2 @ N ) @ one_one_int )
% 5.82/6.14 = ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_power_iff
% 5.82/6.14 thf(fact_5984_is__unit__power__iff,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N ) @ one_one_Code_integer )
% 5.82/6.14 = ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 5.82/6.14 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_power_iff
% 5.82/6.14 thf(fact_5985_dvd__imp__le,axiom,
% 5.82/6.14 ! [K: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ K @ N )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_imp_le
% 5.82/6.14 thf(fact_5986_dvd__mult__cancel,axiom,
% 5.82/6.14 ! [K: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.14 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_cancel
% 5.82/6.14 thf(fact_5987_nat__mult__dvd__cancel1,axiom,
% 5.82/6.14 ! [K: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.82/6.14 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mult_dvd_cancel1
% 5.82/6.14 thf(fact_5988_TBOUND__return,axiom,
% 5.82/6.14 ! [X2: nat] : ( time_TBOUND_nat @ ( heap_Time_return_nat @ X2 ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_return
% 5.82/6.14 thf(fact_5989_TBOUND__return,axiom,
% 5.82/6.14 ! [X2: $o] : ( time_TBOUND_o @ ( heap_Time_return_o @ X2 ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_return
% 5.82/6.14 thf(fact_5990_TBOUND__return,axiom,
% 5.82/6.14 ! [X2: vEBT_VEBTi] : ( time_T5737551269749752165_VEBTi @ ( heap_T3630416162098727440_VEBTi @ X2 ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_return
% 5.82/6.14 thf(fact_5991_TBOUND__return,axiom,
% 5.82/6.14 ! [X2: option_nat] : ( time_T8353473612707095248on_nat @ ( heap_T3487192422709364219on_nat @ X2 ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_return
% 5.82/6.14 thf(fact_5992_real__of__nat__div,axiom,
% 5.82/6.14 ! [D2: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ D2 @ N )
% 5.82/6.14 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D2 ) )
% 5.82/6.14 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % real_of_nat_div
% 5.82/6.14 thf(fact_5993_time__return,axiom,
% 5.82/6.14 ! [X2: nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.14 ( ( time_time_nat @ ( heap_Time_return_nat @ X2 ) @ H2 )
% 5.82/6.14 = one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % time_return
% 5.82/6.14 thf(fact_5994_time__return,axiom,
% 5.82/6.14 ! [X2: $o,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.14 ( ( time_time_o @ ( heap_Time_return_o @ X2 ) @ H2 )
% 5.82/6.14 = one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % time_return
% 5.82/6.14 thf(fact_5995_time__return,axiom,
% 5.82/6.14 ! [X2: vEBT_VEBTi,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.14 ( ( time_time_VEBT_VEBTi @ ( heap_T3630416162098727440_VEBTi @ X2 ) @ H2 )
% 5.82/6.14 = one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % time_return
% 5.82/6.14 thf(fact_5996_time__return,axiom,
% 5.82/6.14 ! [X2: option_nat,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.14 ( ( time_time_option_nat @ ( heap_T3487192422709364219on_nat @ X2 ) @ H2 )
% 5.82/6.14 = one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % time_return
% 5.82/6.14 thf(fact_5997_assn__aci_I10_J,axiom,
% 5.82/6.14 ! [A2: assn,B2: assn,C2: assn] :
% 5.82/6.14 ( ( times_times_assn @ ( times_times_assn @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( times_times_assn @ ( times_times_assn @ A2 @ C2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % assn_aci(10)
% 5.82/6.14 thf(fact_5998_star__aci_I3_J,axiom,
% 5.82/6.14 ! [A2: assn,B2: assn,C2: assn] :
% 5.82/6.14 ( ( times_times_assn @ A2 @ ( times_times_assn @ B2 @ C2 ) )
% 5.82/6.14 = ( times_times_assn @ B2 @ ( times_times_assn @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % star_aci(3)
% 5.82/6.14 thf(fact_5999_star__aci_I2_J,axiom,
% 5.82/6.14 ( times_times_assn
% 5.82/6.14 = ( ^ [A5: assn,B6: assn] : ( times_times_assn @ B6 @ A5 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % star_aci(2)
% 5.82/6.14 thf(fact_6000_star__assoc,axiom,
% 5.82/6.14 ! [A2: assn,B2: assn,C2: assn] :
% 5.82/6.14 ( ( times_times_assn @ ( times_times_assn @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( times_times_assn @ A2 @ ( times_times_assn @ B2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % star_assoc
% 5.82/6.14 thf(fact_6001_is__entails,axiom,
% 5.82/6.14 ! [P: assn,Q: assn] :
% 5.82/6.14 ( ( entails @ P @ Q )
% 5.82/6.14 => ( entails @ P @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_entails
% 5.82/6.14 thf(fact_6002_TBOUND__nth,axiom,
% 5.82/6.14 ! [Xs: array_VEBT_VEBTi,I: nat] : ( time_T5737551269749752165_VEBTi @ ( array_nth_VEBT_VEBTi @ Xs @ I ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_nth
% 5.82/6.14 thf(fact_6003_TBOUND__nth,axiom,
% 5.82/6.14 ! [Xs: array_o,I: nat] : ( time_TBOUND_o @ ( array_nth_o @ Xs @ I ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_nth
% 5.82/6.14 thf(fact_6004_TBOUND__nth,axiom,
% 5.82/6.14 ! [Xs: array_option_nat,I: nat] : ( time_T8353473612707095248on_nat @ ( array_nth_option_nat @ Xs @ I ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_nth
% 5.82/6.14 thf(fact_6005_TBOUND__nth,axiom,
% 5.82/6.14 ! [Xs: array_nat,I: nat] : ( time_TBOUND_nat @ ( array_nth_nat @ Xs @ I ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % TBOUND_nth
% 5.82/6.14 thf(fact_6006_even__zero,axiom,
% 5.82/6.14 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.82/6.14
% 5.82/6.14 % even_zero
% 5.82/6.14 thf(fact_6007_even__zero,axiom,
% 5.82/6.14 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.82/6.14
% 5.82/6.14 % even_zero
% 5.82/6.14 thf(fact_6008_odd__even__add,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.14 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_even_add
% 5.82/6.14 thf(fact_6009_odd__even__add,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.14 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_even_add
% 5.82/6.14 thf(fact_6010_odd__one,axiom,
% 5.82/6.14 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % odd_one
% 5.82/6.14 thf(fact_6011_odd__one,axiom,
% 5.82/6.14 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.82/6.14
% 5.82/6.14 % odd_one
% 5.82/6.14 thf(fact_6012_evenE,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ~ ! [B3: nat] :
% 5.82/6.14 ( A2
% 5.82/6.14 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % evenE
% 5.82/6.14 thf(fact_6013_evenE,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ~ ! [B3: int] :
% 5.82/6.14 ( A2
% 5.82/6.14 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % evenE
% 5.82/6.14 thf(fact_6014_bit__eq__rec,axiom,
% 5.82/6.14 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.82/6.14 = ( ^ [A5: nat,B6: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 )
% 5.82/6.14 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) )
% 5.82/6.14 & ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = ( divide_divide_nat @ B6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bit_eq_rec
% 5.82/6.14 thf(fact_6015_bit__eq__rec,axiom,
% 5.82/6.14 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.82/6.14 = ( ^ [A5: int,B6: int] :
% 5.82/6.14 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 )
% 5.82/6.14 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) )
% 5.82/6.14 & ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = ( divide_divide_int @ B6 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bit_eq_rec
% 5.82/6.14 thf(fact_6016_is__unit__div__mult__cancel__right,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ B2 @ A2 ) )
% 5.82/6.14 = ( divide_divide_nat @ one_one_nat @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_div_mult_cancel_right
% 5.82/6.14 thf(fact_6017_is__unit__div__mult__cancel__right,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( A2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B2 @ A2 ) )
% 5.82/6.14 = ( divide_divide_int @ one_one_int @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_div_mult_cancel_right
% 5.82/6.14 thf(fact_6018_is__unit__div__mult__cancel__left,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ A2 @ B2 ) )
% 5.82/6.14 = ( divide_divide_nat @ one_one_nat @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_div_mult_cancel_left
% 5.82/6.14 thf(fact_6019_is__unit__div__mult__cancel__left,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( A2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( divide_divide_int @ A2 @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.14 = ( divide_divide_int @ one_one_int @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unit_div_mult_cancel_left
% 5.82/6.14 thf(fact_6020_is__unitE,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 5.82/6.14 => ~ ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ! [B3: nat] :
% 5.82/6.14 ( ( B3 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 5.82/6.14 => ( ( ( divide_divide_nat @ one_one_nat @ A2 )
% 5.82/6.14 = B3 )
% 5.82/6.14 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 5.82/6.14 = A2 )
% 5.82/6.14 => ( ( ( times_times_nat @ A2 @ B3 )
% 5.82/6.14 = one_one_nat )
% 5.82/6.14 => ( ( divide_divide_nat @ C2 @ A2 )
% 5.82/6.14 != ( times_times_nat @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unitE
% 5.82/6.14 thf(fact_6021_is__unitE,axiom,
% 5.82/6.14 ! [A2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 5.82/6.14 => ~ ( ( A2 != zero_zero_int )
% 5.82/6.14 => ! [B3: int] :
% 5.82/6.14 ( ( B3 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 5.82/6.14 => ( ( ( divide_divide_int @ one_one_int @ A2 )
% 5.82/6.14 = B3 )
% 5.82/6.14 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 5.82/6.14 = A2 )
% 5.82/6.14 => ( ( ( times_times_int @ A2 @ B3 )
% 5.82/6.14 = one_one_int )
% 5.82/6.14 => ( ( divide_divide_int @ C2 @ A2 )
% 5.82/6.14 != ( times_times_int @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % is_unitE
% 5.82/6.14 thf(fact_6022_odd__numeral,axiom,
% 5.82/6.14 ! [N: num] :
% 5.82/6.14 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_numeral
% 5.82/6.14 thf(fact_6023_odd__numeral,axiom,
% 5.82/6.14 ! [N: num] :
% 5.82/6.14 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_numeral
% 5.82/6.14 thf(fact_6024_dvd__power__iff,axiom,
% 5.82/6.14 ! [X2: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( X2 != zero_zero_nat )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( power_power_nat @ X2 @ M ) @ ( power_power_nat @ X2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ X2 @ one_one_nat )
% 5.82/6.14 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_iff
% 5.82/6.14 thf(fact_6025_dvd__power__iff,axiom,
% 5.82/6.14 ! [X2: int,M: nat,N: nat] :
% 5.82/6.14 ( ( X2 != zero_zero_int )
% 5.82/6.14 => ( ( dvd_dvd_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.82/6.14 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_iff
% 5.82/6.14 thf(fact_6026_dvd__power__iff,axiom,
% 5.82/6.14 ! [X2: code_integer,M: nat,N: nat] :
% 5.82/6.14 ( ( X2 != zero_z3403309356797280102nteger )
% 5.82/6.14 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_Code_integer @ X2 @ one_one_Code_integer )
% 5.82/6.14 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_iff
% 5.82/6.14 thf(fact_6027_dvd__power,axiom,
% 5.82/6.14 ! [N: nat,X2: rat] :
% 5.82/6.14 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 | ( X2 = one_one_rat ) )
% 5.82/6.14 => ( dvd_dvd_rat @ X2 @ ( power_power_rat @ X2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power
% 5.82/6.14 thf(fact_6028_dvd__power,axiom,
% 5.82/6.14 ! [N: nat,X2: nat] :
% 5.82/6.14 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 | ( X2 = one_one_nat ) )
% 5.82/6.14 => ( dvd_dvd_nat @ X2 @ ( power_power_nat @ X2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power
% 5.82/6.14 thf(fact_6029_dvd__power,axiom,
% 5.82/6.14 ! [N: nat,X2: real] :
% 5.82/6.14 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 | ( X2 = one_one_real ) )
% 5.82/6.14 => ( dvd_dvd_real @ X2 @ ( power_power_real @ X2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power
% 5.82/6.14 thf(fact_6030_dvd__power,axiom,
% 5.82/6.14 ! [N: nat,X2: int] :
% 5.82/6.14 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 | ( X2 = one_one_int ) )
% 5.82/6.14 => ( dvd_dvd_int @ X2 @ ( power_power_int @ X2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power
% 5.82/6.14 thf(fact_6031_dvd__power,axiom,
% 5.82/6.14 ! [N: nat,X2: complex] :
% 5.82/6.14 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 | ( X2 = one_one_complex ) )
% 5.82/6.14 => ( dvd_dvd_complex @ X2 @ ( power_power_complex @ X2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power
% 5.82/6.14 thf(fact_6032_dvd__power,axiom,
% 5.82/6.14 ! [N: nat,X2: code_integer] :
% 5.82/6.14 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 | ( X2 = one_one_Code_integer ) )
% 5.82/6.14 => ( dvd_dvd_Code_integer @ X2 @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power
% 5.82/6.14 thf(fact_6033_dvd__mult__cancel1,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.82/6.14 = ( N = one_one_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_cancel1
% 5.82/6.14 thf(fact_6034_dvd__mult__cancel2,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.82/6.14 = ( N = one_one_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mult_cancel2
% 5.82/6.14 thf(fact_6035_power__dvd__imp__le,axiom,
% 5.82/6.14 ! [I: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.82/6.14 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.82/6.14 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_dvd_imp_le
% 5.82/6.14 thf(fact_6036_dvd__minus__add,axiom,
% 5.82/6.14 ! [Q3: nat,N: nat,R2: nat,M: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ Q3 @ N )
% 5.82/6.14 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 5.82/6.14 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_minus_add
% 5.82/6.14 thf(fact_6037_even__two__times__div__two,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_two_times_div_two
% 5.82/6.14 thf(fact_6038_even__two__times__div__two,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_two_times_div_two
% 5.82/6.14 thf(fact_6039_power__mono__odd,axiom,
% 5.82/6.14 ! [N: nat,A2: real,B2: real] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.14 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mono_odd
% 5.82/6.14 thf(fact_6040_power__mono__odd,axiom,
% 5.82/6.14 ! [N: nat,A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 5.82/6.14 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mono_odd
% 5.82/6.14 thf(fact_6041_power__mono__odd,axiom,
% 5.82/6.14 ! [N: nat,A2: rat,B2: rat] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 5.82/6.14 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mono_odd
% 5.82/6.14 thf(fact_6042_power__mono__odd,axiom,
% 5.82/6.14 ! [N: nat,A2: int,B2: int] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_less_eq_int @ A2 @ B2 )
% 5.82/6.14 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mono_odd
% 5.82/6.14 thf(fact_6043_odd__pos,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_pos
% 5.82/6.14 thf(fact_6044_dvd__power__iff__le,axiom,
% 5.82/6.14 ! [K: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.82/6.14 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_power_iff_le
% 5.82/6.14 thf(fact_6045_even__set__bit__iff,axiom,
% 5.82/6.14 ! [M: nat,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A2 ) )
% 5.82/6.14 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 & ( M != zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_set_bit_iff
% 5.82/6.14 thf(fact_6046_even__set__bit__iff,axiom,
% 5.82/6.14 ! [M: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A2 ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 & ( M != zero_zero_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_set_bit_iff
% 5.82/6.14 thf(fact_6047_return__sp__rule,axiom,
% 5.82/6.14 ! [P: assn,X2: vEBT_VEBTi] :
% 5.82/6.14 ( hoare_1429296392585015714_VEBTi @ P @ ( heap_T3630416162098727440_VEBTi @ X2 )
% 5.82/6.14 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ P @ ( pure_assn @ ( R5 = X2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_sp_rule
% 5.82/6.14 thf(fact_6048_return__sp__rule,axiom,
% 5.82/6.14 ! [P: assn,X2: $o] :
% 5.82/6.14 ( hoare_hoare_triple_o @ P @ ( heap_Time_return_o @ X2 )
% 5.82/6.14 @ ^ [R5: $o] : ( times_times_assn @ P @ ( pure_assn @ ( R5 = X2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_sp_rule
% 5.82/6.14 thf(fact_6049_return__sp__rule,axiom,
% 5.82/6.14 ! [P: assn,X2: option_nat] :
% 5.82/6.14 ( hoare_7629718768684598413on_nat @ P @ ( heap_T3487192422709364219on_nat @ X2 )
% 5.82/6.14 @ ^ [R5: option_nat] : ( times_times_assn @ P @ ( pure_assn @ ( R5 = X2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_sp_rule
% 5.82/6.14 thf(fact_6050_return__sp__rule,axiom,
% 5.82/6.14 ! [P: assn,X2: nat] :
% 5.82/6.14 ( hoare_3067605981109127869le_nat @ P @ ( heap_Time_return_nat @ X2 )
% 5.82/6.14 @ ^ [R5: nat] : ( times_times_assn @ P @ ( pure_assn @ ( R5 = X2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % return_sp_rule
% 5.82/6.14 thf(fact_6051_oddE,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ~ ! [B3: nat] :
% 5.82/6.14 ( A2
% 5.82/6.14 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % oddE
% 5.82/6.14 thf(fact_6052_oddE,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ~ ! [B3: int] :
% 5.82/6.14 ( A2
% 5.82/6.14 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % oddE
% 5.82/6.14 thf(fact_6053_zero__le__power__eq,axiom,
% 5.82/6.14 ! [A2: real,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_power_eq
% 5.82/6.14 thf(fact_6054_zero__le__power__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_power_eq
% 5.82/6.14 thf(fact_6055_zero__le__power__eq,axiom,
% 5.82/6.14 ! [A2: rat,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_power_eq
% 5.82/6.14 thf(fact_6056_zero__le__power__eq,axiom,
% 5.82/6.14 ! [A2: int,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) )
% 5.82/6.14 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_power_eq
% 5.82/6.14 thf(fact_6057_zero__le__odd__power,axiom,
% 5.82/6.14 ! [N: nat,A2: real] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) )
% 5.82/6.14 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_odd_power
% 5.82/6.14 thf(fact_6058_zero__le__odd__power,axiom,
% 5.82/6.14 ! [N: nat,A2: code_integer] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.14 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_odd_power
% 5.82/6.14 thf(fact_6059_zero__le__odd__power,axiom,
% 5.82/6.14 ! [N: nat,A2: rat] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) )
% 5.82/6.14 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_odd_power
% 5.82/6.14 thf(fact_6060_zero__le__odd__power,axiom,
% 5.82/6.14 ! [N: nat,A2: int] :
% 5.82/6.14 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) )
% 5.82/6.14 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_odd_power
% 5.82/6.14 thf(fact_6061_zero__le__even__power,axiom,
% 5.82/6.14 ! [N: nat,A2: real] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_even_power
% 5.82/6.14 thf(fact_6062_zero__le__even__power,axiom,
% 5.82/6.14 ! [N: nat,A2: code_integer] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_even_power
% 5.82/6.14 thf(fact_6063_zero__le__even__power,axiom,
% 5.82/6.14 ! [N: nat,A2: rat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_even_power
% 5.82/6.14 thf(fact_6064_zero__le__even__power,axiom,
% 5.82/6.14 ! [N: nat,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_le_even_power
% 5.82/6.14 thf(fact_6065_zero__less__power__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat] :
% 5.82/6.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) )
% 5.82/6.14 = ( ( N = zero_zero_nat )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 != zero_z3403309356797280102nteger ) )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_less_power_eq
% 5.82/6.14 thf(fact_6066_zero__less__power__eq,axiom,
% 5.82/6.14 ! [A2: real,N: nat] :
% 5.82/6.14 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) )
% 5.82/6.14 = ( ( N = zero_zero_nat )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 != zero_zero_real ) )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_real @ zero_zero_real @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_less_power_eq
% 5.82/6.14 thf(fact_6067_zero__less__power__eq,axiom,
% 5.82/6.14 ! [A2: rat,N: nat] :
% 5.82/6.14 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) )
% 5.82/6.14 = ( ( N = zero_zero_nat )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 != zero_zero_rat ) )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_rat @ zero_zero_rat @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_less_power_eq
% 5.82/6.14 thf(fact_6068_zero__less__power__eq,axiom,
% 5.82/6.14 ! [A2: int,N: nat] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) )
% 5.82/6.14 = ( ( N = zero_zero_nat )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 != zero_zero_int ) )
% 5.82/6.14 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_int @ zero_zero_int @ A2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zero_less_power_eq
% 5.82/6.14 thf(fact_6069_fr__rot,axiom,
% 5.82/6.14 ! [A: assn,B: assn,C: assn] :
% 5.82/6.14 ( ( entails @ ( times_times_assn @ A @ B ) @ C )
% 5.82/6.14 => ( entails @ ( times_times_assn @ B @ A ) @ C ) ) ).
% 5.82/6.14
% 5.82/6.14 % fr_rot
% 5.82/6.14 thf(fact_6070_fr__refl,axiom,
% 5.82/6.14 ! [A: assn,B: assn,C: assn] :
% 5.82/6.14 ( ( entails @ A @ B )
% 5.82/6.14 => ( entails @ ( times_times_assn @ A @ C ) @ ( times_times_assn @ B @ C ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % fr_refl
% 5.82/6.14 thf(fact_6071_fr__rot__rhs,axiom,
% 5.82/6.14 ! [A: assn,B: assn,C: assn] :
% 5.82/6.14 ( ( entails @ A @ ( times_times_assn @ B @ C ) )
% 5.82/6.14 => ( entails @ A @ ( times_times_assn @ C @ B ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % fr_rot_rhs
% 5.82/6.14 thf(fact_6072_ent__frame__fwd,axiom,
% 5.82/6.14 ! [P: assn,R: assn,Ps: assn,F3: assn,Q: assn] :
% 5.82/6.14 ( ( entails @ P @ R )
% 5.82/6.14 => ( ( entails @ Ps @ ( times_times_assn @ P @ F3 ) )
% 5.82/6.14 => ( ( entails @ ( times_times_assn @ R @ F3 ) @ Q )
% 5.82/6.14 => ( entails @ Ps @ Q ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % ent_frame_fwd
% 5.82/6.14 thf(fact_6073_norm__assertion__simps_I2_J,axiom,
% 5.82/6.14 ! [A2: assn] :
% 5.82/6.14 ( ( times_times_assn @ A2 @ one_one_assn )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % norm_assertion_simps(2)
% 5.82/6.14 thf(fact_6074_norm__assertion__simps_I1_J,axiom,
% 5.82/6.14 ! [A2: assn] :
% 5.82/6.14 ( ( times_times_assn @ one_one_assn @ A2 )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % norm_assertion_simps(1)
% 5.82/6.14 thf(fact_6075_even__mask__div__iff_H,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mask_div_iff'
% 5.82/6.14 thf(fact_6076_even__mask__div__iff_H,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mask_div_iff'
% 5.82/6.14 thf(fact_6077_even__mask__div__iff_H,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mask_div_iff'
% 5.82/6.14 thf(fact_6078_power__le__zero__eq,axiom,
% 5.82/6.14 ! [A2: real,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ zero_zero_real )
% 5.82/6.14 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_eq_real @ A2 @ zero_zero_real ) )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_zero_eq
% 5.82/6.14 thf(fact_6079_power__le__zero__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ zero_z3403309356797280102nteger )
% 5.82/6.14 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_zero_eq
% 5.82/6.14 thf(fact_6080_power__le__zero__eq,axiom,
% 5.82/6.14 ! [A2: rat,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ zero_zero_rat )
% 5.82/6.14 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_eq_rat @ A2 @ zero_zero_rat ) )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_zero_eq
% 5.82/6.14 thf(fact_6081_power__le__zero__eq,axiom,
% 5.82/6.14 ! [A2: int,N: nat] :
% 5.82/6.14 ( ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ zero_zero_int )
% 5.82/6.14 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( ord_less_eq_int @ A2 @ zero_zero_int ) )
% 5.82/6.14 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 & ( A2 = zero_zero_int ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_le_zero_eq
% 5.82/6.14 thf(fact_6082_even__mask__div__iff,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = zero_z3403309356797280102nteger )
% 5.82/6.14 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mask_div_iff
% 5.82/6.14 thf(fact_6083_even__mask__div__iff,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mask_div_iff
% 5.82/6.14 thf(fact_6084_even__mask__div__iff,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = zero_zero_int )
% 5.82/6.14 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mask_div_iff
% 5.82/6.14 thf(fact_6085_frame__rule__left,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,R: assn] :
% 5.82/6.14 ( ( hoare_1429296392585015714_VEBTi @ P @ C2 @ Q )
% 5.82/6.14 => ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ R @ P ) @ C2
% 5.82/6.14 @ ^ [X3: vEBT_VEBTi] : ( times_times_assn @ R @ ( Q @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % frame_rule_left
% 5.82/6.14 thf(fact_6086_frame__rule__left,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_Time_Heap_o,Q: $o > assn,R: assn] :
% 5.82/6.14 ( ( hoare_hoare_triple_o @ P @ C2 @ Q )
% 5.82/6.14 => ( hoare_hoare_triple_o @ ( times_times_assn @ R @ P ) @ C2
% 5.82/6.14 @ ^ [X3: $o] : ( times_times_assn @ R @ ( Q @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % frame_rule_left
% 5.82/6.14 thf(fact_6087_frame__rule__left,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > assn,R: assn] :
% 5.82/6.14 ( ( hoare_7629718768684598413on_nat @ P @ C2 @ Q )
% 5.82/6.14 => ( hoare_7629718768684598413on_nat @ ( times_times_assn @ R @ P ) @ C2
% 5.82/6.14 @ ^ [X3: option_nat] : ( times_times_assn @ R @ ( Q @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % frame_rule_left
% 5.82/6.14 thf(fact_6088_frame__rule__left,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_Time_Heap_nat,Q: nat > assn,R: assn] :
% 5.82/6.14 ( ( hoare_3067605981109127869le_nat @ P @ C2 @ Q )
% 5.82/6.14 => ( hoare_3067605981109127869le_nat @ ( times_times_assn @ R @ P ) @ C2
% 5.82/6.14 @ ^ [X3: nat] : ( times_times_assn @ R @ ( Q @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % frame_rule_left
% 5.82/6.14 thf(fact_6089_Bernoulli__inequality__even,axiom,
% 5.82/6.14 ! [N: nat,X2: real] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % Bernoulli_inequality_even
% 5.82/6.14 thf(fact_6090_VEBT__internal_OT__vebt__buildupi_Osimps_I3_J,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T_vebt_buildupi.simps(3)
% 5.82/6.14 thf(fact_6091_even__mult__exp__div__exp__iff,axiom,
% 5.82/6.14 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ( ord_less_nat @ N @ M )
% 5.82/6.14 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = zero_z3403309356797280102nteger )
% 5.82/6.14 | ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mult_exp_div_exp_iff
% 5.82/6.14 thf(fact_6092_even__mult__exp__div__exp__iff,axiom,
% 5.82/6.14 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ( ord_less_nat @ N @ M )
% 5.82/6.14 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 | ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mult_exp_div_exp_iff
% 5.82/6.14 thf(fact_6093_even__mult__exp__div__exp__iff,axiom,
% 5.82/6.14 ! [A2: int,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = ( ( ord_less_nat @ N @ M )
% 5.82/6.14 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = zero_zero_int )
% 5.82/6.14 | ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mult_exp_div_exp_iff
% 5.82/6.14 thf(fact_6094_VEBT__internal_OT__vebt__buildupi_Oelims,axiom,
% 5.82/6.14 ! [X2: nat,Y3: nat] :
% 5.82/6.14 ( ( ( vEBT_V441764108873111860ildupi @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( suc @ zero_zero_nat ) ) )
% 5.82/6.14 => ( ( ( X2
% 5.82/6.14 = ( suc @ zero_zero_nat ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( suc @ zero_zero_nat ) ) )
% 5.82/6.14 => ~ ! [N3: nat] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.14 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T_vebt_buildupi.elims
% 5.82/6.14 thf(fact_6095_VEBT__internal_OTb_H_Osimps_I3_J,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.Tb'.simps(3)
% 5.82/6.14 thf(fact_6096_VEBT__internal_OTb_H_Oelims,axiom,
% 5.82/6.14 ! [X2: nat,Y3: nat] :
% 5.82/6.14 ( ( ( vEBT_VEBT_Tb2 @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.82/6.14 => ( ( ( X2
% 5.82/6.14 = ( suc @ zero_zero_nat ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.82/6.14 => ~ ! [N3: nat] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.14 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.Tb'.elims
% 5.82/6.14 thf(fact_6097_VEBT__internal_OTb_Osimps_I3_J,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_VEBT_Tb @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_VEBT_Tb @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.Tb.simps(3)
% 5.82/6.14 thf(fact_6098_mod__frame__fwd,axiom,
% 5.82/6.14 ! [Ps: assn,H2: produc3658429121746597890et_nat,P: assn,R: assn,F3: assn] :
% 5.82/6.14 ( ( rep_assn @ Ps @ H2 )
% 5.82/6.14 => ( ( entails @ P @ R )
% 5.82/6.14 => ( ( entails @ Ps @ ( times_times_assn @ P @ F3 ) )
% 5.82/6.14 => ( rep_assn @ ( times_times_assn @ R @ F3 ) @ H2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_frame_fwd
% 5.82/6.14 thf(fact_6099_VEBT__internal_OT__vebt__buildupi_H_Osimps_I3_J,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 => ( ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ N ) ) )
% 5.82/6.14 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T_vebt_buildupi'.simps(3)
% 5.82/6.14 thf(fact_6100_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,
% 5.82/6.14 ! [Va: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 = ( 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 ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 = ( 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 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(3)
% 5.82/6.14 thf(fact_6101_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,
% 5.82/6.14 ! [Va: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 = ( 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 ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.14 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(3)
% 5.82/6.14 thf(fact_6102_VEBT__internal_OTb_Oelims,axiom,
% 5.82/6.14 ! [X2: nat,Y3: int] :
% 5.82/6.14 ( ( ( vEBT_VEBT_Tb @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_int @ ( bit1 @ one ) ) ) )
% 5.82/6.14 => ( ( ( X2
% 5.82/6.14 = ( suc @ zero_zero_nat ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_int @ ( bit1 @ one ) ) ) )
% 5.82/6.14 => ~ ! [N3: nat] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.14 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.Tb.elims
% 5.82/6.14 thf(fact_6103_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,
% 5.82/6.14 ! [X2: nat,Y3: nat] :
% 5.82/6.14 ( ( ( vEBT_V8346862874174094_d_u_p @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.82/6.14 => ( ( ( X2
% 5.82/6.14 = ( suc @ zero_zero_nat ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.82/6.14 => ~ ! [Va3: nat] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.14 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.elims
% 5.82/6.14 thf(fact_6104_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,
% 5.82/6.14 ! [X2: nat,Y3: nat] :
% 5.82/6.14 ( ( ( vEBT_V8646137997579335489_i_l_d @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.14 => ( ( ( X2
% 5.82/6.14 = ( suc @ zero_zero_nat ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.14 => ~ ! [Va3: nat] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.14 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.elims
% 5.82/6.14 thf(fact_6105_pow__divides__pow__iff,axiom,
% 5.82/6.14 ! [N: nat,A2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) )
% 5.82/6.14 = ( dvd_dvd_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pow_divides_pow_iff
% 5.82/6.14 thf(fact_6106_pow__divides__pow__iff,axiom,
% 5.82/6.14 ! [N: nat,A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( dvd_dvd_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pow_divides_pow_iff
% 5.82/6.14 thf(fact_6107_div2__even__ext__nat,axiom,
% 5.82/6.14 ! [X2: nat,Y3: nat] :
% 5.82/6.14 ( ( ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = ( divide_divide_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.14 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
% 5.82/6.14 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y3 ) )
% 5.82/6.14 => ( X2 = Y3 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div2_even_ext_nat
% 5.82/6.14 thf(fact_6108_lowi__def,axiom,
% 5.82/6.14 ( vEBT_VEBT_lowi
% 5.82/6.14 = ( ^ [X3: nat,N4: nat] : ( heap_Time_return_nat @ ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % lowi_def
% 5.82/6.14 thf(fact_6109_bezout__add__strong__nat,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( A2 != zero_zero_nat )
% 5.82/6.14 => ? [D4: nat,X4: nat,Y4: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ D4 @ A2 )
% 5.82/6.14 & ( dvd_dvd_nat @ D4 @ B2 )
% 5.82/6.14 & ( ( times_times_nat @ A2 @ X4 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y4 ) @ D4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bezout_add_strong_nat
% 5.82/6.14 thf(fact_6110_low__def,axiom,
% 5.82/6.14 ( vEBT_VEBT_low
% 5.82/6.14 = ( ^ [X3: nat,N4: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % low_def
% 5.82/6.14 thf(fact_6111_neg__eucl__rel__int__mult__2,axiom,
% 5.82/6.14 ! [B2: int,A2: int,Q3: int,R2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.82/6.14 => ( ( eucl_rel_int @ ( plus_plus_int @ A2 @ one_one_int ) @ B2 @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.14 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ ( product_Pair_int_int @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % neg_eucl_rel_int_mult_2
% 5.82/6.14 thf(fact_6112_mod__mod__trivial,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mod_trivial
% 5.82/6.14 thf(fact_6113_mod__mod__trivial,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mod_trivial
% 5.82/6.14 thf(fact_6114_mod__mod__trivial,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mod_trivial
% 5.82/6.14 thf(fact_6115_mod__add__self2,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_self2
% 5.82/6.14 thf(fact_6116_mod__add__self2,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_self2
% 5.82/6.14 thf(fact_6117_mod__add__self2,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_self2
% 5.82/6.14 thf(fact_6118_mod__add__self1,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B2 @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_self1
% 5.82/6.14 thf(fact_6119_mod__add__self1,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ B2 @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_self1
% 5.82/6.14 thf(fact_6120_mod__add__self1,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B2 @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_self1
% 5.82/6.14 thf(fact_6121_minus__mod__self2,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_self2
% 5.82/6.14 thf(fact_6122_minus__mod__self2,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_self2
% 5.82/6.14 thf(fact_6123_mod__less,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ M @ N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ M @ N )
% 5.82/6.14 = M ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_less
% 5.82/6.14 thf(fact_6124_nat__mod__eq_H,axiom,
% 5.82/6.14 ! [A2: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ A2 @ N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ N )
% 5.82/6.14 = A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_eq'
% 5.82/6.14 thf(fact_6125_mod__by__1,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ A2 @ one_one_nat )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % mod_by_1
% 5.82/6.14 thf(fact_6126_mod__by__1,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ A2 @ one_one_int )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % mod_by_1
% 5.82/6.14 thf(fact_6127_mod__by__1,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ A2 @ one_one_Code_integer )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % mod_by_1
% 5.82/6.14 thf(fact_6128_bits__mod__by__1,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ A2 @ one_one_nat )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % bits_mod_by_1
% 5.82/6.14 thf(fact_6129_bits__mod__by__1,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ A2 @ one_one_int )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % bits_mod_by_1
% 5.82/6.14 thf(fact_6130_bits__mod__by__1,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ A2 @ one_one_Code_integer )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % bits_mod_by_1
% 5.82/6.14 thf(fact_6131_mod__mult__self1__is__0,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( times_times_nat @ B2 @ A2 ) @ B2 )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self1_is_0
% 5.82/6.14 thf(fact_6132_mod__mult__self1__is__0,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( times_times_int @ B2 @ A2 ) @ B2 )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self1_is_0
% 5.82/6.14 thf(fact_6133_mod__mult__self1__is__0,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B2 @ A2 ) @ B2 )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self1_is_0
% 5.82/6.14 thf(fact_6134_mod__mult__self2__is__0,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self2_is_0
% 5.82/6.14 thf(fact_6135_mod__mult__self2__is__0,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self2_is_0
% 5.82/6.14 thf(fact_6136_mod__mult__self2__is__0,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self2_is_0
% 5.82/6.14 thf(fact_6137_bits__mod__div__trivial,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % bits_mod_div_trivial
% 5.82/6.14 thf(fact_6138_bits__mod__div__trivial,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( divide_divide_int @ ( modulo_modulo_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % bits_mod_div_trivial
% 5.82/6.14 thf(fact_6139_bits__mod__div__trivial,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % bits_mod_div_trivial
% 5.82/6.14 thf(fact_6140_mod__div__trivial,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_trivial
% 5.82/6.14 thf(fact_6141_mod__div__trivial,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( divide_divide_int @ ( modulo_modulo_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_trivial
% 5.82/6.14 thf(fact_6142_mod__div__trivial,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_trivial
% 5.82/6.14 thf(fact_6143_mod__mult__self1,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ ( times_times_nat @ C2 @ B2 ) ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self1
% 5.82/6.14 thf(fact_6144_mod__mult__self1,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ A2 @ ( times_times_int @ C2 @ B2 ) ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self1
% 5.82/6.14 thf(fact_6145_mod__mult__self1,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ C2 @ B2 ) ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self1
% 5.82/6.14 thf(fact_6146_mod__mult__self2,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self2
% 5.82/6.14 thf(fact_6147_mod__mult__self2,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ A2 @ ( times_times_int @ B2 @ C2 ) ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self2
% 5.82/6.14 thf(fact_6148_mod__mult__self2,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ B2 @ C2 ) ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self2
% 5.82/6.14 thf(fact_6149_mod__mult__self3,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B2 ) @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self3
% 5.82/6.14 thf(fact_6150_mod__mult__self3,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B2 ) @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self3
% 5.82/6.14 thf(fact_6151_mod__mult__self3,axiom,
% 5.82/6.14 ! [C2: code_integer,B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C2 @ B2 ) @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self3
% 5.82/6.14 thf(fact_6152_mod__mult__self4,axiom,
% 5.82/6.14 ! [B2: nat,C2: nat,A2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ C2 ) @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self4
% 5.82/6.14 thf(fact_6153_mod__mult__self4,axiom,
% 5.82/6.14 ! [B2: int,C2: int,A2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B2 @ C2 ) @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self4
% 5.82/6.14 thf(fact_6154_mod__mult__self4,axiom,
% 5.82/6.14 ! [B2: code_integer,C2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ C2 ) @ A2 ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_self4
% 5.82/6.14 thf(fact_6155_mod__by__Suc__0,axiom,
% 5.82/6.14 ! [M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % mod_by_Suc_0
% 5.82/6.14 thf(fact_6156_Suc__mod__mult__self1,axiom,
% 5.82/6.14 ! [M: nat,K: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_mod_mult_self1
% 5.82/6.14 thf(fact_6157_Suc__mod__mult__self2,axiom,
% 5.82/6.14 ! [M: nat,N: nat,K: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_mod_mult_self2
% 5.82/6.14 thf(fact_6158_Suc__mod__mult__self3,axiom,
% 5.82/6.14 ! [K: nat,N: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_mod_mult_self3
% 5.82/6.14 thf(fact_6159_Suc__mod__mult__self4,axiom,
% 5.82/6.14 ! [N: nat,K: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_mod_mult_self4
% 5.82/6.14 thf(fact_6160_bits__one__mod__two__eq__one,axiom,
% 5.82/6.14 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % bits_one_mod_two_eq_one
% 5.82/6.14 thf(fact_6161_bits__one__mod__two__eq__one,axiom,
% 5.82/6.14 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_int ) ).
% 5.82/6.14
% 5.82/6.14 % bits_one_mod_two_eq_one
% 5.82/6.14 thf(fact_6162_bits__one__mod__two__eq__one,axiom,
% 5.82/6.14 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_Code_integer ) ).
% 5.82/6.14
% 5.82/6.14 % bits_one_mod_two_eq_one
% 5.82/6.14 thf(fact_6163_one__mod__two__eq__one,axiom,
% 5.82/6.14 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_nat ) ).
% 5.82/6.14
% 5.82/6.14 % one_mod_two_eq_one
% 5.82/6.14 thf(fact_6164_one__mod__two__eq__one,axiom,
% 5.82/6.14 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_int ) ).
% 5.82/6.14
% 5.82/6.14 % one_mod_two_eq_one
% 5.82/6.14 thf(fact_6165_one__mod__two__eq__one,axiom,
% 5.82/6.14 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_Code_integer ) ).
% 5.82/6.14
% 5.82/6.14 % one_mod_two_eq_one
% 5.82/6.14 thf(fact_6166_even__mod__2__iff,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mod_2_iff
% 5.82/6.14 thf(fact_6167_even__mod__2__iff,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mod_2_iff
% 5.82/6.14 thf(fact_6168_even__mod__2__iff,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mod_2_iff
% 5.82/6.14 thf(fact_6169_mod2__Suc__Suc,axiom,
% 5.82/6.14 ! [M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod2_Suc_Suc
% 5.82/6.14 thf(fact_6170_Suc__times__numeral__mod__eq,axiom,
% 5.82/6.14 ! [K: num,N: nat] :
% 5.82/6.14 ( ( ( numeral_numeral_nat @ K )
% 5.82/6.14 != one_one_nat )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.82/6.14 = one_one_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_times_numeral_mod_eq
% 5.82/6.14 thf(fact_6171_not__mod__2__eq__1__eq__0,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_nat )
% 5.82/6.14 = ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod_2_eq_1_eq_0
% 5.82/6.14 thf(fact_6172_not__mod__2__eq__1__eq__0,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_int )
% 5.82/6.14 = ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod_2_eq_1_eq_0
% 5.82/6.14 thf(fact_6173_not__mod__2__eq__1__eq__0,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_Code_integer )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod_2_eq_1_eq_0
% 5.82/6.14 thf(fact_6174_not__mod__2__eq__0__eq__1,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 != zero_zero_nat )
% 5.82/6.14 = ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod_2_eq_0_eq_1
% 5.82/6.14 thf(fact_6175_not__mod__2__eq__0__eq__1,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 != zero_zero_int )
% 5.82/6.14 = ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod_2_eq_0_eq_1
% 5.82/6.14 thf(fact_6176_not__mod__2__eq__0__eq__1,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 != zero_z3403309356797280102nteger )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_Code_integer ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod_2_eq_0_eq_1
% 5.82/6.14 thf(fact_6177_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 != ( suc @ zero_zero_nat ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % not_mod2_eq_Suc_0_eq_0
% 5.82/6.14 thf(fact_6178_add__self__mod__2,axiom,
% 5.82/6.14 ! [M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % add_self_mod_2
% 5.82/6.14 thf(fact_6179_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.82/6.14 ! [M: nat,V: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_mod_eq_add3_mod_numeral
% 5.82/6.14 thf(fact_6180_mod__Suc__eq__mod__add3,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_Suc_eq_mod_add3
% 5.82/6.14 thf(fact_6181_mod2__gr__0,axiom,
% 5.82/6.14 ! [M: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod2_gr_0
% 5.82/6.14 thf(fact_6182_even__succ__mod__exp,axiom,
% 5.82/6.14 ! [A2: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.14 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_succ_mod_exp
% 5.82/6.14 thf(fact_6183_even__succ__mod__exp,axiom,
% 5.82/6.14 ! [A2: int,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.14 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_succ_mod_exp
% 5.82/6.14 thf(fact_6184_even__succ__mod__exp,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_succ_mod_exp
% 5.82/6.14 thf(fact_6185_of__nat__mod,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % of_nat_mod
% 5.82/6.14 thf(fact_6186_of__nat__mod,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % of_nat_mod
% 5.82/6.14 thf(fact_6187_of__nat__mod,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % of_nat_mod
% 5.82/6.14 thf(fact_6188_mod__add__right__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ ( modulo_modulo_nat @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_right_eq
% 5.82/6.14 thf(fact_6189_mod__add__right__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ A2 @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_right_eq
% 5.82/6.14 thf(fact_6190_mod__add__right__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_right_eq
% 5.82/6.14 thf(fact_6191_mod__add__left__eq,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_left_eq
% 5.82/6.14 thf(fact_6192_mod__add__left__eq,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_left_eq
% 5.82/6.14 thf(fact_6193_mod__add__left__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_left_eq
% 5.82/6.14 thf(fact_6194_mod__add__cong,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,A4: nat,B2: nat,B4: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ B2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_cong
% 5.82/6.14 thf(fact_6195_mod__add__cong,axiom,
% 5.82/6.14 ! [A2: int,C2: int,A4: int,B2: int,B4: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ B2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_cong
% 5.82/6.14 thf(fact_6196_mod__add__cong,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,A4: code_integer,B2: code_integer,B4: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo364778990260209775nteger @ B2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_cong
% 5.82/6.14 thf(fact_6197_mod__add__eq,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ C2 ) @ ( modulo_modulo_nat @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_eq
% 5.82/6.14 thf(fact_6198_mod__add__eq,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A2 @ C2 ) @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_eq
% 5.82/6.14 thf(fact_6199_mod__add__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_add_eq
% 5.82/6.14 thf(fact_6200_mod__mult__right__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( times_times_nat @ A2 @ ( modulo_modulo_nat @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_right_eq
% 5.82/6.14 thf(fact_6201_mod__mult__right__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( times_times_int @ A2 @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_right_eq
% 5.82/6.14 thf(fact_6202_mod__mult__right__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_right_eq
% 5.82/6.14 thf(fact_6203_mod__mult__left__eq,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_left_eq
% 5.82/6.14 thf(fact_6204_mod__mult__left__eq,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_left_eq
% 5.82/6.14 thf(fact_6205_mod__mult__left__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_left_eq
% 5.82/6.14 thf(fact_6206_mult__mod__right,axiom,
% 5.82/6.14 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.14 ( ( times_times_nat @ C2 @ ( modulo_modulo_nat @ A2 @ B2 ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( times_times_nat @ C2 @ A2 ) @ ( times_times_nat @ C2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_mod_right
% 5.82/6.14 thf(fact_6207_mult__mod__right,axiom,
% 5.82/6.14 ! [C2: int,A2: int,B2: int] :
% 5.82/6.14 ( ( times_times_int @ C2 @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( times_times_int @ C2 @ A2 ) @ ( times_times_int @ C2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_mod_right
% 5.82/6.14 thf(fact_6208_mult__mod__right,axiom,
% 5.82/6.14 ! [C2: code_integer,A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( times_3573771949741848930nteger @ C2 @ ( modulo364778990260209775nteger @ A2 @ B2 ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C2 @ A2 ) @ ( times_3573771949741848930nteger @ C2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_mod_right
% 5.82/6.14 thf(fact_6209_mod__mult__mult2,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( times_times_nat @ A2 @ C2 ) @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( times_times_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_mult2
% 5.82/6.14 thf(fact_6210_mod__mult__mult2,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( times_times_int @ A2 @ C2 ) @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 = ( times_times_int @ ( modulo_modulo_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_mult2
% 5.82/6.14 thf(fact_6211_mod__mult__mult2,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ C2 ) @ ( times_3573771949741848930nteger @ B2 @ C2 ) )
% 5.82/6.14 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_mult2
% 5.82/6.14 thf(fact_6212_mod__mult__cong,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,A4: nat,B2: nat,B4: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ B2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_cong
% 5.82/6.14 thf(fact_6213_mod__mult__cong,axiom,
% 5.82/6.14 ! [A2: int,C2: int,A4: int,B2: int,B4: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ B2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_cong
% 5.82/6.14 thf(fact_6214_mod__mult__cong,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,A4: code_integer,B2: code_integer,B4: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo364778990260209775nteger @ B2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_cong
% 5.82/6.14 thf(fact_6215_mod__mult__eq,axiom,
% 5.82/6.14 ! [A2: nat,C2: nat,B2: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A2 @ C2 ) @ ( modulo_modulo_nat @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_eq
% 5.82/6.14 thf(fact_6216_mod__mult__eq,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A2 @ C2 ) @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_eq
% 5.82/6.14 thf(fact_6217_mod__mult__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_eq
% 5.82/6.14 thf(fact_6218_mod__diff__right__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( minus_minus_int @ A2 @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_right_eq
% 5.82/6.14 thf(fact_6219_mod__diff__right__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_right_eq
% 5.82/6.14 thf(fact_6220_mod__diff__left__eq,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_left_eq
% 5.82/6.14 thf(fact_6221_mod__diff__left__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_left_eq
% 5.82/6.14 thf(fact_6222_mod__diff__cong,axiom,
% 5.82/6.14 ! [A2: int,C2: int,A4: int,B2: int,B4: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ B2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_cong
% 5.82/6.14 thf(fact_6223_mod__diff__cong,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,A4: code_integer,B2: code_integer,B4: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A4 @ C2 ) )
% 5.82/6.14 => ( ( ( modulo364778990260209775nteger @ B2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ B4 @ C2 ) )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_cong
% 5.82/6.14 thf(fact_6224_mod__diff__eq,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A2 @ C2 ) @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_eq
% 5.82/6.14 thf(fact_6225_mod__diff__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_diff_eq
% 5.82/6.14 thf(fact_6226_power__mod,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ N ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ ( power_power_nat @ A2 @ N ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mod
% 5.82/6.14 thf(fact_6227_power__mod,axiom,
% 5.82/6.14 ! [A2: int,B2: int,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A2 @ B2 ) @ N ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ ( power_power_int @ A2 @ N ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mod
% 5.82/6.14 thf(fact_6228_power__mod,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,N: nat] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ N ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mod
% 5.82/6.14 thf(fact_6229_mod__mod__cancel,axiom,
% 5.82/6.14 ! [C2: nat,B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ C2 @ B2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mod_cancel
% 5.82/6.14 thf(fact_6230_mod__mod__cancel,axiom,
% 5.82/6.14 ! [C2: int,B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ C2 @ B2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mod_cancel
% 5.82/6.14 thf(fact_6231_mod__mod__cancel,axiom,
% 5.82/6.14 ! [C2: code_integer,B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ C2 @ B2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mod_cancel
% 5.82/6.14 thf(fact_6232_dvd__mod,axiom,
% 5.82/6.14 ! [K: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ K @ M )
% 5.82/6.14 => ( ( dvd_dvd_nat @ K @ N )
% 5.82/6.14 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mod
% 5.82/6.14 thf(fact_6233_dvd__mod,axiom,
% 5.82/6.14 ! [K: int,M: int,N: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ K @ M )
% 5.82/6.14 => ( ( dvd_dvd_int @ K @ N )
% 5.82/6.14 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mod
% 5.82/6.14 thf(fact_6234_dvd__mod,axiom,
% 5.82/6.14 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.82/6.14 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.82/6.14 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_mod
% 5.82/6.14 thf(fact_6235_mod__Suc__Suc__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_Suc_Suc_eq
% 5.82/6.14 thf(fact_6236_mod__Suc__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_Suc_eq
% 5.82/6.14 thf(fact_6237_nat__mod__eq,axiom,
% 5.82/6.14 ! [B2: nat,N: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ B2 @ N )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ B2 @ N ) )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ N )
% 5.82/6.14 = B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_eq
% 5.82/6.14 thf(fact_6238_mod__plus__right,axiom,
% 5.82/6.14 ! [A2: nat,X2: nat,M: nat,B2: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ X2 ) @ M )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ B2 @ X2 ) @ M ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ A2 @ M )
% 5.82/6.14 = ( modulo_modulo_nat @ B2 @ M ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_plus_right
% 5.82/6.14 thf(fact_6239_mod__less__eq__dividend,axiom,
% 5.82/6.14 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.82/6.14
% 5.82/6.14 % mod_less_eq_dividend
% 5.82/6.14 thf(fact_6240_zdvd__zdiffD,axiom,
% 5.82/6.14 ! [K: int,M: int,N: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 5.82/6.14 => ( ( dvd_dvd_int @ K @ N )
% 5.82/6.14 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zdvd_zdiffD
% 5.82/6.14 thf(fact_6241_gcd__nat__induct,axiom,
% 5.82/6.14 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.82/6.14 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 5.82/6.14 => ( ! [M5: nat,N3: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.14 => ( ( P @ N3 @ ( modulo_modulo_nat @ M5 @ N3 ) )
% 5.82/6.14 => ( P @ M5 @ N3 ) ) )
% 5.82/6.14 => ( P @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % gcd_nat_induct
% 5.82/6.14 thf(fact_6242_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.14 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.82/6.14 thf(fact_6243_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.14 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.82/6.14 thf(fact_6244_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.14 => ( ord_less_eq_int @ ( modulo_modulo_int @ A2 @ B2 ) @ A2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.82/6.14 thf(fact_6245_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.14 => ( ord_less_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.82/6.14 thf(fact_6246_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ord_less_int @ ( modulo_modulo_int @ A2 @ B2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.82/6.14 thf(fact_6247_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.14 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.82/6.14 thf(fact_6248_cong__exp__iff__simps_I9_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(9)
% 5.82/6.14 thf(fact_6249_cong__exp__iff__simps_I9_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(9)
% 5.82/6.14 thf(fact_6250_cong__exp__iff__simps_I9_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(9)
% 5.82/6.14 thf(fact_6251_cong__exp__iff__simps_I4_J,axiom,
% 5.82/6.14 ! [M: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(4)
% 5.82/6.14 thf(fact_6252_cong__exp__iff__simps_I4_J,axiom,
% 5.82/6.14 ! [M: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(4)
% 5.82/6.14 thf(fact_6253_cong__exp__iff__simps_I4_J,axiom,
% 5.82/6.14 ! [M: num,N: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(4)
% 5.82/6.14 thf(fact_6254_mod__eq__self__iff__div__eq__0,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ A2 @ B2 )
% 5.82/6.14 = A2 )
% 5.82/6.14 = ( ( divide_divide_nat @ A2 @ B2 )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_self_iff_div_eq_0
% 5.82/6.14 thf(fact_6255_mod__eq__self__iff__div__eq__0,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.14 = A2 )
% 5.82/6.14 = ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_self_iff_div_eq_0
% 5.82/6.14 thf(fact_6256_mod__eq__self__iff__div__eq__0,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ B2 )
% 5.82/6.14 = A2 )
% 5.82/6.14 = ( ( divide6298287555418463151nteger @ A2 @ B2 )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_self_iff_div_eq_0
% 5.82/6.14 thf(fact_6257_mod__eqE,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ B2 @ C2 ) )
% 5.82/6.14 => ~ ! [D4: int] :
% 5.82/6.14 ( B2
% 5.82/6.14 != ( plus_plus_int @ A2 @ ( times_times_int @ C2 @ D4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eqE
% 5.82/6.14 thf(fact_6258_mod__eqE,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ B2 @ C2 ) )
% 5.82/6.14 => ~ ! [D4: code_integer] :
% 5.82/6.14 ( B2
% 5.82/6.14 != ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ C2 @ D4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eqE
% 5.82/6.14 thf(fact_6259_div__add1__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ C2 ) @ ( divide_divide_nat @ B2 @ C2 ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ C2 ) @ ( modulo_modulo_nat @ B2 @ C2 ) ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_add1_eq
% 5.82/6.14 thf(fact_6260_div__add1__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( divide_divide_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A2 @ C2 ) @ ( divide_divide_int @ B2 @ C2 ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A2 @ C2 ) @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_add1_eq
% 5.82/6.14 thf(fact_6261_div__add1__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A2 @ C2 ) @ ( divide6298287555418463151nteger @ B2 @ C2 ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ C2 ) @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_add1_eq
% 5.82/6.14 thf(fact_6262_mod__eq__dvd__iff,axiom,
% 5.82/6.14 ! [A2: int,C2: int,B2: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ A2 @ C2 )
% 5.82/6.14 = ( modulo_modulo_int @ B2 @ C2 ) )
% 5.82/6.14 = ( dvd_dvd_int @ C2 @ ( minus_minus_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_dvd_iff
% 5.82/6.14 thf(fact_6263_mod__eq__dvd__iff,axiom,
% 5.82/6.14 ! [A2: code_integer,C2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ A2 @ C2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ B2 @ C2 ) )
% 5.82/6.14 = ( dvd_dvd_Code_integer @ C2 @ ( minus_8373710615458151222nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_dvd_iff
% 5.82/6.14 thf(fact_6264_dvd__minus__mod,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] : ( dvd_dvd_nat @ B2 @ ( minus_minus_nat @ A2 @ ( modulo_modulo_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_minus_mod
% 5.82/6.14 thf(fact_6265_dvd__minus__mod,axiom,
% 5.82/6.14 ! [B2: int,A2: int] : ( dvd_dvd_int @ B2 @ ( minus_minus_int @ A2 @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_minus_mod
% 5.82/6.14 thf(fact_6266_dvd__minus__mod,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] : ( dvd_dvd_Code_integer @ B2 @ ( minus_8373710615458151222nteger @ A2 @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_minus_mod
% 5.82/6.14 thf(fact_6267_mod__Suc,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 = N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.82/6.14 = zero_zero_nat ) )
% 5.82/6.14 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 != N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.82/6.14 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_Suc
% 5.82/6.14 thf(fact_6268_mod__induct,axiom,
% 5.82/6.14 ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 5.82/6.14 ( ( P @ N )
% 5.82/6.14 => ( ( ord_less_nat @ N @ P6 )
% 5.82/6.14 => ( ( ord_less_nat @ M @ P6 )
% 5.82/6.14 => ( ! [N3: nat] :
% 5.82/6.14 ( ( ord_less_nat @ N3 @ P6 )
% 5.82/6.14 => ( ( P @ N3 )
% 5.82/6.14 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P6 ) ) ) )
% 5.82/6.14 => ( P @ M ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_induct
% 5.82/6.14 thf(fact_6269_mod__less__divisor,axiom,
% 5.82/6.14 ! [N: nat,M: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_less_divisor
% 5.82/6.14 thf(fact_6270_nat__mod__lem,axiom,
% 5.82/6.14 ! [N: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( ord_less_nat @ B2 @ N )
% 5.82/6.14 = ( ( modulo_modulo_nat @ B2 @ N )
% 5.82/6.14 = B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_lem
% 5.82/6.14 thf(fact_6271_mod__Suc__le__divisor,axiom,
% 5.82/6.14 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.82/6.14
% 5.82/6.14 % mod_Suc_le_divisor
% 5.82/6.14 thf(fact_6272_word__rot__lem,axiom,
% 5.82/6.14 ! [L: nat,K: nat,D2: nat,N: nat] :
% 5.82/6.14 ( ( ( plus_plus_nat @ L @ K )
% 5.82/6.14 = ( plus_plus_nat @ D2 @ ( modulo_modulo_nat @ K @ L ) ) )
% 5.82/6.14 => ( ( ord_less_nat @ N @ L )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ D2 @ N ) @ L )
% 5.82/6.14 = N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % word_rot_lem
% 5.82/6.14 thf(fact_6273_nat__minus__mod,axiom,
% 5.82/6.14 ! [N: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( minus_minus_nat @ N @ ( modulo_modulo_nat @ N @ M ) ) @ M )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % nat_minus_mod
% 5.82/6.14 thf(fact_6274_mod__if,axiom,
% 5.82/6.14 ( modulo_modulo_nat
% 5.82/6.14 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N4 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_if
% 5.82/6.14 thf(fact_6275_mod__nat__sub,axiom,
% 5.82/6.14 ! [X2: nat,Z: nat,Y3: nat] :
% 5.82/6.14 ( ( ord_less_nat @ X2 @ Z )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( minus_minus_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.14 = ( minus_minus_nat @ X2 @ Y3 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_nat_sub
% 5.82/6.14 thf(fact_6276_mod__geq,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ~ ( ord_less_nat @ M @ N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ M @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_geq
% 5.82/6.14 thf(fact_6277_mod__eq__0D,axiom,
% 5.82/6.14 ! [M: nat,D2: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ M @ D2 )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 => ? [Q4: nat] :
% 5.82/6.14 ( M
% 5.82/6.14 = ( times_times_nat @ D2 @ Q4 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_0D
% 5.82/6.14 thf(fact_6278_nat__minus__mod__plus__right,axiom,
% 5.82/6.14 ! [N: nat,X2: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ X2 ) @ ( modulo_modulo_nat @ N @ M ) ) @ M )
% 5.82/6.14 = ( modulo_modulo_nat @ X2 @ M ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_minus_mod_plus_right
% 5.82/6.14 thf(fact_6279_le__mod__geq,axiom,
% 5.82/6.14 ! [N: nat,M: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( ( modulo_modulo_nat @ M @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % le_mod_geq
% 5.82/6.14 thf(fact_6280_msrevs_I2_J,axiom,
% 5.82/6.14 ! [K: nat,N: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % msrevs(2)
% 5.82/6.14 thf(fact_6281_nat__mod__eq__iff,axiom,
% 5.82/6.14 ! [X2: nat,N: nat,Y3: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ Y3 @ N ) )
% 5.82/6.14 = ( ? [Q1: nat,Q22: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 5.82/6.14 = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_eq_iff
% 5.82/6.14 thf(fact_6282_zdvd__antisym__nonneg,axiom,
% 5.82/6.14 ! [M: int,N: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.82/6.14 => ( ( dvd_dvd_int @ M @ N )
% 5.82/6.14 => ( ( dvd_dvd_int @ N @ M )
% 5.82/6.14 => ( M = N ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zdvd_antisym_nonneg
% 5.82/6.14 thf(fact_6283_zdvd__period,axiom,
% 5.82/6.14 ! [A2: int,D2: int,X2: int,T: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ D2 )
% 5.82/6.14 => ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ X2 @ T ) )
% 5.82/6.14 = ( dvd_dvd_int @ A2 @ ( plus_plus_int @ ( plus_plus_int @ X2 @ ( times_times_int @ C2 @ D2 ) ) @ T ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zdvd_period
% 5.82/6.14 thf(fact_6284_zdvd__reduce,axiom,
% 5.82/6.14 ! [K: int,N: int,M: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.82/6.14 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % zdvd_reduce
% 5.82/6.14 thf(fact_6285_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.14 => ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ B2 )
% 5.82/6.14 = A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_less
% 5.82/6.14 thf(fact_6286_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.14 => ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ B2 )
% 5.82/6.14 = A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_less
% 5.82/6.14 thf(fact_6287_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.14 => ( ( ord_less_int @ A2 @ B2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.14 = A2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_less
% 5.82/6.14 thf(fact_6288_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.14 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.82/6.14 thf(fact_6289_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.14 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.82/6.14 thf(fact_6290_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.82/6.14 thf(fact_6291_cong__exp__iff__simps_I2_J,axiom,
% 5.82/6.14 ! [N: num,Q3: num] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(2)
% 5.82/6.14 thf(fact_6292_cong__exp__iff__simps_I2_J,axiom,
% 5.82/6.14 ! [N: num,Q3: num] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = zero_zero_int )
% 5.82/6.14 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(2)
% 5.82/6.14 thf(fact_6293_cong__exp__iff__simps_I2_J,axiom,
% 5.82/6.14 ! [N: num,Q3: num] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = zero_z3403309356797280102nteger )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(2)
% 5.82/6.14 thf(fact_6294_cong__exp__iff__simps_I1_J,axiom,
% 5.82/6.14 ! [N: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.82/6.14 = zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(1)
% 5.82/6.14 thf(fact_6295_cong__exp__iff__simps_I1_J,axiom,
% 5.82/6.14 ! [N: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.82/6.14 = zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(1)
% 5.82/6.14 thf(fact_6296_cong__exp__iff__simps_I1_J,axiom,
% 5.82/6.14 ! [N: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(1)
% 5.82/6.14 thf(fact_6297_cong__exp__iff__simps_I6_J,axiom,
% 5.82/6.14 ! [Q3: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(6)
% 5.82/6.14 thf(fact_6298_cong__exp__iff__simps_I6_J,axiom,
% 5.82/6.14 ! [Q3: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(6)
% 5.82/6.14 thf(fact_6299_cong__exp__iff__simps_I6_J,axiom,
% 5.82/6.14 ! [Q3: num,N: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(6)
% 5.82/6.14 thf(fact_6300_cong__exp__iff__simps_I8_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(8)
% 5.82/6.14 thf(fact_6301_cong__exp__iff__simps_I8_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(8)
% 5.82/6.14 thf(fact_6302_cong__exp__iff__simps_I8_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(8)
% 5.82/6.14 thf(fact_6303_cong__exp__iff__simps_I10_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(10)
% 5.82/6.14 thf(fact_6304_cong__exp__iff__simps_I10_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(10)
% 5.82/6.14 thf(fact_6305_cong__exp__iff__simps_I10_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(10)
% 5.82/6.14 thf(fact_6306_cong__exp__iff__simps_I12_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(12)
% 5.82/6.14 thf(fact_6307_cong__exp__iff__simps_I12_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(12)
% 5.82/6.14 thf(fact_6308_cong__exp__iff__simps_I12_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(12)
% 5.82/6.14 thf(fact_6309_cong__exp__iff__simps_I13_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(13)
% 5.82/6.14 thf(fact_6310_cong__exp__iff__simps_I13_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(13)
% 5.82/6.14 thf(fact_6311_cong__exp__iff__simps_I13_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(13)
% 5.82/6.14 thf(fact_6312_mult__div__mod__eq,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A2 @ B2 ) ) @ ( modulo_modulo_nat @ A2 @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mult_div_mod_eq
% 5.82/6.14 thf(fact_6313_mult__div__mod__eq,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( plus_plus_int @ ( times_times_int @ B2 @ ( divide_divide_int @ A2 @ B2 ) ) @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mult_div_mod_eq
% 5.82/6.14 thf(fact_6314_mult__div__mod__eq,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A2 @ B2 ) ) @ ( modulo364778990260209775nteger @ A2 @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mult_div_mod_eq
% 5.82/6.14 thf(fact_6315_mod__mult__div__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A2 @ B2 ) ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_div_eq
% 5.82/6.14 thf(fact_6316_mod__mult__div__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( plus_plus_int @ ( modulo_modulo_int @ A2 @ B2 ) @ ( times_times_int @ B2 @ ( divide_divide_int @ A2 @ B2 ) ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_div_eq
% 5.82/6.14 thf(fact_6317_mod__mult__div__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A2 @ B2 ) ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult_div_eq
% 5.82/6.14 thf(fact_6318_mod__div__mult__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ B2 ) @ ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_mult_eq
% 5.82/6.14 thf(fact_6319_mod__div__mult__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( plus_plus_int @ ( modulo_modulo_int @ A2 @ B2 ) @ ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_mult_eq
% 5.82/6.14 thf(fact_6320_mod__div__mult__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_mult_eq
% 5.82/6.14 thf(fact_6321_div__mult__mod__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A2 @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_mod_eq
% 5.82/6.14 thf(fact_6322_div__mult__mod__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_mod_eq
% 5.82/6.14 thf(fact_6323_div__mult__mod__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ B2 ) @ ( modulo364778990260209775nteger @ A2 @ B2 ) )
% 5.82/6.14 = A2 ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult_mod_eq
% 5.82/6.14 thf(fact_6324_mod__div__decomp,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( A2
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_decomp
% 5.82/6.14 thf(fact_6325_mod__div__decomp,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( A2
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_decomp
% 5.82/6.14 thf(fact_6326_mod__div__decomp,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( A2
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ B2 ) @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_decomp
% 5.82/6.14 thf(fact_6327_cancel__div__mod__rules_I1_J,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A2 @ B2 ) ) @ C2 )
% 5.82/6.14 = ( plus_plus_nat @ A2 @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % cancel_div_mod_rules(1)
% 5.82/6.14 thf(fact_6328_cancel__div__mod__rules_I1_J,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A2 @ B2 ) ) @ C2 )
% 5.82/6.14 = ( plus_plus_int @ A2 @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % cancel_div_mod_rules(1)
% 5.82/6.14 thf(fact_6329_cancel__div__mod__rules_I1_J,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ B2 ) @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) @ C2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ A2 @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % cancel_div_mod_rules(1)
% 5.82/6.14 thf(fact_6330_cancel__div__mod__rules_I2_J,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat,C2: nat] :
% 5.82/6.14 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A2 @ B2 ) ) @ ( modulo_modulo_nat @ A2 @ B2 ) ) @ C2 )
% 5.82/6.14 = ( plus_plus_nat @ A2 @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % cancel_div_mod_rules(2)
% 5.82/6.14 thf(fact_6331_cancel__div__mod__rules_I2_J,axiom,
% 5.82/6.14 ! [B2: int,A2: int,C2: int] :
% 5.82/6.14 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B2 @ ( divide_divide_int @ A2 @ B2 ) ) @ ( modulo_modulo_int @ A2 @ B2 ) ) @ C2 )
% 5.82/6.14 = ( plus_plus_int @ A2 @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % cancel_div_mod_rules(2)
% 5.82/6.14 thf(fact_6332_cancel__div__mod__rules_I2_J,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A2 @ B2 ) ) @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) @ C2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ A2 @ C2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % cancel_div_mod_rules(2)
% 5.82/6.14 thf(fact_6333_div__mult1__eq,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( divide_divide_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ A2 @ ( divide_divide_nat @ B2 @ C2 ) ) @ ( divide_divide_nat @ ( times_times_nat @ A2 @ ( modulo_modulo_nat @ B2 @ C2 ) ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult1_eq
% 5.82/6.14 thf(fact_6334_div__mult1__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( divide_divide_int @ ( times_times_int @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ A2 @ ( divide_divide_int @ B2 @ C2 ) ) @ ( divide_divide_int @ ( times_times_int @ A2 @ ( modulo_modulo_int @ B2 @ C2 ) ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult1_eq
% 5.82/6.14 thf(fact_6335_div__mult1__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer,C2: code_integer] :
% 5.82/6.14 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ ( divide6298287555418463151nteger @ B2 @ C2 ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A2 @ ( modulo364778990260209775nteger @ B2 @ C2 ) ) @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mult1_eq
% 5.82/6.14 thf(fact_6336_minus__mult__div__eq__mod,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( minus_minus_nat @ A2 @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A2 @ B2 ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mult_div_eq_mod
% 5.82/6.14 thf(fact_6337_minus__mult__div__eq__mod,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( minus_minus_int @ A2 @ ( times_times_int @ B2 @ ( divide_divide_int @ A2 @ B2 ) ) )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mult_div_eq_mod
% 5.82/6.14 thf(fact_6338_minus__mult__div__eq__mod,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( minus_8373710615458151222nteger @ A2 @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A2 @ B2 ) ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mult_div_eq_mod
% 5.82/6.14 thf(fact_6339_minus__mod__eq__mult__div,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( minus_minus_nat @ A2 @ ( modulo_modulo_nat @ A2 @ B2 ) )
% 5.82/6.14 = ( times_times_nat @ B2 @ ( divide_divide_nat @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_eq_mult_div
% 5.82/6.14 thf(fact_6340_minus__mod__eq__mult__div,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( minus_minus_int @ A2 @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 = ( times_times_int @ B2 @ ( divide_divide_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_eq_mult_div
% 5.82/6.14 thf(fact_6341_minus__mod__eq__mult__div,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( minus_8373710615458151222nteger @ A2 @ ( modulo364778990260209775nteger @ A2 @ B2 ) )
% 5.82/6.14 = ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_eq_mult_div
% 5.82/6.14 thf(fact_6342_minus__mod__eq__div__mult,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( minus_minus_nat @ A2 @ ( modulo_modulo_nat @ A2 @ B2 ) )
% 5.82/6.14 = ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_eq_div_mult
% 5.82/6.14 thf(fact_6343_minus__mod__eq__div__mult,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( minus_minus_int @ A2 @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 = ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_eq_div_mult
% 5.82/6.14 thf(fact_6344_minus__mod__eq__div__mult,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( minus_8373710615458151222nteger @ A2 @ ( modulo364778990260209775nteger @ A2 @ B2 ) )
% 5.82/6.14 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_mod_eq_div_mult
% 5.82/6.14 thf(fact_6345_minus__div__mult__eq__mod,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( minus_minus_nat @ A2 @ ( times_times_nat @ ( divide_divide_nat @ A2 @ B2 ) @ B2 ) )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_div_mult_eq_mod
% 5.82/6.14 thf(fact_6346_minus__div__mult__eq__mod,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( minus_minus_int @ A2 @ ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 ) )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_div_mult_eq_mod
% 5.82/6.14 thf(fact_6347_minus__div__mult__eq__mod,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( minus_8373710615458151222nteger @ A2 @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ B2 ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % minus_div_mult_eq_mod
% 5.82/6.14 thf(fact_6348_zmde,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( times_times_int @ B2 @ ( divide_divide_int @ A2 @ B2 ) )
% 5.82/6.14 = ( minus_minus_int @ A2 @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmde
% 5.82/6.14 thf(fact_6349_zmde,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A2 @ B2 ) )
% 5.82/6.14 = ( minus_8373710615458151222nteger @ A2 @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmde
% 5.82/6.14 thf(fact_6350_unit__imp__mod__eq__0,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ B2 )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_imp_mod_eq_0
% 5.82/6.14 thf(fact_6351_unit__imp__mod__eq__0,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_imp_mod_eq_0
% 5.82/6.14 thf(fact_6352_unit__imp__mod__eq__0,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ B2 )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % unit_imp_mod_eq_0
% 5.82/6.14 thf(fact_6353_mod__le__divisor,axiom,
% 5.82/6.14 ! [N: nat,M: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_le_divisor
% 5.82/6.14 thf(fact_6354_div__less__mono,axiom,
% 5.82/6.14 ! [A: nat,B: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ A @ B )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ A @ N )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ B @ N )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 => ( ord_less_nat @ ( divide_divide_nat @ A @ N ) @ ( divide_divide_nat @ B @ N ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_less_mono
% 5.82/6.14 thf(fact_6355_mod__nat__add,axiom,
% 5.82/6.14 ! [X2: nat,Z: nat,Y3: nat] :
% 5.82/6.14 ( ( ord_less_nat @ X2 @ Z )
% 5.82/6.14 => ( ( ord_less_nat @ Y3 @ Z )
% 5.82/6.14 => ( ( ( ord_less_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.14 = ( plus_plus_nat @ X2 @ Y3 ) ) )
% 5.82/6.14 & ( ~ ( ord_less_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ Z )
% 5.82/6.14 = ( minus_minus_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ Z ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_nat_add
% 5.82/6.14 thf(fact_6356_nat__mod__eq__lemma,axiom,
% 5.82/6.14 ! [X2: nat,N: nat,Y3: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ Y3 @ N ) )
% 5.82/6.14 => ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.82/6.14 => ? [Q4: nat] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_eq_lemma
% 5.82/6.14 thf(fact_6357_mod__eq__nat2E,axiom,
% 5.82/6.14 ! [M: nat,Q3: nat,N: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.82/6.14 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.82/6.14 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ~ ! [S3: nat] :
% 5.82/6.14 ( N
% 5.82/6.14 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_nat2E
% 5.82/6.14 thf(fact_6358_mod__eq__nat1E,axiom,
% 5.82/6.14 ! [M: nat,Q3: nat,N: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.82/6.14 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.82/6.14 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ~ ! [S3: nat] :
% 5.82/6.14 ( M
% 5.82/6.14 != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_nat1E
% 5.82/6.14 thf(fact_6359_mod__greater__zero__iff__not__dvd,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_greater_zero_iff_not_dvd
% 5.82/6.14 thf(fact_6360_divmod_H__nat__def,axiom,
% 5.82/6.14 ( unique5055182867167087721od_nat
% 5.82/6.14 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod'_nat_def
% 5.82/6.14 thf(fact_6361_div__mod__decomp,axiom,
% 5.82/6.14 ! [A: nat,N: nat] :
% 5.82/6.14 ( A
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ N ) @ N ) @ ( modulo_modulo_nat @ A @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mod_decomp
% 5.82/6.14 thf(fact_6362_mod__mult2__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q3 ) )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult2_eq
% 5.82/6.14 thf(fact_6363_modulo__nat__def,axiom,
% 5.82/6.14 ( modulo_modulo_nat
% 5.82/6.14 = ( ^ [M6: nat,N4: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N4 ) @ N4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % modulo_nat_def
% 5.82/6.14 thf(fact_6364_mod__eq__dvd__iff__nat,axiom,
% 5.82/6.14 ! [N: nat,M: nat,Q3: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.82/6.14 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.82/6.14 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_eq_dvd_iff_nat
% 5.82/6.14 thf(fact_6365_zdvd__imp__le,axiom,
% 5.82/6.14 ! [Z: int,N: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ Z @ N )
% 5.82/6.14 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.82/6.14 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zdvd_imp_le
% 5.82/6.14 thf(fact_6366_VEBT__internal_OminNulli_Osimps_I5_J,axiom,
% 5.82/6.14 ! [Uz: product_prod_nat_nat,Va: nat,Vb: array_VEBT_VEBTi,Vc: vEBT_VEBTi] :
% 5.82/6.14 ( ( vEBT_VEBT_minNulli @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 5.82/6.14 = ( heap_Time_return_o @ $false ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.minNulli.simps(5)
% 5.82/6.14 thf(fact_6367_VEBT__internal_OminNulli_Osimps_I4_J,axiom,
% 5.82/6.14 ! [Uw: nat,Ux: array_VEBT_VEBTi,Uy: vEBT_VEBTi] :
% 5.82/6.14 ( ( vEBT_VEBT_minNulli @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.82/6.14 = ( heap_Time_return_o @ $true ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.minNulli.simps(4)
% 5.82/6.14 thf(fact_6368_prod__decode__aux_Ocases,axiom,
% 5.82/6.14 ! [X2: product_prod_nat_nat] :
% 5.82/6.14 ~ ! [K2: nat,M5: nat] :
% 5.82/6.14 ( X2
% 5.82/6.14 != ( product_Pair_nat_nat @ K2 @ M5 ) ) ).
% 5.82/6.14
% 5.82/6.14 % prod_decode_aux.cases
% 5.82/6.14 thf(fact_6369_cong__exp__iff__simps_I3_J,axiom,
% 5.82/6.14 ! [N: num,Q3: num] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != zero_zero_nat ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(3)
% 5.82/6.14 thf(fact_6370_cong__exp__iff__simps_I3_J,axiom,
% 5.82/6.14 ! [N: num,Q3: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != zero_zero_int ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(3)
% 5.82/6.14 thf(fact_6371_cong__exp__iff__simps_I3_J,axiom,
% 5.82/6.14 ! [N: num,Q3: num] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 != zero_z3403309356797280102nteger ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(3)
% 5.82/6.14 thf(fact_6372_mod__mult2__eq_H,axiom,
% 5.82/6.14 ! [A2: code_integer,M: nat,N: nat] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A2 @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A2 @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult2_eq'
% 5.82/6.14 thf(fact_6373_mod__mult2__eq_H,axiom,
% 5.82/6.14 ! [A2: int,M: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_int @ A2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult2_eq'
% 5.82/6.14 thf(fact_6374_mod__mult2__eq_H,axiom,
% 5.82/6.14 ! [A2: nat,M: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A2 @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_mult2_eq'
% 5.82/6.14 thf(fact_6375_even__even__mod__4__iff,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.14 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_even_mod_4_iff
% 5.82/6.14 thf(fact_6376_field__char__0__class_Oof__nat__div,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.14 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % field_char_0_class.of_nat_div
% 5.82/6.14 thf(fact_6377_field__char__0__class_Oof__nat__div,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.14 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % field_char_0_class.of_nat_div
% 5.82/6.14 thf(fact_6378_field__char__0__class_Oof__nat__div,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.82/6.14 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % field_char_0_class.of_nat_div
% 5.82/6.14 thf(fact_6379_split__mod,axiom,
% 5.82/6.14 ! [P: nat > $o,M: nat,N: nat] :
% 5.82/6.14 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.82/6.14 = ( ( ( N = zero_zero_nat )
% 5.82/6.14 => ( P @ M ) )
% 5.82/6.14 & ( ( N != zero_zero_nat )
% 5.82/6.14 => ! [I4: nat,J3: nat] :
% 5.82/6.14 ( ( ord_less_nat @ J3 @ N )
% 5.82/6.14 => ( ( M
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.82/6.14 => ( P @ J3 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % split_mod
% 5.82/6.14 thf(fact_6380_mod__lemma,axiom,
% 5.82/6.14 ! [C2: nat,R2: nat,B2: nat,Q3: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.14 => ( ( ord_less_nat @ R2 @ B2 )
% 5.82/6.14 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ ( modulo_modulo_nat @ Q3 @ C2 ) ) @ R2 ) @ ( times_times_nat @ B2 @ C2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_lemma
% 5.82/6.14 thf(fact_6381_divmod__def,axiom,
% 5.82/6.14 ( unique3479559517661332726nteger
% 5.82/6.14 = ( ^ [M6: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_def
% 5.82/6.14 thf(fact_6382_divmod__def,axiom,
% 5.82/6.14 ( unique5055182867167087721od_nat
% 5.82/6.14 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_def
% 5.82/6.14 thf(fact_6383_divmod__def,axiom,
% 5.82/6.14 ( unique5052692396658037445od_int
% 5.82/6.14 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_def
% 5.82/6.14 thf(fact_6384_mod__nat__eqI,axiom,
% 5.82/6.14 ! [R2: nat,N: nat,M: nat] :
% 5.82/6.14 ( ( ord_less_nat @ R2 @ N )
% 5.82/6.14 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.82/6.14 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.82/6.14 => ( ( modulo_modulo_nat @ M @ N )
% 5.82/6.14 = R2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_nat_eqI
% 5.82/6.14 thf(fact_6385_diff__mod__le,axiom,
% 5.82/6.14 ! [A2: nat,D2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ A2 @ D2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ B2 @ D2 )
% 5.82/6.14 => ( ord_less_eq_nat @ ( minus_minus_nat @ A2 @ ( modulo_modulo_nat @ A2 @ B2 ) ) @ ( minus_minus_nat @ D2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % diff_mod_le
% 5.82/6.14 thf(fact_6386_VEBT__internal_Ovebt__buildupi_H_Osimps_I2_J,axiom,
% 5.82/6.14 ( ( vEBT_V739175172307565963ildupi @ ( suc @ zero_zero_nat ) )
% 5.82/6.14 = ( heap_T3630416162098727440_VEBTi @ ( vEBT_Leafi @ $false @ $false ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.vebt_buildupi'.simps(2)
% 5.82/6.14 thf(fact_6387_vebt__buildupi_Osimps_I2_J,axiom,
% 5.82/6.14 ( ( vEBT_vebt_buildupi @ ( suc @ zero_zero_nat ) )
% 5.82/6.14 = ( heap_T3630416162098727440_VEBTi @ ( vEBT_Leafi @ $false @ $false ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_buildupi.simps(2)
% 5.82/6.14 thf(fact_6388_real__of__nat__div__aux,axiom,
% 5.82/6.14 ! [X2: nat,D2: nat] :
% 5.82/6.14 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ D2 ) )
% 5.82/6.14 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X2 @ D2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X2 @ D2 ) ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % real_of_nat_div_aux
% 5.82/6.14 thf(fact_6389_vebt__minti_Osimps_I2_J,axiom,
% 5.82/6.14 ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 5.82/6.14 ( ( vEBT_vebt_minti @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_minti.simps(2)
% 5.82/6.14 thf(fact_6390_vebt__maxti_Osimps_I2_J,axiom,
% 5.82/6.14 ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 5.82/6.14 ( ( vEBT_vebt_maxti @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_maxti.simps(2)
% 5.82/6.14 thf(fact_6391_int__div__sub__1,axiom,
% 5.82/6.14 ! [M: int,N: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ one_one_int @ M )
% 5.82/6.14 => ( ( ( dvd_dvd_int @ M @ N )
% 5.82/6.14 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 5.82/6.14 = ( minus_minus_int @ ( divide_divide_int @ N @ M ) @ one_one_int ) ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_int @ M @ N )
% 5.82/6.14 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 5.82/6.14 = ( divide_divide_int @ N @ M ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % int_div_sub_1
% 5.82/6.14 thf(fact_6392_bset_I9_J,axiom,
% 5.82/6.14 ! [D2: int,D: int,B: set_int,T: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ D )
% 5.82/6.14 => ! [X8: int] :
% 5.82/6.14 ( ! [Xa3: int] :
% 5.82/6.14 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.14 => ! [Xb3: int] :
% 5.82/6.14 ( ( member_int @ Xb3 @ B )
% 5.82/6.14 => ( X8
% 5.82/6.14 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.14 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 5.82/6.14 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ D ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bset(9)
% 5.82/6.14 thf(fact_6393_bset_I10_J,axiom,
% 5.82/6.14 ! [D2: int,D: int,B: set_int,T: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ D )
% 5.82/6.14 => ! [X8: int] :
% 5.82/6.14 ( ! [Xa3: int] :
% 5.82/6.14 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.14 => ! [Xb3: int] :
% 5.82/6.14 ( ( member_int @ Xb3 @ B )
% 5.82/6.14 => ( X8
% 5.82/6.14 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.14 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 5.82/6.14 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X8 @ D ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bset(10)
% 5.82/6.14 thf(fact_6394_aset_I9_J,axiom,
% 5.82/6.14 ! [D2: int,D: int,A: set_int,T: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ D )
% 5.82/6.14 => ! [X8: int] :
% 5.82/6.14 ( ! [Xa3: int] :
% 5.82/6.14 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.14 => ! [Xb3: int] :
% 5.82/6.14 ( ( member_int @ Xb3 @ A )
% 5.82/6.14 => ( X8
% 5.82/6.14 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.14 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 5.82/6.14 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X8 @ D ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % aset(9)
% 5.82/6.14 thf(fact_6395_aset_I10_J,axiom,
% 5.82/6.14 ! [D2: int,D: int,A: set_int,T: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ D2 @ D )
% 5.82/6.14 => ! [X8: int] :
% 5.82/6.14 ( ! [Xa3: int] :
% 5.82/6.14 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.82/6.14 => ! [Xb3: int] :
% 5.82/6.14 ( ( member_int @ Xb3 @ A )
% 5.82/6.14 => ( X8
% 5.82/6.14 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.82/6.14 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X8 @ T ) )
% 5.82/6.14 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X8 @ D ) @ T ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % aset(10)
% 5.82/6.14 thf(fact_6396_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.82/6.14 ! [C2: code_integer,A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ B2 @ C2 ) )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A2 @ B2 ) @ C2 ) ) @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.82/6.14 thf(fact_6397_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.82/6.14 ! [C2: nat,A2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ B2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ A2 @ B2 ) @ C2 ) ) @ ( modulo_modulo_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.82/6.14 thf(fact_6398_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.82/6.14 ! [C2: int,A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ B2 @ ( modulo_modulo_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.82/6.14 thf(fact_6399_cong__exp__iff__simps_I7_J,axiom,
% 5.82/6.14 ! [Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(7)
% 5.82/6.14 thf(fact_6400_cong__exp__iff__simps_I7_J,axiom,
% 5.82/6.14 ! [Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(7)
% 5.82/6.14 thf(fact_6401_cong__exp__iff__simps_I7_J,axiom,
% 5.82/6.14 ! [Q3: num,N: num] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(7)
% 5.82/6.14 thf(fact_6402_cong__exp__iff__simps_I11_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(11)
% 5.82/6.14 thf(fact_6403_cong__exp__iff__simps_I11_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(11)
% 5.82/6.14 thf(fact_6404_cong__exp__iff__simps_I11_J,axiom,
% 5.82/6.14 ! [M: num,Q3: num] :
% 5.82/6.14 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % cong_exp_iff_simps(11)
% 5.82/6.14 thf(fact_6405_even__iff__mod__2__eq__zero,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 = ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_iff_mod_2_eq_zero
% 5.82/6.14 thf(fact_6406_even__iff__mod__2__eq__zero,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 = ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_iff_mod_2_eq_zero
% 5.82/6.14 thf(fact_6407_even__iff__mod__2__eq__zero,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_iff_mod_2_eq_zero
% 5.82/6.14 thf(fact_6408_odd__iff__mod__2__eq__one,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.14 = ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_iff_mod_2_eq_one
% 5.82/6.14 thf(fact_6409_odd__iff__mod__2__eq__one,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.14 = ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_iff_mod_2_eq_one
% 5.82/6.14 thf(fact_6410_odd__iff__mod__2__eq__one,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.14 = ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_Code_integer ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_iff_mod_2_eq_one
% 5.82/6.14 thf(fact_6411_Suc__mod__eq__add3__mod,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.82/6.14 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_mod_eq_add3_mod
% 5.82/6.14 thf(fact_6412_Suc__times__mod__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.82/6.14 = one_one_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % Suc_times_mod_eq
% 5.82/6.14 thf(fact_6413_even__diff__iff,axiom,
% 5.82/6.14 ! [K: int,L: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.82/6.14 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_diff_iff
% 5.82/6.14 thf(fact_6414_VEBT__internal_OminNulli_Oelims,axiom,
% 5.82/6.14 ! [X2: vEBT_VEBTi,Y3: heap_Time_Heap_o] :
% 5.82/6.14 ( ( ( vEBT_VEBT_minNulli @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ( ( X2
% 5.82/6.14 = ( vEBT_Leafi @ $false @ $false ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_Time_return_o @ $true ) ) )
% 5.82/6.14 => ( ( ? [Uv2: $o] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Leafi @ $true @ Uv2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_Time_return_o @ $false ) ) )
% 5.82/6.14 => ( ( ? [Uu2: $o] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Leafi @ Uu2 @ $true ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_Time_return_o @ $false ) ) )
% 5.82/6.14 => ( ( ? [Uw2: nat,Ux2: array_VEBT_VEBTi,Uy2: vEBT_VEBTi] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_Time_return_o @ $true ) ) )
% 5.82/6.14 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: array_VEBT_VEBTi,Vc2: vEBT_VEBTi] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_Time_return_o @ $false ) ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % VEBT_internal.minNulli.elims
% 5.82/6.14 thf(fact_6415_vebt__minti_Osimps_I3_J,axiom,
% 5.82/6.14 ! [Mi: nat,Ma: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz: vEBT_VEBTi] :
% 5.82/6.14 ( ( vEBT_vebt_minti @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_minti.simps(3)
% 5.82/6.14 thf(fact_6416_vebt__maxti_Osimps_I3_J,axiom,
% 5.82/6.14 ! [Mi: nat,Ma: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz: vEBT_VEBTi] :
% 5.82/6.14 ( ( vEBT_vebt_maxti @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_maxti.simps(3)
% 5.82/6.14 thf(fact_6417_divmod__digit__0_I2_J,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.14 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_0(2)
% 5.82/6.14 thf(fact_6418_divmod__digit__0_I2_J,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_int @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_0(2)
% 5.82/6.14 thf(fact_6419_divmod__digit__0_I2_J,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.14 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_0(2)
% 5.82/6.14 thf(fact_6420_bits__stable__imp__add__self,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = A2 )
% 5.82/6.14 => ( ( plus_plus_nat @ A2 @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = zero_zero_nat ) ) ).
% 5.82/6.14
% 5.82/6.14 % bits_stable_imp_add_self
% 5.82/6.14 thf(fact_6421_bits__stable__imp__add__self,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = A2 )
% 5.82/6.14 => ( ( plus_plus_int @ A2 @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % bits_stable_imp_add_self
% 5.82/6.14 thf(fact_6422_bits__stable__imp__add__self,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = A2 )
% 5.82/6.14 => ( ( plus_p5714425477246183910nteger @ A2 @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) ) ).
% 5.82/6.14
% 5.82/6.14 % bits_stable_imp_add_self
% 5.82/6.14 thf(fact_6423_parity__cases,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 != zero_zero_nat ) )
% 5.82/6.14 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % parity_cases
% 5.82/6.14 thf(fact_6424_parity__cases,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 != zero_zero_int ) )
% 5.82/6.14 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_int ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % parity_cases
% 5.82/6.14 thf(fact_6425_parity__cases,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 != zero_z3403309356797280102nteger ) )
% 5.82/6.14 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_Code_integer ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % parity_cases
% 5.82/6.14 thf(fact_6426_mod2__eq__if,axiom,
% 5.82/6.14 ! [A2: nat] :
% 5.82/6.14 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_nat ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_nat ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod2_eq_if
% 5.82/6.14 thf(fact_6427_mod2__eq__if,axiom,
% 5.82/6.14 ! [A2: int] :
% 5.82/6.14 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_int ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_int ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod2_eq_if
% 5.82/6.14 thf(fact_6428_mod2__eq__if,axiom,
% 5.82/6.14 ! [A2: code_integer] :
% 5.82/6.14 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_z3403309356797280102nteger ) )
% 5.82/6.14 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_Code_integer ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod2_eq_if
% 5.82/6.14 thf(fact_6429_div__exp__mod__exp__eq,axiom,
% 5.82/6.14 ! [A2: nat,N: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( divide_divide_nat @ ( modulo_modulo_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_exp_mod_exp_eq
% 5.82/6.14 thf(fact_6430_div__exp__mod__exp__eq,axiom,
% 5.82/6.14 ! [A2: int,N: nat,M: nat] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( divide_divide_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( divide_divide_int @ ( modulo_modulo_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_exp_mod_exp_eq
% 5.82/6.14 thf(fact_6431_div__exp__mod__exp__eq,axiom,
% 5.82/6.14 ! [A2: code_integer,N: nat,M: nat] :
% 5.82/6.14 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_exp_mod_exp_eq
% 5.82/6.14 thf(fact_6432_power__mod__div,axiom,
% 5.82/6.14 ! [X2: nat,N: nat,M: nat] :
% 5.82/6.14 ( ( divide_divide_nat @ ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % power_mod_div
% 5.82/6.14 thf(fact_6433_verit__le__mono__div,axiom,
% 5.82/6.14 ! [A: nat,B: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_nat @ A @ B )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ord_less_eq_nat
% 5.82/6.14 @ ( plus_plus_nat @ ( divide_divide_nat @ A @ N )
% 5.82/6.14 @ ( if_nat
% 5.82/6.14 @ ( ( modulo_modulo_nat @ B @ N )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 @ one_one_nat
% 5.82/6.14 @ zero_zero_nat ) )
% 5.82/6.14 @ ( divide_divide_nat @ B @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % verit_le_mono_div
% 5.82/6.14 thf(fact_6434_vebt__maxti_Osimps_I1_J,axiom,
% 5.82/6.14 ! [B2: $o,A2: $o] :
% 5.82/6.14 ( ( B2
% 5.82/6.14 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A2 @ B2 ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 5.82/6.14 & ( ~ B2
% 5.82/6.14 => ( ( A2
% 5.82/6.14 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A2 @ B2 ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 5.82/6.14 & ( ~ A2
% 5.82/6.14 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A2 @ B2 ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_maxti.simps(1)
% 5.82/6.14 thf(fact_6435_vebt__minti_Osimps_I1_J,axiom,
% 5.82/6.14 ! [A2: $o,B2: $o] :
% 5.82/6.14 ( ( A2
% 5.82/6.14 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A2 @ B2 ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 5.82/6.14 & ( ~ A2
% 5.82/6.14 => ( ( B2
% 5.82/6.14 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A2 @ B2 ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 5.82/6.14 & ( ~ B2
% 5.82/6.14 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A2 @ B2 ) )
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_minti.simps(1)
% 5.82/6.14 thf(fact_6436_nat__dvd__iff,axiom,
% 5.82/6.14 ! [Z: int,M: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.82/6.14 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.14 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.82/6.14 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.14 => ( M = zero_zero_nat ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_dvd_iff
% 5.82/6.14 thf(fact_6437_divmod__digit__0_I1_J,axiom,
% 5.82/6.14 ! [B2: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.14 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 = ( divide_divide_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_0(1)
% 5.82/6.14 thf(fact_6438_divmod__digit__0_I1_J,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_int @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 = ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_0(1)
% 5.82/6.14 thf(fact_6439_divmod__digit__0_I1_J,axiom,
% 5.82/6.14 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.14 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 = ( divide6298287555418463151nteger @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_0(1)
% 5.82/6.14 thf(fact_6440_mult__exp__mod__exp__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( ( modulo_modulo_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.14 = ( times_times_nat @ ( modulo_modulo_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_exp_mod_exp_eq
% 5.82/6.14 thf(fact_6441_mult__exp__mod__exp__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: int] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( times_times_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.14 = ( times_times_int @ ( modulo_modulo_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_exp_mod_exp_eq
% 5.82/6.14 thf(fact_6442_mult__exp__mod__exp__eq,axiom,
% 5.82/6.14 ! [M: nat,N: nat,A2: code_integer] :
% 5.82/6.14 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.14 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mult_exp_mod_exp_eq
% 5.82/6.14 thf(fact_6443_list__decode_Ocases,axiom,
% 5.82/6.14 ! [X2: nat] :
% 5.82/6.14 ( ( X2 != zero_zero_nat )
% 5.82/6.14 => ~ ! [N3: nat] :
% 5.82/6.14 ( X2
% 5.82/6.14 != ( suc @ N3 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % list_decode.cases
% 5.82/6.14 thf(fact_6444_dvd__productE,axiom,
% 5.82/6.14 ! [P6: nat,A2: nat,B2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ P6 @ ( times_times_nat @ A2 @ B2 ) )
% 5.82/6.14 => ~ ! [X4: nat,Y4: nat] :
% 5.82/6.14 ( ( P6
% 5.82/6.14 = ( times_times_nat @ X4 @ Y4 ) )
% 5.82/6.14 => ( ( dvd_dvd_nat @ X4 @ A2 )
% 5.82/6.14 => ~ ( dvd_dvd_nat @ Y4 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_productE
% 5.82/6.14 thf(fact_6445_dvd__productE,axiom,
% 5.82/6.14 ! [P6: int,A2: int,B2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ P6 @ ( times_times_int @ A2 @ B2 ) )
% 5.82/6.14 => ~ ! [X4: int,Y4: int] :
% 5.82/6.14 ( ( P6
% 5.82/6.14 = ( times_times_int @ X4 @ Y4 ) )
% 5.82/6.14 => ( ( dvd_dvd_int @ X4 @ A2 )
% 5.82/6.14 => ~ ( dvd_dvd_int @ Y4 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_productE
% 5.82/6.14 thf(fact_6446_division__decomp,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat,C2: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B2 @ C2 ) )
% 5.82/6.14 => ? [B7: nat,C5: nat] :
% 5.82/6.14 ( ( A2
% 5.82/6.14 = ( times_times_nat @ B7 @ C5 ) )
% 5.82/6.14 & ( dvd_dvd_nat @ B7 @ B2 )
% 5.82/6.14 & ( dvd_dvd_nat @ C5 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % division_decomp
% 5.82/6.14 thf(fact_6447_division__decomp,axiom,
% 5.82/6.14 ! [A2: int,B2: int,C2: int] :
% 5.82/6.14 ( ( dvd_dvd_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.14 => ? [B7: int,C5: int] :
% 5.82/6.14 ( ( A2
% 5.82/6.14 = ( times_times_int @ B7 @ C5 ) )
% 5.82/6.14 & ( dvd_dvd_int @ B7 @ B2 )
% 5.82/6.14 & ( dvd_dvd_int @ C5 @ C2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % division_decomp
% 5.82/6.14 thf(fact_6448_Euclid__induct,axiom,
% 5.82/6.14 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 5.82/6.14 ( ! [A3: nat,B3: nat] :
% 5.82/6.14 ( ( P @ A3 @ B3 )
% 5.82/6.14 = ( P @ B3 @ A3 ) )
% 5.82/6.14 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.82/6.14 => ( ! [A3: nat,B3: nat] :
% 5.82/6.14 ( ( P @ A3 @ B3 )
% 5.82/6.14 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 5.82/6.14 => ( P @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % Euclid_induct
% 5.82/6.14 thf(fact_6449_eucl__rel__int__iff,axiom,
% 5.82/6.14 ! [K: int,L: int,Q3: int,R2: int] :
% 5.82/6.14 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.14 = ( ( K
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 5.82/6.14 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.82/6.14 & ( ord_less_int @ R2 @ L ) ) )
% 5.82/6.14 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.14 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.82/6.14 => ( ( ord_less_int @ L @ R2 )
% 5.82/6.14 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.82/6.14 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.82/6.14 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % eucl_rel_int_iff
% 5.82/6.14 thf(fact_6450_mod__double__modulus,axiom,
% 5.82/6.14 ! [M: code_integer,X2: code_integer] :
% 5.82/6.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.82/6.14 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.82/6.14 => ( ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( modulo364778990260209775nteger @ X2 @ M ) )
% 5.82/6.14 | ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_double_modulus
% 5.82/6.14 thf(fact_6451_mod__double__modulus,axiom,
% 5.82/6.14 ! [M: nat,X2: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.82/6.14 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( modulo_modulo_nat @ X2 @ M ) )
% 5.82/6.14 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_double_modulus
% 5.82/6.14 thf(fact_6452_mod__double__modulus,axiom,
% 5.82/6.14 ! [M: int,X2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ M )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( modulo_modulo_int @ X2 @ M ) )
% 5.82/6.14 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.82/6.14 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_double_modulus
% 5.82/6.14 thf(fact_6453_divmod__digit__1_I2_J,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.14 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.14 => ( ( ord_le3102999989581377725nteger @ B2 @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 = ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_1(2)
% 5.82/6.14 thf(fact_6454_divmod__digit__1_I2_J,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ B2 @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_nat @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_1(2)
% 5.82/6.14 thf(fact_6455_divmod__digit__1_I2_J,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.14 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_int @ B2 @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 => ( ( minus_minus_int @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_1(2)
% 5.82/6.14 thf(fact_6456_unset__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: nat] :
% 5.82/6.14 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unset_bit_Suc
% 5.82/6.14 thf(fact_6457_unset__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: code_integer] :
% 5.82/6.14 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unset_bit_Suc
% 5.82/6.14 thf(fact_6458_unset__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: int] :
% 5.82/6.14 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_plus_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % unset_bit_Suc
% 5.82/6.14 thf(fact_6459_set__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: code_integer] :
% 5.82/6.14 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % set_bit_Suc
% 5.82/6.14 thf(fact_6460_set__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: int] :
% 5.82/6.14 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_plus_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % set_bit_Suc
% 5.82/6.14 thf(fact_6461_set__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: nat] :
% 5.82/6.14 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % set_bit_Suc
% 5.82/6.14 thf(fact_6462_even__mod__4__div__2,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( suc @ zero_zero_nat ) )
% 5.82/6.14 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_mod_4_div_2
% 5.82/6.14 thf(fact_6463_even__nat__iff,axiom,
% 5.82/6.14 ! [K: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.14 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.82/6.14 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % even_nat_iff
% 5.82/6.14 thf(fact_6464_odd__mod__4__div__2,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.14 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % odd_mod_4_div_2
% 5.82/6.14 thf(fact_6465_divmod__digit__1_I1_J,axiom,
% 5.82/6.14 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.82/6.14 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.82/6.14 => ( ( ord_le3102999989581377725nteger @ B2 @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_Code_integer )
% 5.82/6.14 = ( divide6298287555418463151nteger @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_1(1)
% 5.82/6.14 thf(fact_6466_divmod__digit__1_I1_J,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.82/6.14 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_nat @ B2 @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_nat )
% 5.82/6.14 = ( divide_divide_nat @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_1(1)
% 5.82/6.14 thf(fact_6467_divmod__digit__1_I1_J,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.14 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_int @ B2 @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.82/6.14 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_int )
% 5.82/6.14 = ( divide_divide_int @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % divmod_digit_1(1)
% 5.82/6.14 thf(fact_6468_vebt__minti_Oelims,axiom,
% 5.82/6.14 ! [X2: vEBT_VEBTi,Y3: heap_T2636463487746394924on_nat] :
% 5.82/6.14 ( ( ( vEBT_vebt_minti @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ! [A3: $o,B3: $o] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.14 => ~ ( ( A3
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 5.82/6.14 & ( ~ A3
% 5.82/6.14 => ( ( B3
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 5.82/6.14 & ( ~ B3
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) )
% 5.82/6.14 => ( ( ? [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_T3487192422709364219on_nat @ none_nat ) ) )
% 5.82/6.14 => ~ ! [Mi2: nat] :
% 5.82/6.14 ( ? [Ma2: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi2 ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_minti.elims
% 5.82/6.14 thf(fact_6469_vebt__maxti_Oelims,axiom,
% 5.82/6.14 ! [X2: vEBT_VEBTi,Y3: heap_T2636463487746394924on_nat] :
% 5.82/6.14 ( ( ( vEBT_vebt_maxti @ X2 )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ! [A3: $o,B3: $o] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.14 => ~ ( ( B3
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 5.82/6.14 & ( ~ B3
% 5.82/6.14 => ( ( A3
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 5.82/6.14 & ( ~ A3
% 5.82/6.14 => ( Y3
% 5.82/6.14 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) )
% 5.82/6.14 => ( ( ? [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_T3487192422709364219on_nat @ none_nat ) ) )
% 5.82/6.14 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.82/6.14 ( ? [Ux2: nat,Uy2: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma2 ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_maxti.elims
% 5.82/6.14 thf(fact_6470_dvd__pos__nat,axiom,
% 5.82/6.14 ! [N: nat,M: nat] :
% 5.82/6.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.14 => ( ( dvd_dvd_nat @ M @ N )
% 5.82/6.14 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % dvd_pos_nat
% 5.82/6.14 thf(fact_6471_bezout__add__nat,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ? [D4: nat,X4: nat,Y4: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ D4 @ A2 )
% 5.82/6.14 & ( dvd_dvd_nat @ D4 @ B2 )
% 5.82/6.14 & ( ( ( times_times_nat @ A2 @ X4 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y4 ) @ D4 ) )
% 5.82/6.14 | ( ( times_times_nat @ B2 @ X4 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ A2 @ Y4 ) @ D4 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bezout_add_nat
% 5.82/6.14 thf(fact_6472_bezout__lemma__nat,axiom,
% 5.82/6.14 ! [D2: nat,A2: nat,B2: nat,X2: nat,Y3: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ D2 @ A2 )
% 5.82/6.14 => ( ( dvd_dvd_nat @ D2 @ B2 )
% 5.82/6.14 => ( ( ( ( times_times_nat @ A2 @ X2 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y3 ) @ D2 ) )
% 5.82/6.14 | ( ( times_times_nat @ B2 @ X2 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ A2 @ Y3 ) @ D2 ) ) )
% 5.82/6.14 => ? [X4: nat,Y4: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ D2 @ A2 )
% 5.82/6.14 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 5.82/6.14 & ( ( ( times_times_nat @ A2 @ X4 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ Y4 ) @ D2 ) )
% 5.82/6.14 | ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ X4 )
% 5.82/6.14 = ( plus_plus_nat @ ( times_times_nat @ A2 @ Y4 ) @ D2 ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bezout_lemma_nat
% 5.82/6.14 thf(fact_6473_bezout1__nat,axiom,
% 5.82/6.14 ! [A2: nat,B2: nat] :
% 5.82/6.14 ? [D4: nat,X4: nat,Y4: nat] :
% 5.82/6.14 ( ( dvd_dvd_nat @ D4 @ A2 )
% 5.82/6.14 & ( dvd_dvd_nat @ D4 @ B2 )
% 5.82/6.14 & ( ( ( minus_minus_nat @ ( times_times_nat @ A2 @ X4 ) @ ( times_times_nat @ B2 @ Y4 ) )
% 5.82/6.14 = D4 )
% 5.82/6.14 | ( ( minus_minus_nat @ ( times_times_nat @ B2 @ X4 ) @ ( times_times_nat @ A2 @ Y4 ) )
% 5.82/6.14 = D4 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % bezout1_nat
% 5.82/6.14 thf(fact_6474_pos__eucl__rel__int__mult__2,axiom,
% 5.82/6.14 ! [B2: int,A2: int,Q3: int,R2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.14 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ ( product_Pair_int_int @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pos_eucl_rel_int_mult_2
% 5.82/6.14 thf(fact_6475_div__half__nat,axiom,
% 5.82/6.14 ! [Y3: nat,X2: nat] :
% 5.82/6.14 ( ( Y3 != zero_zero_nat )
% 5.82/6.14 => ( ( product_Pair_nat_nat @ ( divide_divide_nat @ X2 @ Y3 ) @ ( modulo_modulo_nat @ X2 @ Y3 ) )
% 5.82/6.14 = ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ Y3 @ ( minus_minus_nat @ X2 @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) @ Y3 ) ) ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( minus_minus_nat @ X2 @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) @ Y3 ) ) @ Y3 ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) @ ( minus_minus_nat @ X2 @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) @ Y3 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_half_nat
% 5.82/6.14 thf(fact_6476_mod__exhaust__less__4,axiom,
% 5.82/6.14 ! [M: nat] :
% 5.82/6.14 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = zero_zero_nat )
% 5.82/6.14 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = one_one_nat )
% 5.82/6.14 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.14 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.14 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_exhaust_less_4
% 5.82/6.14 thf(fact_6477_flip__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: code_integer] :
% 5.82/6.14 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % flip_bit_Suc
% 5.82/6.14 thf(fact_6478_flip__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: int] :
% 5.82/6.14 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_plus_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % flip_bit_Suc
% 5.82/6.14 thf(fact_6479_flip__bit__Suc,axiom,
% 5.82/6.14 ! [N: nat,A2: nat] :
% 5.82/6.14 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A2 )
% 5.82/6.14 = ( plus_plus_nat @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % flip_bit_Suc
% 5.82/6.14 thf(fact_6480_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_Code_integer,Ys: list_Code_integer] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_s3445333598471063425nteger @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr2304437835452373666nteger @ ( produc8792966785426426881nteger @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) @ ( nth_Code_integer @ Ys @ ( modulo_modulo_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6481_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_num,Ys: list_num] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6482_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_int,Ys: list_int] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( product_Pair_int_int @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6483_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6484_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_real] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_real @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr6842391030413306568T_real @ ( produc4908677263432625371T_real @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc8117437818029410057T_real @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_real @ Ys ) ) ) @ ( nth_real @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_real @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6485_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6486_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6487_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s7982070591426661849_VEBTi @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr316670251186196177_VEBTi @ ( produc316462671093861988_VEBTi @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc6084888613844515218_VEBTi @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s7982070591426661849_VEBTi @ Ys ) ) ) @ ( nth_VEBT_VEBTi @ Ys @ ( modulo_modulo_nat @ N @ ( size_s7982070591426661849_VEBTi @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6488_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_real,Ys: list_VEBT_VEBT] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr5429231388385915574T_VEBT @ ( produc3722688996059531265T_VEBT @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc6931449550656315951T_VEBT @ ( nth_real @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6489_product__nth,axiom,
% 5.82/6.14 ! [N: nat,Xs: list_real,Ys: list_real] :
% 5.82/6.14 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_size_list_real @ Ys ) ) )
% 5.82/6.14 => ( ( nth_Pr7489471911767062336l_real @ ( product_real_real @ Xs @ Ys ) @ N )
% 5.82/6.14 = ( produc4511245868158468465l_real @ ( nth_real @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_real @ Ys ) ) ) @ ( nth_real @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_real @ Ys ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % product_nth
% 5.82/6.14 thf(fact_6490_vebt__assn__raw_Oelims,axiom,
% 5.82/6.14 ! [X2: vEBT_VEBT,Xa: vEBT_VEBTi,Y3: assn] :
% 5.82/6.14 ( ( ( vEBT_vebt_assn_raw @ X2 @ Xa )
% 5.82/6.14 = Y3 )
% 5.82/6.14 => ( ! [A3: $o,B3: $o] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.14 => ! [Ai2: $o,Bi2: $o] :
% 5.82/6.14 ( ( Xa
% 5.82/6.14 = ( vEBT_Leafi @ Ai2 @ Bi2 ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( pure_assn
% 5.82/6.14 @ ( ( Ai2 = A3 )
% 5.82/6.14 & ( Bi2 = B3 ) ) ) ) ) )
% 5.82/6.14 => ( ! [Mmo: option4927543243414619207at_nat,Deg2: nat,Tree_list: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.14 ( ( X2
% 5.82/6.14 = ( vEBT_Node @ Mmo @ Deg2 @ Tree_list @ Summary2 ) )
% 5.82/6.14 => ! [Mmoi: option4927543243414619207at_nat,Degi: nat,Tree_array: array_VEBT_VEBTi,Summaryi: vEBT_VEBTi] :
% 5.82/6.14 ( ( Xa
% 5.82/6.14 = ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) )
% 5.82/6.14 => ( Y3
% 5.82/6.14 != ( times_times_assn
% 5.82/6.14 @ ( times_times_assn
% 5.82/6.14 @ ( pure_assn
% 5.82/6.14 @ ( ( Mmoi = Mmo )
% 5.82/6.14 & ( Degi = Deg2 ) ) )
% 5.82/6.14 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi ) )
% 5.82/6.14 @ ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [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 ) ) ) ) ) ) )
% 5.82/6.14 => ( ( ? [V2: option4927543243414619207at_nat,Va3: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Node @ V2 @ Va3 @ Vb3 @ Vc3 ) )
% 5.82/6.14 => ( ? [Vd: $o,Ve: $o] :
% 5.82/6.14 ( Xa
% 5.82/6.14 = ( vEBT_Leafi @ Vd @ Ve ) )
% 5.82/6.14 => ( Y3 != bot_bot_assn ) ) )
% 5.82/6.14 => ~ ( ? [Vd: $o,Ve: $o] :
% 5.82/6.14 ( X2
% 5.82/6.14 = ( vEBT_Leaf @ Vd @ Ve ) )
% 5.82/6.14 => ( ? [V2: option4927543243414619207at_nat,Va3: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 5.82/6.14 ( Xa
% 5.82/6.14 = ( vEBT_Nodei @ V2 @ Va3 @ Vb3 @ Vc3 ) )
% 5.82/6.14 => ( Y3 != bot_bot_assn ) ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % vebt_assn_raw.elims
% 5.82/6.14 thf(fact_6491_ex__assn__const,axiom,
% 5.82/6.14 ! [C2: assn] :
% 5.82/6.14 ( ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : C2 )
% 5.82/6.14 = C2 ) ).
% 5.82/6.14
% 5.82/6.14 % ex_assn_const
% 5.82/6.14 thf(fact_6492_flip__bit__nonnegative__int__iff,axiom,
% 5.82/6.14 ! [N: nat,K: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.82/6.14 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.14
% 5.82/6.14 % flip_bit_nonnegative_int_iff
% 5.82/6.14 thf(fact_6493_norm__assertion__simps_I17_J,axiom,
% 5.82/6.14 ! [R: assn,Q: list_VEBT_VEBTi > assn] :
% 5.82/6.14 ( ( times_times_assn @ R @ ( ex_ass463751140784270563_VEBTi @ Q ) )
% 5.82/6.14 = ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( times_times_assn @ R @ ( Q @ X3 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_assertion_simps(17)
% 5.82/6.14 thf(fact_6494_norm__assertion__simps_I16_J,axiom,
% 5.82/6.14 ! [Q: list_VEBT_VEBTi > assn,R: assn] :
% 5.82/6.14 ( ( times_times_assn @ ( ex_ass463751140784270563_VEBTi @ Q ) @ R )
% 5.82/6.14 = ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( times_times_assn @ ( Q @ X3 ) @ R ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_assertion_simps(16)
% 5.82/6.14 thf(fact_6495_triv__exI,axiom,
% 5.82/6.14 ! [Q: list_VEBT_VEBTi > assn,X2: list_VEBT_VEBTi] : ( entails @ ( Q @ X2 ) @ ( ex_ass463751140784270563_VEBTi @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % triv_exI
% 5.82/6.14 thf(fact_6496_mod__ex__dist,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.14 ( ( rep_assn @ ( ex_ass463751140784270563_VEBTi @ P ) @ H2 )
% 5.82/6.14 = ( ? [X3: list_VEBT_VEBTi] : ( rep_assn @ ( P @ X3 ) @ H2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_ex_dist
% 5.82/6.14 thf(fact_6497_mod__neg__neg__trivial,axiom,
% 5.82/6.14 ! [K: int,L: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.82/6.14 => ( ( ord_less_int @ L @ K )
% 5.82/6.14 => ( ( modulo_modulo_int @ K @ L )
% 5.82/6.14 = K ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_neg_neg_trivial
% 5.82/6.14 thf(fact_6498_mod__pos__pos__trivial,axiom,
% 5.82/6.14 ! [K: int,L: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.14 => ( ( ord_less_int @ K @ L )
% 5.82/6.14 => ( ( modulo_modulo_int @ K @ L )
% 5.82/6.14 = K ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_pos_pos_trivial
% 5.82/6.14 thf(fact_6499_length__product,axiom,
% 5.82/6.14 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.82/6.14 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6500_length__product,axiom,
% 5.82/6.14 ! [Xs: list_VEBT_VEBT,Ys: list_real] :
% 5.82/6.14 ( ( size_s5035110155006384947T_real @ ( produc4908677263432625371T_real @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_real @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6501_length__product,axiom,
% 5.82/6.14 ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.82/6.14 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6502_length__product,axiom,
% 5.82/6.14 ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.82/6.14 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6503_length__product,axiom,
% 5.82/6.14 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( size_s3387956428969716412_VEBTi @ ( produc316462671093861988_VEBTi @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s7982070591426661849_VEBTi @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6504_length__product,axiom,
% 5.82/6.14 ! [Xs: list_real,Ys: list_VEBT_VEBT] :
% 5.82/6.14 ( ( size_s3289364478449617953T_VEBT @ ( produc3722688996059531265T_VEBT @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6505_length__product,axiom,
% 5.82/6.14 ! [Xs: list_real,Ys: list_real] :
% 5.82/6.14 ( ( size_s3932428310213730859l_real @ ( product_real_real @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_size_list_real @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6506_length__product,axiom,
% 5.82/6.14 ! [Xs: list_real,Ys: list_o] :
% 5.82/6.14 ( ( size_s987546567493390085real_o @ ( product_real_o @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6507_length__product,axiom,
% 5.82/6.14 ! [Xs: list_real,Ys: list_nat] :
% 5.82/6.14 ( ( size_s1877336372972134351al_nat @ ( product_real_nat @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6508_length__product,axiom,
% 5.82/6.14 ! [Xs: list_real,Ys: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( size_s6963394564282275252_VEBTi @ ( produc5599769701989005224_VEBTi @ Xs @ Ys ) )
% 5.82/6.14 = ( times_times_nat @ ( size_size_list_real @ Xs ) @ ( size_s7982070591426661849_VEBTi @ Ys ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % length_product
% 5.82/6.14 thf(fact_6509_zmod__numeral__Bit0,axiom,
% 5.82/6.14 ! [V: num,W: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.82/6.14 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmod_numeral_Bit0
% 5.82/6.14 thf(fact_6510_mod__h__bot__iff_I8_J,axiom,
% 5.82/6.14 ! [R: list_VEBT_VEBTi > assn,H2: heap_e7401611519738050253t_unit] :
% 5.82/6.14 ( ( rep_assn @ ( ex_ass463751140784270563_VEBTi @ R ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 5.82/6.14 = ( ? [X3: list_VEBT_VEBTi] : ( rep_assn @ ( R @ X3 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_h_bot_iff(8)
% 5.82/6.14 thf(fact_6511_one__mod__exp__eq__one,axiom,
% 5.82/6.14 ! [N: nat] :
% 5.82/6.14 ( ( modulo_modulo_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.14 = one_one_int ) ).
% 5.82/6.14
% 5.82/6.14 % one_mod_exp_eq_one
% 5.82/6.14 thf(fact_6512_zmod__numeral__Bit1,axiom,
% 5.82/6.14 ! [V: num,W: num] :
% 5.82/6.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmod_numeral_Bit1
% 5.82/6.14 thf(fact_6513_mod__plus__cong,axiom,
% 5.82/6.14 ! [B2: int,B4: int,X2: int,X5: int,Y3: int,Y7: int,Z6: int] :
% 5.82/6.14 ( ( B2 = B4 )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ X2 @ B4 )
% 5.82/6.14 = ( modulo_modulo_int @ X5 @ B4 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ Y3 @ B4 )
% 5.82/6.14 = ( modulo_modulo_int @ Y7 @ B4 ) )
% 5.82/6.14 => ( ( ( plus_plus_int @ X5 @ Y7 )
% 5.82/6.14 = Z6 )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( plus_plus_int @ X2 @ Y3 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ Z6 @ B4 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_plus_cong
% 5.82/6.14 thf(fact_6514_zmod__helper,axiom,
% 5.82/6.14 ! [N: int,M: int,K: int,A2: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ N @ M )
% 5.82/6.14 = K )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( plus_plus_int @ N @ A2 ) @ M )
% 5.82/6.14 = ( modulo_modulo_int @ ( plus_plus_int @ K @ A2 ) @ M ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmod_helper
% 5.82/6.14 thf(fact_6515_Word_Omod__minus__cong,axiom,
% 5.82/6.14 ! [B2: int,B4: int,X2: int,X5: int,Y3: int,Y7: int,Z6: int] :
% 5.82/6.14 ( ( B2 = B4 )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ X2 @ B4 )
% 5.82/6.14 = ( modulo_modulo_int @ X5 @ B4 ) )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ Y3 @ B4 )
% 5.82/6.14 = ( modulo_modulo_int @ Y7 @ B4 ) )
% 5.82/6.14 => ( ( ( minus_minus_int @ X5 @ Y7 )
% 5.82/6.14 = Z6 )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( minus_minus_int @ X2 @ Y3 ) @ B2 )
% 5.82/6.14 = ( modulo_modulo_int @ Z6 @ B4 ) ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % Word.mod_minus_cong
% 5.82/6.14 thf(fact_6516_ex__distrib__star,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,Q: assn] :
% 5.82/6.14 ( ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( times_times_assn @ ( P @ X3 ) @ Q ) )
% 5.82/6.14 = ( times_times_assn @ ( ex_ass463751140784270563_VEBTi @ P ) @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % ex_distrib_star
% 5.82/6.14 thf(fact_6517_enorm__exI_H,axiom,
% 5.82/6.14 ! [Z7: list_VEBT_VEBTi > $o,P: assn,Q: list_VEBT_VEBTi > assn] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( Z7 @ X4 )
% 5.82/6.14 => ( entails @ P @ ( Q @ X4 ) ) )
% 5.82/6.14 => ( ? [X_12: list_VEBT_VEBTi] : ( Z7 @ X_12 )
% 5.82/6.14 => ( entails @ P @ ( ex_ass463751140784270563_VEBTi @ Q ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % enorm_exI'
% 5.82/6.14 thf(fact_6518_ent__ex__preI,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,Q: assn] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( entails @ ( P @ X4 ) @ Q )
% 5.82/6.14 => ( entails @ ( ex_ass463751140784270563_VEBTi @ P ) @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % ent_ex_preI
% 5.82/6.14 thf(fact_6519_ent__ex__postI,axiom,
% 5.82/6.14 ! [P: assn,Q: list_VEBT_VEBTi > assn,X2: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( entails @ P @ ( Q @ X2 ) )
% 5.82/6.14 => ( entails @ P @ ( ex_ass463751140784270563_VEBTi @ Q ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % ent_ex_postI
% 5.82/6.14 thf(fact_6520_norm__pre__ex__rule,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( hoare_1429296392585015714_VEBTi @ ( P @ X4 ) @ F @ Q )
% 5.82/6.14 => ( hoare_1429296392585015714_VEBTi @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule
% 5.82/6.14 thf(fact_6521_norm__pre__ex__rule,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_Time_Heap_o,Q: $o > assn] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( hoare_hoare_triple_o @ ( P @ X4 ) @ F @ Q )
% 5.82/6.14 => ( hoare_hoare_triple_o @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule
% 5.82/6.14 thf(fact_6522_norm__pre__ex__rule,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_T2636463487746394924on_nat,Q: option_nat > assn] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( hoare_7629718768684598413on_nat @ ( P @ X4 ) @ F @ Q )
% 5.82/6.14 => ( hoare_7629718768684598413on_nat @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule
% 5.82/6.14 thf(fact_6523_norm__pre__ex__rule,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_Time_Heap_nat,Q: nat > assn] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( hoare_3067605981109127869le_nat @ ( P @ X4 ) @ F @ Q )
% 5.82/6.14 => ( hoare_3067605981109127869le_nat @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule
% 5.82/6.14 thf(fact_6524_post__exI__rule,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > list_VEBT_VEBTi > assn,X2: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.14 @ ^ [R5: vEBT_VEBTi] : ( Q @ R5 @ X2 ) )
% 5.82/6.14 => ( hoare_1429296392585015714_VEBTi @ P @ C2
% 5.82/6.14 @ ^ [R5: vEBT_VEBTi] : ( ex_ass463751140784270563_VEBTi @ ( Q @ R5 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % post_exI_rule
% 5.82/6.14 thf(fact_6525_post__exI__rule,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_Time_Heap_o,Q: $o > list_VEBT_VEBTi > assn,X2: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( hoare_hoare_triple_o @ P @ C2
% 5.82/6.14 @ ^ [R5: $o] : ( Q @ R5 @ X2 ) )
% 5.82/6.14 => ( hoare_hoare_triple_o @ P @ C2
% 5.82/6.14 @ ^ [R5: $o] : ( ex_ass463751140784270563_VEBTi @ ( Q @ R5 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % post_exI_rule
% 5.82/6.14 thf(fact_6526_post__exI__rule,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_T2636463487746394924on_nat,Q: option_nat > list_VEBT_VEBTi > assn,X2: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( hoare_7629718768684598413on_nat @ P @ C2
% 5.82/6.14 @ ^ [R5: option_nat] : ( Q @ R5 @ X2 ) )
% 5.82/6.14 => ( hoare_7629718768684598413on_nat @ P @ C2
% 5.82/6.14 @ ^ [R5: option_nat] : ( ex_ass463751140784270563_VEBTi @ ( Q @ R5 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % post_exI_rule
% 5.82/6.14 thf(fact_6527_post__exI__rule,axiom,
% 5.82/6.14 ! [P: assn,C2: heap_Time_Heap_nat,Q: nat > list_VEBT_VEBTi > assn,X2: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( hoare_3067605981109127869le_nat @ P @ C2
% 5.82/6.14 @ ^ [R5: nat] : ( Q @ R5 @ X2 ) )
% 5.82/6.14 => ( hoare_3067605981109127869le_nat @ P @ C2
% 5.82/6.14 @ ^ [R5: nat] : ( ex_ass463751140784270563_VEBTi @ ( Q @ R5 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % post_exI_rule
% 5.82/6.14 thf(fact_6528_mod__exE,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.14 ( ( rep_assn @ ( ex_ass463751140784270563_VEBTi @ P ) @ H2 )
% 5.82/6.14 => ~ ! [X4: list_VEBT_VEBTi] :
% 5.82/6.14 ~ ( rep_assn @ ( P @ X4 ) @ H2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_exE
% 5.82/6.14 thf(fact_6529_mod__exI,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.14 ( ? [X8: list_VEBT_VEBTi] : ( rep_assn @ ( P @ X8 ) @ H2 )
% 5.82/6.14 => ( rep_assn @ ( ex_ass463751140784270563_VEBTi @ P ) @ H2 ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_exI
% 5.82/6.14 thf(fact_6530_ex__one__point__gen,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,V: list_VEBT_VEBTi] :
% 5.82/6.14 ( ! [H3: produc3658429121746597890et_nat,X4: list_VEBT_VEBTi] :
% 5.82/6.14 ( ( rep_assn @ ( P @ X4 ) @ H3 )
% 5.82/6.14 => ( X4 = V ) )
% 5.82/6.14 => ( ( ex_ass463751140784270563_VEBTi @ P )
% 5.82/6.14 = ( P @ V ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % ex_one_point_gen
% 5.82/6.14 thf(fact_6531_norm__post__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: assn,F: heap_T8145700208782473153_VEBTi,Q: list_VEBT_VEBTi > vEBT_VEBTi > assn,X2: list_VEBT_VEBTi,T: nat] :
% 5.82/6.14 ( ( time_htt_VEBT_VEBTi @ P @ F @ ( Q @ X2 ) @ T )
% 5.82/6.14 => ( time_htt_VEBT_VEBTi @ P @ F
% 5.82/6.14 @ ^ [R5: vEBT_VEBTi] :
% 5.82/6.14 ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( Q @ X3 @ R5 ) )
% 5.82/6.14 @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_post_ex_rule_htt
% 5.82/6.14 thf(fact_6532_norm__post__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: assn,F: heap_Time_Heap_o,Q: list_VEBT_VEBTi > $o > assn,X2: list_VEBT_VEBTi,T: nat] :
% 5.82/6.14 ( ( time_htt_o @ P @ F @ ( Q @ X2 ) @ T )
% 5.82/6.14 => ( time_htt_o @ P @ F
% 5.82/6.14 @ ^ [R5: $o] :
% 5.82/6.14 ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( Q @ X3 @ R5 ) )
% 5.82/6.14 @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_post_ex_rule_htt
% 5.82/6.14 thf(fact_6533_norm__post__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: assn,F: heap_T2636463487746394924on_nat,Q: list_VEBT_VEBTi > option_nat > assn,X2: list_VEBT_VEBTi,T: nat] :
% 5.82/6.14 ( ( time_htt_option_nat @ P @ F @ ( Q @ X2 ) @ T )
% 5.82/6.14 => ( time_htt_option_nat @ P @ F
% 5.82/6.14 @ ^ [R5: option_nat] :
% 5.82/6.14 ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( Q @ X3 @ R5 ) )
% 5.82/6.14 @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_post_ex_rule_htt
% 5.82/6.14 thf(fact_6534_norm__post__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: assn,F: heap_Time_Heap_nat,Q: list_VEBT_VEBTi > nat > assn,X2: list_VEBT_VEBTi,T: nat] :
% 5.82/6.14 ( ( time_htt_nat @ P @ F @ ( Q @ X2 ) @ T )
% 5.82/6.14 => ( time_htt_nat @ P @ F
% 5.82/6.14 @ ^ [R5: nat] :
% 5.82/6.14 ( ex_ass463751140784270563_VEBTi
% 5.82/6.14 @ ^ [X3: list_VEBT_VEBTi] : ( Q @ X3 @ R5 ) )
% 5.82/6.14 @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_post_ex_rule_htt
% 5.82/6.14 thf(fact_6535_norm__pre__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_T8145700208782473153_VEBTi,Q: vEBT_VEBTi > assn,T: nat] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( time_htt_VEBT_VEBTi @ ( P @ X4 ) @ F @ Q @ T )
% 5.82/6.14 => ( time_htt_VEBT_VEBTi @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule_htt
% 5.82/6.14 thf(fact_6536_norm__pre__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_Time_Heap_o,Q: $o > assn,T: nat] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( time_htt_o @ ( P @ X4 ) @ F @ Q @ T )
% 5.82/6.14 => ( time_htt_o @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule_htt
% 5.82/6.14 thf(fact_6537_norm__pre__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_T2636463487746394924on_nat,Q: option_nat > assn,T: nat] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( time_htt_option_nat @ ( P @ X4 ) @ F @ Q @ T )
% 5.82/6.14 => ( time_htt_option_nat @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule_htt
% 5.82/6.14 thf(fact_6538_norm__pre__ex__rule__htt,axiom,
% 5.82/6.14 ! [P: list_VEBT_VEBTi > assn,F: heap_Time_Heap_nat,Q: nat > assn,T: nat] :
% 5.82/6.14 ( ! [X4: list_VEBT_VEBTi] : ( time_htt_nat @ ( P @ X4 ) @ F @ Q @ T )
% 5.82/6.14 => ( time_htt_nat @ ( ex_ass463751140784270563_VEBTi @ P ) @ F @ Q @ T ) ) ).
% 5.82/6.14
% 5.82/6.14 % norm_pre_ex_rule_htt
% 5.82/6.14 thf(fact_6539_zmod__le__nonneg__dividend,axiom,
% 5.82/6.14 ! [M: int,K: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.82/6.14 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmod_le_nonneg_dividend
% 5.82/6.14 thf(fact_6540_Euclidean__Division_Opos__mod__bound,axiom,
% 5.82/6.14 ! [L: int,K: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.14 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.82/6.14
% 5.82/6.14 % Euclidean_Division.pos_mod_bound
% 5.82/6.14 thf(fact_6541_neg__mod__bound,axiom,
% 5.82/6.14 ! [L: int,K: int] :
% 5.82/6.14 ( ( ord_less_int @ L @ zero_zero_int )
% 5.82/6.14 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % neg_mod_bound
% 5.82/6.14 thf(fact_6542_int__mod__ge,axiom,
% 5.82/6.14 ! [A2: int,N: int] :
% 5.82/6.14 ( ( ord_less_int @ A2 @ N )
% 5.82/6.14 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.82/6.14 => ( ord_less_eq_int @ A2 @ ( modulo_modulo_int @ A2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % int_mod_ge
% 5.82/6.14 thf(fact_6543_neg__mod__conj,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.14 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A2 @ B2 ) @ zero_zero_int )
% 5.82/6.14 & ( ord_less_int @ B2 @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % neg_mod_conj
% 5.82/6.14 thf(fact_6544_pos__mod__conj,axiom,
% 5.82/6.14 ! [B2: int,A2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 & ( ord_less_int @ ( modulo_modulo_int @ A2 @ B2 ) @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pos_mod_conj
% 5.82/6.14 thf(fact_6545_zmod__trivial__iff,axiom,
% 5.82/6.14 ! [I: int,K: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ I @ K )
% 5.82/6.14 = I )
% 5.82/6.14 = ( ( K = zero_zero_int )
% 5.82/6.14 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.82/6.14 & ( ord_less_int @ I @ K ) )
% 5.82/6.14 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.82/6.14 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % zmod_trivial_iff
% 5.82/6.14 thf(fact_6546_neg__mod__sign,axiom,
% 5.82/6.14 ! [L: int,K: int] :
% 5.82/6.14 ( ( ord_less_int @ L @ zero_zero_int )
% 5.82/6.14 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % neg_mod_sign
% 5.82/6.14 thf(fact_6547_Euclidean__Division_Opos__mod__sign,axiom,
% 5.82/6.14 ! [L: int,K: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.14 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % Euclidean_Division.pos_mod_sign
% 5.82/6.14 thf(fact_6548_int__mod__lem,axiom,
% 5.82/6.14 ! [N: int,B2: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ N )
% 5.82/6.14 => ( ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.14 & ( ord_less_int @ B2 @ N ) )
% 5.82/6.14 = ( ( modulo_modulo_int @ B2 @ N )
% 5.82/6.14 = B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % int_mod_lem
% 5.82/6.14 thf(fact_6549_int__mod__eq,axiom,
% 5.82/6.14 ! [B2: int,N: int,A2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_int @ B2 @ N )
% 5.82/6.14 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.82/6.14 = ( modulo_modulo_int @ B2 @ N ) )
% 5.82/6.14 => ( ( modulo_modulo_int @ A2 @ N )
% 5.82/6.14 = B2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % int_mod_eq
% 5.82/6.14 thf(fact_6550_int__mod__le_H,axiom,
% 5.82/6.14 ! [B2: int,N: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ B2 @ N ) )
% 5.82/6.14 => ( ord_less_eq_int @ ( modulo_modulo_int @ B2 @ N ) @ ( minus_minus_int @ B2 @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % int_mod_le'
% 5.82/6.14 thf(fact_6551_nonneg__mod__div,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A2 @ B2 ) )
% 5.82/6.14 & ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nonneg_mod_div
% 5.82/6.14 thf(fact_6552_div__mod__decomp__int,axiom,
% 5.82/6.14 ! [A: int,N: int] :
% 5.82/6.14 ( A
% 5.82/6.14 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ N ) @ N ) @ ( modulo_modulo_int @ A @ N ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % div_mod_decomp_int
% 5.82/6.14 thf(fact_6553_mod__div__equality__div__eq,axiom,
% 5.82/6.14 ! [A2: int,B2: int] :
% 5.82/6.14 ( ( times_times_int @ ( divide_divide_int @ A2 @ B2 ) @ B2 )
% 5.82/6.14 = ( minus_minus_int @ A2 @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_div_equality_div_eq
% 5.82/6.14 thf(fact_6554_nat__mod__as__int,axiom,
% 5.82/6.14 ( modulo_modulo_nat
% 5.82/6.14 = ( ^ [A5: nat,B6: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_as_int
% 5.82/6.14 thf(fact_6555_pos__mod__bound2,axiom,
% 5.82/6.14 ! [A2: int] : ( ord_less_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pos_mod_bound2
% 5.82/6.14 thf(fact_6556_mod__pos__neg__trivial,axiom,
% 5.82/6.14 ! [K: int,L: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.14 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.82/6.14 => ( ( modulo_modulo_int @ K @ L )
% 5.82/6.14 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_pos_neg_trivial
% 5.82/6.14 thf(fact_6557_int__mod__ge_H,axiom,
% 5.82/6.14 ! [B2: int,N: int] :
% 5.82/6.14 ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.14 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.82/6.14 => ( ord_less_eq_int @ ( plus_plus_int @ B2 @ N ) @ ( modulo_modulo_int @ B2 @ N ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % int_mod_ge'
% 5.82/6.14 thf(fact_6558_mod__pos__geq,axiom,
% 5.82/6.14 ! [L: int,K: int] :
% 5.82/6.14 ( ( ord_less_int @ zero_zero_int @ L )
% 5.82/6.14 => ( ( ord_less_eq_int @ L @ K )
% 5.82/6.14 => ( ( modulo_modulo_int @ K @ L )
% 5.82/6.14 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_pos_geq
% 5.82/6.14 thf(fact_6559_mod__int__pos__iff,axiom,
% 5.82/6.14 ! [K: int,L: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.82/6.14 = ( ( dvd_dvd_int @ L @ K )
% 5.82/6.14 | ( ( L = zero_zero_int )
% 5.82/6.14 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.82/6.14 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_int_pos_iff
% 5.82/6.14 thf(fact_6560_nat__mod__distrib,axiom,
% 5.82/6.14 ! [X2: int,Y3: int] :
% 5.82/6.14 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.14 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.14 => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y3 ) )
% 5.82/6.14 = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % nat_mod_distrib
% 5.82/6.14 thf(fact_6561_real__of__int__div__aux,axiom,
% 5.82/6.14 ! [X2: int,D2: int] :
% 5.82/6.14 ( ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ D2 ) )
% 5.82/6.14 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X2 @ D2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X2 @ D2 ) ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % real_of_int_div_aux
% 5.82/6.14 thf(fact_6562_pos__mod__sign2,axiom,
% 5.82/6.14 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % pos_mod_sign2
% 5.82/6.14 thf(fact_6563_nmod2,axiom,
% 5.82/6.14 ! [N: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_int )
% 5.82/6.14 | ( ( modulo_modulo_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = one_one_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % nmod2
% 5.82/6.14 thf(fact_6564_mod__2__neq__1__eq__eq__0,axiom,
% 5.82/6.14 ! [K: int] :
% 5.82/6.14 ( ( ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 != one_one_int )
% 5.82/6.14 = ( ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.14 = zero_zero_int ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_2_neq_1_eq_eq_0
% 5.82/6.14 thf(fact_6565_mod__exp__less__eq__exp,axiom,
% 5.82/6.14 ! [A2: int,N: nat] : ( ord_less_int @ ( modulo_modulo_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_exp_less_eq_exp
% 5.82/6.14 thf(fact_6566_mod__power__lem,axiom,
% 5.82/6.14 ! [A2: int,M: nat,N: nat] :
% 5.82/6.14 ( ( ord_less_int @ one_one_int @ A2 )
% 5.82/6.14 => ( ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ M ) )
% 5.82/6.14 = zero_zero_int ) )
% 5.82/6.14 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.82/6.14 => ( ( modulo_modulo_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ M ) )
% 5.82/6.14 = ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.82/6.14
% 5.82/6.14 % mod_power_lem
% 5.82/6.14 thf(fact_6567_split__zmod,axiom,
% 5.82/6.14 ! [P: int > $o,N: int,K: int] :
% 5.82/6.14 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.82/6.14 = ( ( ( K = zero_zero_int )
% 5.82/6.14 => ( P @ N ) )
% 5.82/6.14 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.14 => ! [I4: int,J3: int] :
% 5.82/6.14 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.82/6.14 & ( ord_less_int @ J3 @ K )
% 5.82/6.14 & ( N
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.82/6.15 => ( P @ J3 ) ) )
% 5.82/6.15 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.82/6.15 => ! [I4: int,J3: int] :
% 5.82/6.15 ( ( ( ord_less_int @ K @ J3 )
% 5.82/6.15 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.82/6.15 & ( N
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.82/6.15 => ( P @ J3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % split_zmod
% 5.82/6.15 thf(fact_6568_int__mod__neg__eq,axiom,
% 5.82/6.15 ! [A2: int,B2: int,Q3: int,R2: int] :
% 5.82/6.15 ( ( A2
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 ) )
% 5.82/6.15 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.82/6.15 => ( ( ord_less_int @ B2 @ R2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.15 = R2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % int_mod_neg_eq
% 5.82/6.15 thf(fact_6569_int__mod__pos__eq,axiom,
% 5.82/6.15 ! [A2: int,B2: int,Q3: int,R2: int] :
% 5.82/6.15 ( ( A2
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ B2 @ Q3 ) @ R2 ) )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.82/6.15 => ( ( ord_less_int @ R2 @ B2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.15 = R2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % int_mod_pos_eq
% 5.82/6.15 thf(fact_6570_mod__add__if__z,axiom,
% 5.82/6.15 ! [X2: int,Z: int,Y3: int] :
% 5.82/6.15 ( ( ord_less_int @ X2 @ Z )
% 5.82/6.15 => ( ( ord_less_int @ Y3 @ Z )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.15 => ( ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y3 ) @ Z )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( plus_plus_int @ X2 @ Y3 ) @ Z )
% 5.82/6.15 = ( plus_plus_int @ X2 @ Y3 ) ) )
% 5.82/6.15 & ( ~ ( ord_less_int @ ( plus_plus_int @ X2 @ Y3 ) @ Z )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( plus_plus_int @ X2 @ Y3 ) @ Z )
% 5.82/6.15 = ( minus_minus_int @ ( plus_plus_int @ X2 @ Y3 ) @ Z ) ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % mod_add_if_z
% 5.82/6.15 thf(fact_6571_mod__sub__if__z,axiom,
% 5.82/6.15 ! [X2: int,Z: int,Y3: int] :
% 5.82/6.15 ( ( ord_less_int @ X2 @ Z )
% 5.82/6.15 => ( ( ord_less_int @ Y3 @ Z )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.82/6.15 => ( ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( minus_minus_int @ X2 @ Y3 ) @ Z )
% 5.82/6.15 = ( minus_minus_int @ X2 @ Y3 ) ) )
% 5.82/6.15 & ( ~ ( ord_less_eq_int @ Y3 @ X2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( minus_minus_int @ X2 @ Y3 ) @ Z )
% 5.82/6.15 = ( plus_plus_int @ ( minus_minus_int @ X2 @ Y3 ) @ Z ) ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % mod_sub_if_z
% 5.82/6.15 thf(fact_6572_zmod__zmult2__eq,axiom,
% 5.82/6.15 ! [C2: int,A2: int,B2: int] :
% 5.82/6.15 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ B2 @ C2 ) )
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ B2 @ ( modulo_modulo_int @ ( divide_divide_int @ A2 @ B2 ) @ C2 ) ) @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % zmod_zmult2_eq
% 5.82/6.15 thf(fact_6573_axxmod2,axiom,
% 5.82/6.15 ! [X2: int] :
% 5.82/6.15 ( ( ( modulo_modulo_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X2 ) @ X2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.15 = one_one_int )
% 5.82/6.15 & ( ( modulo_modulo_int @ ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ X2 ) @ X2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.15 = zero_zero_int ) ) ).
% 5.82/6.15
% 5.82/6.15 % axxmod2
% 5.82/6.15 thf(fact_6574_z1pmod2,axiom,
% 5.82/6.15 ! [B2: int] :
% 5.82/6.15 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.15 = one_one_int ) ).
% 5.82/6.15
% 5.82/6.15 % z1pmod2
% 5.82/6.15 thf(fact_6575_verit__le__mono__div__int,axiom,
% 5.82/6.15 ! [A: int,B: int,N: int] :
% 5.82/6.15 ( ( ord_less_int @ A @ B )
% 5.82/6.15 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.82/6.15 => ( ord_less_eq_int
% 5.82/6.15 @ ( plus_plus_int @ ( divide_divide_int @ A @ N )
% 5.82/6.15 @ ( if_int
% 5.82/6.15 @ ( ( modulo_modulo_int @ B @ N )
% 5.82/6.15 = zero_zero_int )
% 5.82/6.15 @ one_one_int
% 5.82/6.15 @ zero_zero_int ) )
% 5.82/6.15 @ ( divide_divide_int @ B @ N ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % verit_le_mono_div_int
% 5.82/6.15 thf(fact_6576_split__neg__lemma,axiom,
% 5.82/6.15 ! [K: int,P: int > int > $o,N: int] :
% 5.82/6.15 ( ( ord_less_int @ K @ zero_zero_int )
% 5.82/6.15 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.82/6.15 = ( ! [I4: int,J3: int] :
% 5.82/6.15 ( ( ( ord_less_int @ K @ J3 )
% 5.82/6.15 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.82/6.15 & ( N
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.82/6.15 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % split_neg_lemma
% 5.82/6.15 thf(fact_6577_split__pos__lemma,axiom,
% 5.82/6.15 ! [K: int,P: int > int > $o,N: int] :
% 5.82/6.15 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.15 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.82/6.15 = ( ! [I4: int,J3: int] :
% 5.82/6.15 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.82/6.15 & ( ord_less_int @ J3 @ K )
% 5.82/6.15 & ( N
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.82/6.15 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % split_pos_lemma
% 5.82/6.15 thf(fact_6578_p1mod22k,axiom,
% 5.82/6.15 ! [B2: int,N: nat] :
% 5.82/6.15 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.15 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ one_one_int ) ) ).
% 5.82/6.15
% 5.82/6.15 % p1mod22k
% 5.82/6.15 thf(fact_6579_p1mod22k_H,axiom,
% 5.82/6.15 ! [B2: int,N: nat] :
% 5.82/6.15 ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.15 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % p1mod22k'
% 5.82/6.15 thf(fact_6580_eq__diff__eq_H,axiom,
% 5.82/6.15 ! [X2: real,Y3: real,Z: real] :
% 5.82/6.15 ( ( X2
% 5.82/6.15 = ( minus_minus_real @ Y3 @ Z ) )
% 5.82/6.15 = ( Y3
% 5.82/6.15 = ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % eq_diff_eq'
% 5.82/6.15 thf(fact_6581_pos__zmod__mult__2,axiom,
% 5.82/6.15 ! [A2: int,B2: int] :
% 5.82/6.15 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.15 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B2 @ A2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pos_zmod_mult_2
% 5.82/6.15 thf(fact_6582_eme1p,axiom,
% 5.82/6.15 ! [N: int,D2: int] :
% 5.82/6.15 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.15 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D2 )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ D2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ N ) @ D2 )
% 5.82/6.15 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ N @ D2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % eme1p
% 5.82/6.15 thf(fact_6583_emep1,axiom,
% 5.82/6.15 ! [N: int,D2: int] :
% 5.82/6.15 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.15 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D2 )
% 5.82/6.15 => ( ( ord_less_eq_int @ zero_zero_int @ D2 )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( plus_plus_int @ N @ one_one_int ) @ D2 )
% 5.82/6.15 = ( plus_plus_int @ ( modulo_modulo_int @ N @ D2 ) @ one_one_int ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % emep1
% 5.82/6.15 thf(fact_6584_even__flip__bit__iff,axiom,
% 5.82/6.15 ! [M: nat,A2: int] :
% 5.82/6.15 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A2 ) )
% 5.82/6.15 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.15 != ( M = zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % even_flip_bit_iff
% 5.82/6.15 thf(fact_6585_even__flip__bit__iff,axiom,
% 5.82/6.15 ! [M: nat,A2: nat] :
% 5.82/6.15 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A2 ) )
% 5.82/6.15 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 )
% 5.82/6.15 != ( M = zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % even_flip_bit_iff
% 5.82/6.15 thf(fact_6586_sb__inc__lem,axiom,
% 5.82/6.15 ! [A2: int,K: nat] :
% 5.82/6.15 ( ( ord_less_int @ ( plus_plus_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ zero_zero_int )
% 5.82/6.15 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A2 @ ( 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 @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sb_inc_lem
% 5.82/6.15 thf(fact_6587_vebt__assn__raw_Osimps_I2_J,axiom,
% 5.82/6.15 ! [Mmo2: option4927543243414619207at_nat,Deg: nat,Tree_list2: list_VEBT_VEBT,Summary: vEBT_VEBT,Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 5.82/6.15 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ Mmo2 @ Deg @ Tree_list2 @ Summary ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 5.82/6.15 = ( times_times_assn
% 5.82/6.15 @ ( times_times_assn
% 5.82/6.15 @ ( pure_assn
% 5.82/6.15 @ ( ( Mmoi2 = Mmo2 )
% 5.82/6.15 & ( Degi2 = Deg ) ) )
% 5.82/6.15 @ ( vEBT_vebt_assn_raw @ Summary @ Summaryi2 ) )
% 5.82/6.15 @ ( ex_ass463751140784270563_VEBTi
% 5.82/6.15 @ ^ [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 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % vebt_assn_raw.simps(2)
% 5.82/6.15 thf(fact_6588_neg__zmod__mult__2,axiom,
% 5.82/6.15 ! [A2: int,B2: int] :
% 5.82/6.15 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.15 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.82/6.15 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B2 @ one_one_int ) @ A2 ) ) @ one_one_int ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % neg_zmod_mult_2
% 5.82/6.15 thf(fact_6589_triangle__def,axiom,
% 5.82/6.15 ( nat_triangle
% 5.82/6.15 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % triangle_def
% 5.82/6.15 thf(fact_6590_obtain__set__pred,axiom,
% 5.82/6.15 ! [Z: nat,X2: nat,A: set_nat] :
% 5.82/6.15 ( ( ord_less_nat @ Z @ X2 )
% 5.82/6.15 => ( ( vEBT_VEBT_min_in_set @ A @ Z )
% 5.82/6.15 => ( ( finite_finite_nat @ A )
% 5.82/6.15 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A @ X2 @ X_1 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % obtain_set_pred
% 5.82/6.15 thf(fact_6591_obtain__set__succ,axiom,
% 5.82/6.15 ! [X2: nat,Z: nat,A: set_nat,B: set_nat] :
% 5.82/6.15 ( ( ord_less_nat @ X2 @ Z )
% 5.82/6.15 => ( ( vEBT_VEBT_max_in_set @ A @ Z )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( A = B )
% 5.82/6.15 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A @ X2 @ X_1 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % obtain_set_succ
% 5.82/6.15 thf(fact_6592_vebt__buildup_Oelims,axiom,
% 5.82/6.15 ! [X2: nat,Y3: vEBT_VEBT] :
% 5.82/6.15 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.82/6.15 = Y3 )
% 5.82/6.15 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.15 => ( Y3
% 5.82/6.15 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.82/6.15 => ( ( ( X2
% 5.82/6.15 = ( suc @ zero_zero_nat ) )
% 5.82/6.15 => ( Y3
% 5.82/6.15 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.82/6.15 => ~ ! [Va3: nat] :
% 5.82/6.15 ( ( X2
% 5.82/6.15 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.15 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.15 => ( Y3
% 5.82/6.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.15 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.15 => ( Y3
% 5.82/6.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % vebt_buildup.elims
% 5.82/6.15 thf(fact_6593_ceiling__log__eq__powr__iff,axiom,
% 5.82/6.15 ! [X2: real,B2: real,K: nat] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ( archim7802044766580827645g_real @ ( log @ B2 @ X2 ) )
% 5.82/6.15 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.82/6.15 = ( ( ord_less_real @ ( powr_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.82/6.15 & ( ord_less_eq_real @ X2 @ ( powr_real @ B2 @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ceiling_log_eq_powr_iff
% 5.82/6.15 thf(fact_6594_intind,axiom,
% 5.82/6.15 ! [I: nat,N: nat,P: vEBT_VEBTi > $o,X2: vEBT_VEBTi] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( P @ X2 )
% 5.82/6.15 => ( P @ ( nth_VEBT_VEBTi @ ( replicate_VEBT_VEBTi @ N @ X2 ) @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % intind
% 5.82/6.15 thf(fact_6595_intind,axiom,
% 5.82/6.15 ! [I: nat,N: nat,P: nat > $o,X2: nat] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( P @ X2 )
% 5.82/6.15 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % intind
% 5.82/6.15 thf(fact_6596_intind,axiom,
% 5.82/6.15 ! [I: nat,N: nat,P: $o > $o,X2: $o] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( P @ X2 )
% 5.82/6.15 => ( P @ ( nth_o @ ( replicate_o @ N @ X2 ) @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % intind
% 5.82/6.15 thf(fact_6597_intind,axiom,
% 5.82/6.15 ! [I: nat,N: nat,P: real > $o,X2: real] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( P @ X2 )
% 5.82/6.15 => ( P @ ( nth_real @ ( replicate_real @ N @ X2 ) @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % intind
% 5.82/6.15 thf(fact_6598_intind,axiom,
% 5.82/6.15 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( P @ X2 )
% 5.82/6.15 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % intind
% 5.82/6.15 thf(fact_6599_set__vebt__finite,axiom,
% 5.82/6.15 ! [T: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( vEBT_invar_vebt @ T @ N )
% 5.82/6.15 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_vebt_finite
% 5.82/6.15 thf(fact_6600_succ__none__empty,axiom,
% 5.82/6.15 ! [Xs: set_nat,A2: nat] :
% 5.82/6.15 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A2 @ X_1 )
% 5.82/6.15 => ( ( finite_finite_nat @ Xs )
% 5.82/6.15 => ~ ? [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ Xs )
% 5.82/6.15 & ( ord_less_nat @ A2 @ X8 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % succ_none_empty
% 5.82/6.15 thf(fact_6601_pred__none__empty,axiom,
% 5.82/6.15 ! [Xs: set_nat,A2: nat] :
% 5.82/6.15 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A2 @ X_1 )
% 5.82/6.15 => ( ( finite_finite_nat @ Xs )
% 5.82/6.15 => ~ ? [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ Xs )
% 5.82/6.15 & ( ord_less_nat @ X8 @ A2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pred_none_empty
% 5.82/6.15 thf(fact_6602_repli__cons__repl,axiom,
% 5.82/6.15 ! [Q: assn,X2: heap_T8145700208782473153_VEBTi,A: vEBT_VEBT > vEBT_VEBTi > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_1429296392585015714_VEBTi @ Q @ X2
% 5.82/6.15 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ Q @ ( A @ Y3 @ R5 ) ) )
% 5.82/6.15 => ( hoare_3904069481286416050_VEBTi @ Q @ ( vEBT_V1859673955506687831_VEBTi @ N @ X2 )
% 5.82/6.15 @ ^ [R5: list_VEBT_VEBTi] : ( times_times_assn @ Q @ ( vEBT_L6296928887356842470_VEBTi @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) @ R5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_cons_repl
% 5.82/6.15 thf(fact_6603_repli__cons__repl,axiom,
% 5.82/6.15 ! [Q: assn,X2: heap_Time_Heap_o,A: vEBT_VEBT > $o > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_hoare_triple_o @ Q @ X2
% 5.82/6.15 @ ^ [R5: $o] : ( times_times_assn @ Q @ ( A @ Y3 @ R5 ) ) )
% 5.82/6.15 => ( hoare_9089481587091695345list_o @ Q @ ( vEBT_V2326993469660664182atei_o @ N @ X2 )
% 5.82/6.15 @ ^ [R5: list_o] : ( times_times_assn @ Q @ ( vEBT_L7489408758114837031VEBT_o @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) @ R5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_cons_repl
% 5.82/6.15 thf(fact_6604_repli__cons__repl,axiom,
% 5.82/6.15 ! [Q: assn,X2: heap_T2636463487746394924on_nat,A: vEBT_VEBT > option_nat > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_7629718768684598413on_nat @ Q @ X2
% 5.82/6.15 @ ^ [R5: option_nat] : ( times_times_assn @ Q @ ( A @ Y3 @ R5 ) ) )
% 5.82/6.15 => ( hoare_6480275734082232733on_nat @ Q @ ( vEBT_V792416675989592002on_nat @ N @ X2 )
% 5.82/6.15 @ ^ [R5: list_option_nat] : ( times_times_assn @ Q @ ( vEBT_L8010285020845282001on_nat @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) @ R5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_cons_repl
% 5.82/6.15 thf(fact_6605_repli__cons__repl,axiom,
% 5.82/6.15 ! [Q: assn,X2: heap_Time_Heap_nat,A: vEBT_VEBT > nat > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_3067605981109127869le_nat @ Q @ X2
% 5.82/6.15 @ ^ [R5: nat] : ( times_times_assn @ Q @ ( A @ Y3 @ R5 ) ) )
% 5.82/6.15 => ( hoare_7964568885773372237st_nat @ Q @ ( vEBT_V7726092123322077554ei_nat @ N @ X2 )
% 5.82/6.15 @ ^ [R5: list_nat] : ( times_times_assn @ Q @ ( vEBT_L8296926524756676353BT_nat @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) @ R5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_cons_repl
% 5.82/6.15 thf(fact_6606_repli__emp,axiom,
% 5.82/6.15 ! [X2: heap_T8145700208782473153_VEBTi,A: vEBT_VEBT > vEBT_VEBTi > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_1429296392585015714_VEBTi @ one_one_assn @ X2 @ ( A @ Y3 ) )
% 5.82/6.15 => ( hoare_3904069481286416050_VEBTi @ one_one_assn @ ( vEBT_V1859673955506687831_VEBTi @ N @ X2 ) @ ( vEBT_L6296928887356842470_VEBTi @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_emp
% 5.82/6.15 thf(fact_6607_repli__emp,axiom,
% 5.82/6.15 ! [X2: heap_Time_Heap_o,A: vEBT_VEBT > $o > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_hoare_triple_o @ one_one_assn @ X2 @ ( A @ Y3 ) )
% 5.82/6.15 => ( hoare_9089481587091695345list_o @ one_one_assn @ ( vEBT_V2326993469660664182atei_o @ N @ X2 ) @ ( vEBT_L7489408758114837031VEBT_o @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_emp
% 5.82/6.15 thf(fact_6608_repli__emp,axiom,
% 5.82/6.15 ! [X2: heap_T2636463487746394924on_nat,A: vEBT_VEBT > option_nat > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_7629718768684598413on_nat @ one_one_assn @ X2 @ ( A @ Y3 ) )
% 5.82/6.15 => ( hoare_6480275734082232733on_nat @ one_one_assn @ ( vEBT_V792416675989592002on_nat @ N @ X2 ) @ ( vEBT_L8010285020845282001on_nat @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_emp
% 5.82/6.15 thf(fact_6609_repli__emp,axiom,
% 5.82/6.15 ! [X2: heap_Time_Heap_nat,A: vEBT_VEBT > nat > assn,Y3: vEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( hoare_3067605981109127869le_nat @ one_one_assn @ X2 @ ( A @ Y3 ) )
% 5.82/6.15 => ( hoare_7964568885773372237st_nat @ one_one_assn @ ( vEBT_V7726092123322077554ei_nat @ N @ X2 ) @ ( vEBT_L8296926524756676353BT_nat @ A @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % repli_emp
% 5.82/6.15 thf(fact_6610_List_Ofinite__set,axiom,
% 5.82/6.15 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % List.finite_set
% 5.82/6.15 thf(fact_6611_List_Ofinite__set,axiom,
% 5.82/6.15 ! [Xs: list_real] : ( finite_finite_real @ ( set_real2 @ Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % List.finite_set
% 5.82/6.15 thf(fact_6612_List_Ofinite__set,axiom,
% 5.82/6.15 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % List.finite_set
% 5.82/6.15 thf(fact_6613_List_Ofinite__set,axiom,
% 5.82/6.15 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % List.finite_set
% 5.82/6.15 thf(fact_6614_List_Ofinite__set,axiom,
% 5.82/6.15 ! [Xs: list_Code_integer] : ( finite6017078050557962740nteger @ ( set_Code_integer2 @ Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % List.finite_set
% 5.82/6.15 thf(fact_6615_List_Ofinite__set,axiom,
% 5.82/6.15 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % List.finite_set
% 5.82/6.15 thf(fact_6616_powr__one__eq__one,axiom,
% 5.82/6.15 ! [A2: real] :
% 5.82/6.15 ( ( powr_real @ one_one_real @ A2 )
% 5.82/6.15 = one_one_real ) ).
% 5.82/6.15
% 5.82/6.15 % powr_one_eq_one
% 5.82/6.15 thf(fact_6617_replicate__eq__replicate,axiom,
% 5.82/6.15 ! [M: nat,X2: vEBT_VEBT,N: nat,Y3: vEBT_VEBT] :
% 5.82/6.15 ( ( ( replicate_VEBT_VEBT @ M @ X2 )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ N @ Y3 ) )
% 5.82/6.15 = ( ( M = N )
% 5.82/6.15 & ( ( M != zero_zero_nat )
% 5.82/6.15 => ( X2 = Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eq_replicate
% 5.82/6.15 thf(fact_6618_length__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = N ) ).
% 5.82/6.15
% 5.82/6.15 % length_replicate
% 5.82/6.15 thf(fact_6619_length__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: real] :
% 5.82/6.15 ( ( size_size_list_real @ ( replicate_real @ N @ X2 ) )
% 5.82/6.15 = N ) ).
% 5.82/6.15
% 5.82/6.15 % length_replicate
% 5.82/6.15 thf(fact_6620_length__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: $o] :
% 5.82/6.15 ( ( size_size_list_o @ ( replicate_o @ N @ X2 ) )
% 5.82/6.15 = N ) ).
% 5.82/6.15
% 5.82/6.15 % length_replicate
% 5.82/6.15 thf(fact_6621_length__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: nat] :
% 5.82/6.15 ( ( size_size_list_nat @ ( replicate_nat @ N @ X2 ) )
% 5.82/6.15 = N ) ).
% 5.82/6.15
% 5.82/6.15 % length_replicate
% 5.82/6.15 thf(fact_6622_length__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: vEBT_VEBTi] :
% 5.82/6.15 ( ( size_s7982070591426661849_VEBTi @ ( replicate_VEBT_VEBTi @ N @ X2 ) )
% 5.82/6.15 = N ) ).
% 5.82/6.15
% 5.82/6.15 % length_replicate
% 5.82/6.15 thf(fact_6623_map__replicate,axiom,
% 5.82/6.15 ! [F: vEBT_VEBT > nat,N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( map_VEBT_VEBT_nat @ F @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = ( replicate_nat @ N @ ( F @ X2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate
% 5.82/6.15 thf(fact_6624_map__replicate,axiom,
% 5.82/6.15 ! [F: vEBT_VEBT > real,N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( map_VEBT_VEBT_real @ F @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = ( replicate_real @ N @ ( F @ X2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate
% 5.82/6.15 thf(fact_6625_map__replicate,axiom,
% 5.82/6.15 ! [F: vEBT_VEBT > vEBT_VEBT,N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( map_VE8901447254227204932T_VEBT @ F @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ N @ ( F @ X2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate
% 5.82/6.15 thf(fact_6626_infinite__Icc__iff,axiom,
% 5.82/6.15 ! [A2: rat,B2: rat] :
% 5.82/6.15 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A2 @ B2 ) ) )
% 5.82/6.15 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Icc_iff
% 5.82/6.15 thf(fact_6627_infinite__Icc__iff,axiom,
% 5.82/6.15 ! [A2: real,B2: real] :
% 5.82/6.15 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) ) )
% 5.82/6.15 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Icc_iff
% 5.82/6.15 thf(fact_6628_infinite__Ico__iff,axiom,
% 5.82/6.15 ! [A2: real,B2: real] :
% 5.82/6.15 ( ( ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A2 @ B2 ) ) )
% 5.82/6.15 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Ico_iff
% 5.82/6.15 thf(fact_6629_infinite__Ico__iff,axiom,
% 5.82/6.15 ! [A2: rat,B2: rat] :
% 5.82/6.15 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A2 @ B2 ) ) )
% 5.82/6.15 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Ico_iff
% 5.82/6.15 thf(fact_6630_powr__zero__eq__one,axiom,
% 5.82/6.15 ! [X2: real] :
% 5.82/6.15 ( ( ( X2 = zero_zero_real )
% 5.82/6.15 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.82/6.15 = zero_zero_real ) )
% 5.82/6.15 & ( ( X2 != zero_zero_real )
% 5.82/6.15 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.82/6.15 = one_one_real ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_zero_eq_one
% 5.82/6.15 thf(fact_6631_Ball__set__replicate,axiom,
% 5.82/6.15 ! [N: nat,A2: real,P: real > $o] :
% 5.82/6.15 ( ( ! [X3: real] :
% 5.82/6.15 ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ A2 ) ) )
% 5.82/6.15 => ( P @ X3 ) ) )
% 5.82/6.15 = ( ( P @ A2 )
% 5.82/6.15 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Ball_set_replicate
% 5.82/6.15 thf(fact_6632_Ball__set__replicate,axiom,
% 5.82/6.15 ! [N: nat,A2: nat,P: nat > $o] :
% 5.82/6.15 ( ( ! [X3: nat] :
% 5.82/6.15 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A2 ) ) )
% 5.82/6.15 => ( P @ X3 ) ) )
% 5.82/6.15 = ( ( P @ A2 )
% 5.82/6.15 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Ball_set_replicate
% 5.82/6.15 thf(fact_6633_Ball__set__replicate,axiom,
% 5.82/6.15 ! [N: nat,A2: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.15 ( ( ! [X3: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A2 ) ) )
% 5.82/6.15 => ( P @ X3 ) ) )
% 5.82/6.15 = ( ( P @ A2 )
% 5.82/6.15 | ( N = zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Ball_set_replicate
% 5.82/6.15 thf(fact_6634_Bex__set__replicate,axiom,
% 5.82/6.15 ! [N: nat,A2: real,P: real > $o] :
% 5.82/6.15 ( ( ? [X3: real] :
% 5.82/6.15 ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ A2 ) ) )
% 5.82/6.15 & ( P @ X3 ) ) )
% 5.82/6.15 = ( ( P @ A2 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Bex_set_replicate
% 5.82/6.15 thf(fact_6635_Bex__set__replicate,axiom,
% 5.82/6.15 ! [N: nat,A2: nat,P: nat > $o] :
% 5.82/6.15 ( ( ? [X3: nat] :
% 5.82/6.15 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A2 ) ) )
% 5.82/6.15 & ( P @ X3 ) ) )
% 5.82/6.15 = ( ( P @ A2 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Bex_set_replicate
% 5.82/6.15 thf(fact_6636_Bex__set__replicate,axiom,
% 5.82/6.15 ! [N: nat,A2: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.82/6.15 ( ( ? [X3: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A2 ) ) )
% 5.82/6.15 & ( P @ X3 ) ) )
% 5.82/6.15 = ( ( P @ A2 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Bex_set_replicate
% 5.82/6.15 thf(fact_6637_in__set__replicate,axiom,
% 5.82/6.15 ! [X2: int,N: nat,Y3: int] :
% 5.82/6.15 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ Y3 ) ) )
% 5.82/6.15 = ( ( X2 = Y3 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % in_set_replicate
% 5.82/6.15 thf(fact_6638_in__set__replicate,axiom,
% 5.82/6.15 ! [X2: real,N: nat,Y3: real] :
% 5.82/6.15 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N @ Y3 ) ) )
% 5.82/6.15 = ( ( X2 = Y3 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % in_set_replicate
% 5.82/6.15 thf(fact_6639_in__set__replicate,axiom,
% 5.82/6.15 ! [X2: nat,N: nat,Y3: nat] :
% 5.82/6.15 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ Y3 ) ) )
% 5.82/6.15 = ( ( X2 = Y3 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % in_set_replicate
% 5.82/6.15 thf(fact_6640_in__set__replicate,axiom,
% 5.82/6.15 ! [X2: vEBT_VEBT,N: nat,Y3: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y3 ) ) )
% 5.82/6.15 = ( ( X2 = Y3 )
% 5.82/6.15 & ( N != zero_zero_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % in_set_replicate
% 5.82/6.15 thf(fact_6641_nth__replicate,axiom,
% 5.82/6.15 ! [I: nat,N: nat,X2: vEBT_VEBTi] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( nth_VEBT_VEBTi @ ( replicate_VEBT_VEBTi @ N @ X2 ) @ I )
% 5.82/6.15 = X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % nth_replicate
% 5.82/6.15 thf(fact_6642_nth__replicate,axiom,
% 5.82/6.15 ! [I: nat,N: nat,X2: nat] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I )
% 5.82/6.15 = X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % nth_replicate
% 5.82/6.15 thf(fact_6643_nth__replicate,axiom,
% 5.82/6.15 ! [I: nat,N: nat,X2: $o] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( nth_o @ ( replicate_o @ N @ X2 ) @ I )
% 5.82/6.15 = X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % nth_replicate
% 5.82/6.15 thf(fact_6644_nth__replicate,axiom,
% 5.82/6.15 ! [I: nat,N: nat,X2: real] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( nth_real @ ( replicate_real @ N @ X2 ) @ I )
% 5.82/6.15 = X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % nth_replicate
% 5.82/6.15 thf(fact_6645_nth__replicate,axiom,
% 5.82/6.15 ! [I: nat,N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( ord_less_nat @ I @ N )
% 5.82/6.15 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I )
% 5.82/6.15 = X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % nth_replicate
% 5.82/6.15 thf(fact_6646_powr__nonneg__iff,axiom,
% 5.82/6.15 ! [A2: real,X2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ ( powr_real @ A2 @ X2 ) @ zero_zero_real )
% 5.82/6.15 = ( A2 = zero_zero_real ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_nonneg_iff
% 5.82/6.15 thf(fact_6647_powr__less__cancel__iff,axiom,
% 5.82/6.15 ! [X2: real,A2: real,B2: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B2 ) )
% 5.82/6.15 = ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_less_cancel_iff
% 5.82/6.15 thf(fact_6648_triangle__Suc,axiom,
% 5.82/6.15 ! [N: nat] :
% 5.82/6.15 ( ( nat_triangle @ ( suc @ N ) )
% 5.82/6.15 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % triangle_Suc
% 5.82/6.15 thf(fact_6649_powr__eq__one__iff,axiom,
% 5.82/6.15 ! [A2: real,X2: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ A2 )
% 5.82/6.15 => ( ( ( powr_real @ A2 @ X2 )
% 5.82/6.15 = one_one_real )
% 5.82/6.15 = ( X2 = zero_zero_real ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_eq_one_iff
% 5.82/6.15 thf(fact_6650_powr__one__gt__zero__iff,axiom,
% 5.82/6.15 ! [X2: real] :
% 5.82/6.15 ( ( ( powr_real @ X2 @ one_one_real )
% 5.82/6.15 = X2 )
% 5.82/6.15 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_one_gt_zero_iff
% 5.82/6.15 thf(fact_6651_powr__one,axiom,
% 5.82/6.15 ! [X2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( powr_real @ X2 @ one_one_real )
% 5.82/6.15 = X2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_one
% 5.82/6.15 thf(fact_6652_powr__le__cancel__iff,axiom,
% 5.82/6.15 ! [X2: real,A2: real,B2: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B2 ) )
% 5.82/6.15 = ( ord_less_eq_real @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_le_cancel_iff
% 5.82/6.15 thf(fact_6653_numeral__powr__numeral__real,axiom,
% 5.82/6.15 ! [M: num,N: num] :
% 5.82/6.15 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.82/6.15 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % numeral_powr_numeral_real
% 5.82/6.15 thf(fact_6654_set__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: real] :
% 5.82/6.15 ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.82/6.15 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate
% 5.82/6.15 thf(fact_6655_set__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate
% 5.82/6.15 thf(fact_6656_set__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: nat] :
% 5.82/6.15 ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.82/6.15 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate
% 5.82/6.15 thf(fact_6657_set__replicate,axiom,
% 5.82/6.15 ! [N: nat,X2: int] :
% 5.82/6.15 ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.82/6.15 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate
% 5.82/6.15 thf(fact_6658_powr__log__cancel,axiom,
% 5.82/6.15 ! [A2: real,X2: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( A2 != one_one_real )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( powr_real @ A2 @ ( log @ A2 @ X2 ) )
% 5.82/6.15 = X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_log_cancel
% 5.82/6.15 thf(fact_6659_log__powr__cancel,axiom,
% 5.82/6.15 ! [A2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( A2 != one_one_real )
% 5.82/6.15 => ( ( log @ A2 @ ( powr_real @ A2 @ Y3 ) )
% 5.82/6.15 = Y3 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % log_powr_cancel
% 5.82/6.15 thf(fact_6660_powr__numeral,axiom,
% 5.82/6.15 ! [X2: real,N: num] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N ) )
% 5.82/6.15 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_numeral
% 5.82/6.15 thf(fact_6661_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 5.82/6.15 ! [L: code_integer,U: code_integer] :
% 5.82/6.15 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 5.82/6.15 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 5.82/6.15
% 5.82/6.15 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 5.82/6.15 thf(fact_6662_finite__if__eq__beyond__finite,axiom,
% 5.82/6.15 ! [S: set_int,S4: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( finite6197958912794628473et_int
% 5.82/6.15 @ ( collect_set_int
% 5.82/6.15 @ ^ [S5: set_int] :
% 5.82/6.15 ( ( minus_minus_set_int @ S5 @ S )
% 5.82/6.15 = ( minus_minus_set_int @ S4 @ S ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_if_eq_beyond_finite
% 5.82/6.15 thf(fact_6663_finite__if__eq__beyond__finite,axiom,
% 5.82/6.15 ! [S: set_Code_integer,S4: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( finite6931041176100689706nteger
% 5.82/6.15 @ ( collec574505750873337192nteger
% 5.82/6.15 @ ^ [S5: set_Code_integer] :
% 5.82/6.15 ( ( minus_2355218937544613996nteger @ S5 @ S )
% 5.82/6.15 = ( minus_2355218937544613996nteger @ S4 @ S ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_if_eq_beyond_finite
% 5.82/6.15 thf(fact_6664_finite__if__eq__beyond__finite,axiom,
% 5.82/6.15 ! [S: set_complex,S4: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ( finite6551019134538273531omplex
% 5.82/6.15 @ ( collect_set_complex
% 5.82/6.15 @ ^ [S5: set_complex] :
% 5.82/6.15 ( ( minus_811609699411566653omplex @ S5 @ S )
% 5.82/6.15 = ( minus_811609699411566653omplex @ S4 @ S ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_if_eq_beyond_finite
% 5.82/6.15 thf(fact_6665_finite__if__eq__beyond__finite,axiom,
% 5.82/6.15 ! [S: set_nat,S4: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ S )
% 5.82/6.15 => ( finite1152437895449049373et_nat
% 5.82/6.15 @ ( collect_set_nat
% 5.82/6.15 @ ^ [S5: set_nat] :
% 5.82/6.15 ( ( minus_minus_set_nat @ S5 @ S )
% 5.82/6.15 = ( minus_minus_set_nat @ S4 @ S ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_if_eq_beyond_finite
% 5.82/6.15 thf(fact_6666_bounded__nat__set__is__finite,axiom,
% 5.82/6.15 ! [N7: set_nat,N: nat] :
% 5.82/6.15 ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ N7 )
% 5.82/6.15 => ( ord_less_nat @ X4 @ N ) )
% 5.82/6.15 => ( finite_finite_nat @ N7 ) ) ).
% 5.82/6.15
% 5.82/6.15 % bounded_nat_set_is_finite
% 5.82/6.15 thf(fact_6667_finite__nat__set__iff__bounded,axiom,
% 5.82/6.15 ( finite_finite_nat
% 5.82/6.15 = ( ^ [N8: set_nat] :
% 5.82/6.15 ? [M6: nat] :
% 5.82/6.15 ! [X3: nat] :
% 5.82/6.15 ( ( member_nat @ X3 @ N8 )
% 5.82/6.15 => ( ord_less_nat @ X3 @ M6 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_nat_set_iff_bounded
% 5.82/6.15 thf(fact_6668_finite__nat__set__iff__bounded__le,axiom,
% 5.82/6.15 ( finite_finite_nat
% 5.82/6.15 = ( ^ [N8: set_nat] :
% 5.82/6.15 ? [M6: nat] :
% 5.82/6.15 ! [X3: nat] :
% 5.82/6.15 ( ( member_nat @ X3 @ N8 )
% 5.82/6.15 => ( ord_less_eq_nat @ X3 @ M6 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_nat_set_iff_bounded_le
% 5.82/6.15 thf(fact_6669_finite__list,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ? [Xs3: list_VEBT_VEBT] :
% 5.82/6.15 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.82/6.15 = A ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_list
% 5.82/6.15 thf(fact_6670_finite__list,axiom,
% 5.82/6.15 ! [A: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ? [Xs3: list_real] :
% 5.82/6.15 ( ( set_real2 @ Xs3 )
% 5.82/6.15 = A ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_list
% 5.82/6.15 thf(fact_6671_finite__list,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ? [Xs3: list_nat] :
% 5.82/6.15 ( ( set_nat2 @ Xs3 )
% 5.82/6.15 = A ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_list
% 5.82/6.15 thf(fact_6672_finite__list,axiom,
% 5.82/6.15 ! [A: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ? [Xs3: list_int] :
% 5.82/6.15 ( ( set_int2 @ Xs3 )
% 5.82/6.15 = A ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_list
% 5.82/6.15 thf(fact_6673_finite__list,axiom,
% 5.82/6.15 ! [A: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ? [Xs3: list_Code_integer] :
% 5.82/6.15 ( ( set_Code_integer2 @ Xs3 )
% 5.82/6.15 = A ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_list
% 5.82/6.15 thf(fact_6674_finite__list,axiom,
% 5.82/6.15 ! [A: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ? [Xs3: list_complex] :
% 5.82/6.15 ( ( set_complex2 @ Xs3 )
% 5.82/6.15 = A ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_list
% 5.82/6.15 thf(fact_6675_finite__M__bounded__by__nat,axiom,
% 5.82/6.15 ! [P: nat > $o,I: nat] :
% 5.82/6.15 ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [K3: nat] :
% 5.82/6.15 ( ( P @ K3 )
% 5.82/6.15 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_M_bounded_by_nat
% 5.82/6.15 thf(fact_6676_finite__less__ub,axiom,
% 5.82/6.15 ! [F: nat > nat,U: nat] :
% 5.82/6.15 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ U ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_less_ub
% 5.82/6.15 thf(fact_6677_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_Code_integer,N: nat] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( finite1283093830868386564nteger
% 5.82/6.15 @ ( collec3483841146883906114nteger
% 5.82/6.15 @ ^ [Xs2: list_Code_integer] :
% 5.82/6.15 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6678_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_complex,N: nat] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( finite8712137658972009173omplex
% 5.82/6.15 @ ( collect_list_complex
% 5.82/6.15 @ ^ [Xs2: list_complex] :
% 5.82/6.15 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6679_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( finite3004134309566078307T_VEBT
% 5.82/6.15 @ ( collec5608196760682091941T_VEBT
% 5.82/6.15 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.82/6.15 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6680_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_real,N: nat] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( finite306553202115118035t_real
% 5.82/6.15 @ ( collect_list_real
% 5.82/6.15 @ ^ [Xs2: list_real] :
% 5.82/6.15 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_size_list_real @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6681_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_o,N: nat] :
% 5.82/6.15 ( ( finite_finite_o @ A )
% 5.82/6.15 => ( finite_finite_list_o
% 5.82/6.15 @ ( collect_list_o
% 5.82/6.15 @ ^ [Xs2: list_o] :
% 5.82/6.15 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_size_list_o @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6682_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_nat,N: nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( finite8100373058378681591st_nat
% 5.82/6.15 @ ( collect_list_nat
% 5.82/6.15 @ ^ [Xs2: list_nat] :
% 5.82/6.15 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_size_list_nat @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6683_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBTi,N: nat] :
% 5.82/6.15 ( ( finite6580341952239402572_VEBTi @ A )
% 5.82/6.15 => ( finite5722435864697464412_VEBTi
% 5.82/6.15 @ ( collec1288327022334394266_VEBTi
% 5.82/6.15 @ ^ [Xs2: list_VEBT_VEBTi] :
% 5.82/6.15 ( ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6684_finite__lists__length__eq,axiom,
% 5.82/6.15 ! [A: set_int,N: nat] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( finite3922522038869484883st_int
% 5.82/6.15 @ ( collect_list_int
% 5.82/6.15 @ ^ [Xs2: list_int] :
% 5.82/6.15 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ( size_size_list_int @ Xs2 )
% 5.82/6.15 = N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_eq
% 5.82/6.15 thf(fact_6685_powr__ge__pzero,axiom,
% 5.82/6.15 ! [X2: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X2 @ Y3 ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_ge_pzero
% 5.82/6.15 thf(fact_6686_powr__mono2,axiom,
% 5.82/6.15 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.15 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_mono2
% 5.82/6.15 thf(fact_6687_powr__less__mono,axiom,
% 5.82/6.15 ! [A2: real,B2: real,X2: real] :
% 5.82/6.15 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_less_mono
% 5.82/6.15 thf(fact_6688_powr__less__cancel,axiom,
% 5.82/6.15 ! [X2: real,A2: real,B2: real] :
% 5.82/6.15 ( ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B2 ) )
% 5.82/6.15 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ord_less_real @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_less_cancel
% 5.82/6.15 thf(fact_6689_powr__mono,axiom,
% 5.82/6.15 ! [A2: real,B2: real,X2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_mono
% 5.82/6.15 thf(fact_6690_replicate__eqI,axiom,
% 5.82/6.15 ! [Xs: list_int,N: nat,X2: int] :
% 5.82/6.15 ( ( ( size_size_list_int @ Xs )
% 5.82/6.15 = N )
% 5.82/6.15 => ( ! [Y4: int] :
% 5.82/6.15 ( ( member_int @ Y4 @ ( set_int2 @ Xs ) )
% 5.82/6.15 => ( Y4 = X2 ) )
% 5.82/6.15 => ( Xs
% 5.82/6.15 = ( replicate_int @ N @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eqI
% 5.82/6.15 thf(fact_6691_replicate__eqI,axiom,
% 5.82/6.15 ! [Xs: list_VEBT_VEBT,N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.82/6.15 = N )
% 5.82/6.15 => ( ! [Y4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ Y4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.15 => ( Y4 = X2 ) )
% 5.82/6.15 => ( Xs
% 5.82/6.15 = ( replicate_VEBT_VEBT @ N @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eqI
% 5.82/6.15 thf(fact_6692_replicate__eqI,axiom,
% 5.82/6.15 ! [Xs: list_real,N: nat,X2: real] :
% 5.82/6.15 ( ( ( size_size_list_real @ Xs )
% 5.82/6.15 = N )
% 5.82/6.15 => ( ! [Y4: real] :
% 5.82/6.15 ( ( member_real @ Y4 @ ( set_real2 @ Xs ) )
% 5.82/6.15 => ( Y4 = X2 ) )
% 5.82/6.15 => ( Xs
% 5.82/6.15 = ( replicate_real @ N @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eqI
% 5.82/6.15 thf(fact_6693_replicate__eqI,axiom,
% 5.82/6.15 ! [Xs: list_o,N: nat,X2: $o] :
% 5.82/6.15 ( ( ( size_size_list_o @ Xs )
% 5.82/6.15 = N )
% 5.82/6.15 => ( ! [Y4: $o] :
% 5.82/6.15 ( ( member_o @ Y4 @ ( set_o2 @ Xs ) )
% 5.82/6.15 => ( Y4 = X2 ) )
% 5.82/6.15 => ( Xs
% 5.82/6.15 = ( replicate_o @ N @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eqI
% 5.82/6.15 thf(fact_6694_replicate__eqI,axiom,
% 5.82/6.15 ! [Xs: list_nat,N: nat,X2: nat] :
% 5.82/6.15 ( ( ( size_size_list_nat @ Xs )
% 5.82/6.15 = N )
% 5.82/6.15 => ( ! [Y4: nat] :
% 5.82/6.15 ( ( member_nat @ Y4 @ ( set_nat2 @ Xs ) )
% 5.82/6.15 => ( Y4 = X2 ) )
% 5.82/6.15 => ( Xs
% 5.82/6.15 = ( replicate_nat @ N @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eqI
% 5.82/6.15 thf(fact_6695_replicate__eqI,axiom,
% 5.82/6.15 ! [Xs: list_VEBT_VEBTi,N: nat,X2: vEBT_VEBTi] :
% 5.82/6.15 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 5.82/6.15 = N )
% 5.82/6.15 => ( ! [Y4: vEBT_VEBTi] :
% 5.82/6.15 ( ( member_VEBT_VEBTi @ Y4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.15 => ( Y4 = X2 ) )
% 5.82/6.15 => ( Xs
% 5.82/6.15 = ( replicate_VEBT_VEBTi @ N @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_eqI
% 5.82/6.15 thf(fact_6696_replicate__length__same,axiom,
% 5.82/6.15 ! [Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.82/6.15 ( ! [X4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.82/6.15 => ( X4 = X2 ) )
% 5.82/6.15 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X2 )
% 5.82/6.15 = Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_length_same
% 5.82/6.15 thf(fact_6697_replicate__length__same,axiom,
% 5.82/6.15 ! [Xs: list_real,X2: real] :
% 5.82/6.15 ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.82/6.15 => ( X4 = X2 ) )
% 5.82/6.15 => ( ( replicate_real @ ( size_size_list_real @ Xs ) @ X2 )
% 5.82/6.15 = Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_length_same
% 5.82/6.15 thf(fact_6698_replicate__length__same,axiom,
% 5.82/6.15 ! [Xs: list_o,X2: $o] :
% 5.82/6.15 ( ! [X4: $o] :
% 5.82/6.15 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.82/6.15 => ( X4 = X2 ) )
% 5.82/6.15 => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X2 )
% 5.82/6.15 = Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_length_same
% 5.82/6.15 thf(fact_6699_replicate__length__same,axiom,
% 5.82/6.15 ! [Xs: list_nat,X2: nat] :
% 5.82/6.15 ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.82/6.15 => ( X4 = X2 ) )
% 5.82/6.15 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X2 )
% 5.82/6.15 = Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_length_same
% 5.82/6.15 thf(fact_6700_replicate__length__same,axiom,
% 5.82/6.15 ! [Xs: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.82/6.15 ( ! [X4: vEBT_VEBTi] :
% 5.82/6.15 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 5.82/6.15 => ( X4 = X2 ) )
% 5.82/6.15 => ( ( replicate_VEBT_VEBTi @ ( size_s7982070591426661849_VEBTi @ Xs ) @ X2 )
% 5.82/6.15 = Xs ) ) ).
% 5.82/6.15
% 5.82/6.15 % replicate_length_same
% 5.82/6.15 thf(fact_6701_infinite__Icc,axiom,
% 5.82/6.15 ! [A2: rat,B2: rat] :
% 5.82/6.15 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.15 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Icc
% 5.82/6.15 thf(fact_6702_infinite__Icc,axiom,
% 5.82/6.15 ! [A2: real,B2: real] :
% 5.82/6.15 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.15 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Icc
% 5.82/6.15 thf(fact_6703_infinite__Ico,axiom,
% 5.82/6.15 ! [A2: real,B2: real] :
% 5.82/6.15 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.15 => ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Ico
% 5.82/6.15 thf(fact_6704_infinite__Ico,axiom,
% 5.82/6.15 ! [A2: rat,B2: rat] :
% 5.82/6.15 ( ( ord_less_rat @ A2 @ B2 )
% 5.82/6.15 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_Ico
% 5.82/6.15 thf(fact_6705_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_Code_integer,N: nat] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( finite1283093830868386564nteger
% 5.82/6.15 @ ( collec3483841146883906114nteger
% 5.82/6.15 @ ^ [Xs2: list_Code_integer] :
% 5.82/6.15 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6706_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_complex,N: nat] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( finite8712137658972009173omplex
% 5.82/6.15 @ ( collect_list_complex
% 5.82/6.15 @ ^ [Xs2: list_complex] :
% 5.82/6.15 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6707_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,N: nat] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( finite3004134309566078307T_VEBT
% 5.82/6.15 @ ( collec5608196760682091941T_VEBT
% 5.82/6.15 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.82/6.15 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6708_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_real,N: nat] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( finite306553202115118035t_real
% 5.82/6.15 @ ( collect_list_real
% 5.82/6.15 @ ^ [Xs2: list_real] :
% 5.82/6.15 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_size_list_real @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6709_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_o,N: nat] :
% 5.82/6.15 ( ( finite_finite_o @ A )
% 5.82/6.15 => ( finite_finite_list_o
% 5.82/6.15 @ ( collect_list_o
% 5.82/6.15 @ ^ [Xs2: list_o] :
% 5.82/6.15 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6710_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_nat,N: nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( finite8100373058378681591st_nat
% 5.82/6.15 @ ( collect_list_nat
% 5.82/6.15 @ ^ [Xs2: list_nat] :
% 5.82/6.15 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6711_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBTi,N: nat] :
% 5.82/6.15 ( ( finite6580341952239402572_VEBTi @ A )
% 5.82/6.15 => ( finite5722435864697464412_VEBTi
% 5.82/6.15 @ ( collec1288327022334394266_VEBTi
% 5.82/6.15 @ ^ [Xs2: list_VEBT_VEBTi] :
% 5.82/6.15 ( ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_s7982070591426661849_VEBTi @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6712_finite__lists__length__le,axiom,
% 5.82/6.15 ! [A: set_int,N: nat] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( finite3922522038869484883st_int
% 5.82/6.15 @ ( collect_list_int
% 5.82/6.15 @ ^ [Xs2: list_int] :
% 5.82/6.15 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_lists_length_le
% 5.82/6.15 thf(fact_6713_map__replicate__const,axiom,
% 5.82/6.15 ! [K: nat,Lst: list_VEBT_VEBT] :
% 5.82/6.15 ( ( map_VEBT_VEBT_nat
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_nat @ ( size_s6755466524823107622T_VEBT @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6714_map__replicate__const,axiom,
% 5.82/6.15 ! [K: real,Lst: list_VEBT_VEBT] :
% 5.82/6.15 ( ( map_VEBT_VEBT_real
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_real @ ( size_s6755466524823107622T_VEBT @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6715_map__replicate__const,axiom,
% 5.82/6.15 ! [K: vEBT_VEBT,Lst: list_VEBT_VEBT] :
% 5.82/6.15 ( ( map_VE8901447254227204932T_VEBT
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6716_map__replicate__const,axiom,
% 5.82/6.15 ! [K: vEBT_VEBT,Lst: list_real] :
% 5.82/6.15 ( ( map_real_VEBT_VEBT
% 5.82/6.15 @ ^ [X3: real] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ ( size_size_list_real @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6717_map__replicate__const,axiom,
% 5.82/6.15 ! [K: vEBT_VEBT,Lst: list_o] :
% 5.82/6.15 ( ( map_o_VEBT_VEBT
% 5.82/6.15 @ ^ [X3: $o] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ ( size_size_list_o @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6718_map__replicate__const,axiom,
% 5.82/6.15 ! [K: vEBT_VEBT,Lst: list_nat] :
% 5.82/6.15 ( ( map_nat_VEBT_VEBT
% 5.82/6.15 @ ^ [X3: nat] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ ( size_size_list_nat @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6719_map__replicate__const,axiom,
% 5.82/6.15 ! [K: vEBT_VEBT,Lst: list_VEBT_VEBTi] :
% 5.82/6.15 ( ( map_VE7998069337340375161T_VEBT
% 5.82/6.15 @ ^ [X3: vEBT_VEBTi] : K
% 5.82/6.15 @ Lst )
% 5.82/6.15 = ( replicate_VEBT_VEBT @ ( size_s7982070591426661849_VEBTi @ Lst ) @ K ) ) ).
% 5.82/6.15
% 5.82/6.15 % map_replicate_const
% 5.82/6.15 thf(fact_6720_powr__mono2_H,axiom,
% 5.82/6.15 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.15 => ( ord_less_eq_real @ ( powr_real @ Y3 @ A2 ) @ ( powr_real @ X2 @ A2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_mono2'
% 5.82/6.15 thf(fact_6721_powr__less__mono2,axiom,
% 5.82/6.15 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.15 => ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_less_mono2
% 5.82/6.15 thf(fact_6722_gr__one__powr,axiom,
% 5.82/6.15 ! [X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.15 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % gr_one_powr
% 5.82/6.15 thf(fact_6723_powr__inj,axiom,
% 5.82/6.15 ! [A2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( A2 != one_one_real )
% 5.82/6.15 => ( ( ( powr_real @ A2 @ X2 )
% 5.82/6.15 = ( powr_real @ A2 @ Y3 ) )
% 5.82/6.15 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_inj
% 5.82/6.15 thf(fact_6724_ge__one__powr__ge__zero,axiom,
% 5.82/6.15 ! [X2: real,A2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X2 @ A2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ge_one_powr_ge_zero
% 5.82/6.15 thf(fact_6725_powr__mono__both,axiom,
% 5.82/6.15 ! [A2: real,B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.15 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ B2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_mono_both
% 5.82/6.15 thf(fact_6726_powr__le1,axiom,
% 5.82/6.15 ! [A2: real,X2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.15 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ one_one_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_le1
% 5.82/6.15 thf(fact_6727_powr__divide,axiom,
% 5.82/6.15 ! [X2: real,Y3: real,A2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.15 => ( ( powr_real @ ( divide_divide_real @ X2 @ Y3 ) @ A2 )
% 5.82/6.15 = ( divide_divide_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_divide
% 5.82/6.15 thf(fact_6728_powr__mult,axiom,
% 5.82/6.15 ! [X2: real,Y3: real,A2: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.15 => ( ( powr_real @ ( times_times_real @ X2 @ Y3 ) @ A2 )
% 5.82/6.15 = ( times_times_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_mult
% 5.82/6.15 thf(fact_6729_powr__add,axiom,
% 5.82/6.15 ! [X2: real,A2: real,B2: real] :
% 5.82/6.15 ( ( powr_real @ X2 @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.15 = ( times_times_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B2 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_add
% 5.82/6.15 thf(fact_6730_powr__diff,axiom,
% 5.82/6.15 ! [W: real,Z1: real,Z22: real] :
% 5.82/6.15 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.82/6.15 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_diff
% 5.82/6.15 thf(fact_6731_finite__divisors__nat,axiom,
% 5.82/6.15 ! [M: nat] :
% 5.82/6.15 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ M ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_divisors_nat
% 5.82/6.15 thf(fact_6732_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.82/6.15 ! [N7: set_nat,N: nat] :
% 5.82/6.15 ( ( ord_less_eq_set_nat @ N7 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.82/6.15 => ( finite_finite_nat @ N7 ) ) ).
% 5.82/6.15
% 5.82/6.15 % subset_eq_atLeast0_lessThan_finite
% 5.82/6.15 thf(fact_6733_subset__eq__atLeast0__atMost__finite,axiom,
% 5.82/6.15 ! [N7: set_nat,N: nat] :
% 5.82/6.15 ( ( ord_less_eq_set_nat @ N7 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.15 => ( finite_finite_nat @ N7 ) ) ).
% 5.82/6.15
% 5.82/6.15 % subset_eq_atLeast0_atMost_finite
% 5.82/6.15 thf(fact_6734_set__replicate__Suc,axiom,
% 5.82/6.15 ! [N: nat,X2: real] :
% 5.82/6.15 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X2 ) )
% 5.82/6.15 = ( insert_real @ X2 @ bot_bot_set_real ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_Suc
% 5.82/6.15 thf(fact_6735_set__replicate__Suc,axiom,
% 5.82/6.15 ! [N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X2 ) )
% 5.82/6.15 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_Suc
% 5.82/6.15 thf(fact_6736_set__replicate__Suc,axiom,
% 5.82/6.15 ! [N: nat,X2: nat] :
% 5.82/6.15 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X2 ) )
% 5.82/6.15 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_Suc
% 5.82/6.15 thf(fact_6737_set__replicate__Suc,axiom,
% 5.82/6.15 ! [N: nat,X2: int] :
% 5.82/6.15 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X2 ) )
% 5.82/6.15 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_Suc
% 5.82/6.15 thf(fact_6738_set__replicate__conv__if,axiom,
% 5.82/6.15 ! [N: nat,X2: real] :
% 5.82/6.15 ( ( ( N = zero_zero_nat )
% 5.82/6.15 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.82/6.15 = bot_bot_set_real ) )
% 5.82/6.15 & ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.82/6.15 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_conv_if
% 5.82/6.15 thf(fact_6739_set__replicate__conv__if,axiom,
% 5.82/6.15 ! [N: nat,X2: vEBT_VEBT] :
% 5.82/6.15 ( ( ( N = zero_zero_nat )
% 5.82/6.15 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = bot_bo8194388402131092736T_VEBT ) )
% 5.82/6.15 & ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.82/6.15 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_conv_if
% 5.82/6.15 thf(fact_6740_set__replicate__conv__if,axiom,
% 5.82/6.15 ! [N: nat,X2: nat] :
% 5.82/6.15 ( ( ( N = zero_zero_nat )
% 5.82/6.15 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.82/6.15 = bot_bot_set_nat ) )
% 5.82/6.15 & ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.82/6.15 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_conv_if
% 5.82/6.15 thf(fact_6741_set__replicate__conv__if,axiom,
% 5.82/6.15 ! [N: nat,X2: int] :
% 5.82/6.15 ( ( ( N = zero_zero_nat )
% 5.82/6.15 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.82/6.15 = bot_bot_set_int ) )
% 5.82/6.15 & ( ( N != zero_zero_nat )
% 5.82/6.15 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.82/6.15 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_replicate_conv_if
% 5.82/6.15 thf(fact_6742_powr__less__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ ( powr_real @ B2 @ Y3 ) @ X2 )
% 5.82/6.15 = ( ord_less_real @ Y3 @ ( log @ B2 @ X2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_less_iff
% 5.82/6.15 thf(fact_6743_less__powr__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ X2 @ ( powr_real @ B2 @ Y3 ) )
% 5.82/6.15 = ( ord_less_real @ ( log @ B2 @ X2 ) @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % less_powr_iff
% 5.82/6.15 thf(fact_6744_log__less__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ ( log @ B2 @ X2 ) @ Y3 )
% 5.82/6.15 = ( ord_less_real @ X2 @ ( powr_real @ B2 @ Y3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % log_less_iff
% 5.82/6.15 thf(fact_6745_less__log__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_real @ Y3 @ ( log @ B2 @ X2 ) )
% 5.82/6.15 = ( ord_less_real @ ( powr_real @ B2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % less_log_iff
% 5.82/6.15 thf(fact_6746_finite__roots__unity,axiom,
% 5.82/6.15 ! [N: nat] :
% 5.82/6.15 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.15 => ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [Z4: real] :
% 5.82/6.15 ( ( power_power_real @ Z4 @ N )
% 5.82/6.15 = one_one_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_roots_unity
% 5.82/6.15 thf(fact_6747_finite__roots__unity,axiom,
% 5.82/6.15 ! [N: nat] :
% 5.82/6.15 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Z4: complex] :
% 5.82/6.15 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.15 = one_one_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_roots_unity
% 5.82/6.15 thf(fact_6748_powr__mult__base,axiom,
% 5.82/6.15 ! [X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( times_times_real @ X2 @ ( powr_real @ X2 @ Y3 ) )
% 5.82/6.15 = ( powr_real @ X2 @ ( plus_plus_real @ one_one_real @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_mult_base
% 5.82/6.15 thf(fact_6749_powr__le__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ ( powr_real @ B2 @ Y3 ) @ X2 )
% 5.82/6.15 = ( ord_less_eq_real @ Y3 @ ( log @ B2 @ X2 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % powr_le_iff
% 5.82/6.15 thf(fact_6750_le__powr__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B2 @ Y3 ) )
% 5.82/6.15 = ( ord_less_eq_real @ ( log @ B2 @ X2 ) @ Y3 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % le_powr_iff
% 5.82/6.15 thf(fact_6751_log__le__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ ( log @ B2 @ X2 ) @ Y3 )
% 5.82/6.15 = ( ord_less_eq_real @ X2 @ ( powr_real @ B2 @ Y3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % log_le_iff
% 5.82/6.15 thf(fact_6752_le__log__iff,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( ord_less_eq_real @ Y3 @ ( log @ B2 @ X2 ) )
% 5.82/6.15 = ( ord_less_eq_real @ ( powr_real @ B2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % le_log_iff
% 5.82/6.15 thf(fact_6753_log__add__eq__powr,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.15 => ( ( B2 != one_one_real )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( plus_plus_real @ ( log @ B2 @ X2 ) @ Y3 )
% 5.82/6.15 = ( log @ B2 @ ( times_times_real @ X2 @ ( powr_real @ B2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % log_add_eq_powr
% 5.82/6.15 thf(fact_6754_add__log__eq__powr,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.15 => ( ( B2 != one_one_real )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( plus_plus_real @ Y3 @ ( log @ B2 @ X2 ) )
% 5.82/6.15 = ( log @ B2 @ ( times_times_real @ ( powr_real @ B2 @ Y3 ) @ X2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % add_log_eq_powr
% 5.82/6.15 thf(fact_6755_minus__log__eq__powr,axiom,
% 5.82/6.15 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.15 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.15 => ( ( B2 != one_one_real )
% 5.82/6.15 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.15 => ( ( minus_minus_real @ Y3 @ ( log @ B2 @ X2 ) )
% 5.82/6.15 = ( log @ B2 @ ( divide_divide_real @ ( powr_real @ B2 @ Y3 ) @ X2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % minus_log_eq_powr
% 5.82/6.15 thf(fact_6756_vebt__buildup_Osimps_I3_J,axiom,
% 5.82/6.15 ! [Va: nat] :
% 5.82/6.15 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.15 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.15 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.15 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.82/6.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % vebt_buildup.simps(3)
% 5.82/6.15 thf(fact_6757_finite__Diff__insert,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,A2: vEBT_VEBT,B: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ B ) ) )
% 5.82/6.15 = ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff_insert
% 5.82/6.15 thf(fact_6758_finite__Diff__insert,axiom,
% 5.82/6.15 ! [A: set_int,A2: int,B: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B ) ) )
% 5.82/6.15 = ( finite_finite_int @ ( minus_minus_set_int @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff_insert
% 5.82/6.15 thf(fact_6759_finite__Diff__insert,axiom,
% 5.82/6.15 ! [A: set_Code_integer,A2: code_integer,B: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ B ) ) )
% 5.82/6.15 = ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff_insert
% 5.82/6.15 thf(fact_6760_finite__Diff__insert,axiom,
% 5.82/6.15 ! [A: set_complex,A2: complex,B: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ B ) ) )
% 5.82/6.15 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff_insert
% 5.82/6.15 thf(fact_6761_finite__Diff__insert,axiom,
% 5.82/6.15 ! [A: set_nat,A2: nat,B: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B ) ) )
% 5.82/6.15 = ( finite_finite_nat @ ( minus_minus_set_nat @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff_insert
% 5.82/6.15 thf(fact_6762_finite__Collect__le__nat,axiom,
% 5.82/6.15 ! [K: nat] :
% 5.82/6.15 ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_le_nat
% 5.82/6.15 thf(fact_6763_finite__Collect__less__nat,axiom,
% 5.82/6.15 ! [K: nat] :
% 5.82/6.15 ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [N4: nat] : ( ord_less_nat @ N4 @ K ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_less_nat
% 5.82/6.15 thf(fact_6764_finite__Collect__subsets,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( finite1152437895449049373et_nat
% 5.82/6.15 @ ( collect_set_nat
% 5.82/6.15 @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_subsets
% 5.82/6.15 thf(fact_6765_finite__Collect__subsets,axiom,
% 5.82/6.15 ! [A: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( finite6931041176100689706nteger
% 5.82/6.15 @ ( collec574505750873337192nteger
% 5.82/6.15 @ ^ [B5: set_Code_integer] : ( ord_le7084787975880047091nteger @ B5 @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_subsets
% 5.82/6.15 thf(fact_6766_finite__Collect__subsets,axiom,
% 5.82/6.15 ! [A: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( finite6551019134538273531omplex
% 5.82/6.15 @ ( collect_set_complex
% 5.82/6.15 @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_subsets
% 5.82/6.15 thf(fact_6767_finite__Collect__subsets,axiom,
% 5.82/6.15 ! [A: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( finite6197958912794628473et_int
% 5.82/6.15 @ ( collect_set_int
% 5.82/6.15 @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_subsets
% 5.82/6.15 thf(fact_6768_finite__induct__select,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ! [T4: set_VEBT_VEBT] :
% 5.82/6.15 ( ( ord_le3480810397992357184T_VEBT @ T4 @ S )
% 5.82/6.15 => ( ( P @ T4 )
% 5.82/6.15 => ? [X8: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X8 @ ( minus_5127226145743854075T_VEBT @ S @ T4 ) )
% 5.82/6.15 & ( P @ ( insert_VEBT_VEBT @ X8 @ T4 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_induct_select
% 5.82/6.15 thf(fact_6769_finite__induct__select,axiom,
% 5.82/6.15 ! [S: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [T4: set_Code_integer] :
% 5.82/6.15 ( ( ord_le1307284697595431911nteger @ T4 @ S )
% 5.82/6.15 => ( ( P @ T4 )
% 5.82/6.15 => ? [X8: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X8 @ ( minus_2355218937544613996nteger @ S @ T4 ) )
% 5.82/6.15 & ( P @ ( insert_Code_integer @ X8 @ T4 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_induct_select
% 5.82/6.15 thf(fact_6770_finite__induct__select,axiom,
% 5.82/6.15 ! [S: set_complex,P: set_complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ! [T4: set_complex] :
% 5.82/6.15 ( ( ord_less_set_complex @ T4 @ S )
% 5.82/6.15 => ( ( P @ T4 )
% 5.82/6.15 => ? [X8: complex] :
% 5.82/6.15 ( ( member_complex @ X8 @ ( minus_811609699411566653omplex @ S @ T4 ) )
% 5.82/6.15 & ( P @ ( insert_complex @ X8 @ T4 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_induct_select
% 5.82/6.15 thf(fact_6771_finite__induct__select,axiom,
% 5.82/6.15 ! [S: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [T4: set_int] :
% 5.82/6.15 ( ( ord_less_set_int @ T4 @ S )
% 5.82/6.15 => ( ( P @ T4 )
% 5.82/6.15 => ? [X8: int] :
% 5.82/6.15 ( ( member_int @ X8 @ ( minus_minus_set_int @ S @ T4 ) )
% 5.82/6.15 & ( P @ ( insert_int @ X8 @ T4 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_induct_select
% 5.82/6.15 thf(fact_6772_finite__induct__select,axiom,
% 5.82/6.15 ! [S: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [T4: set_nat] :
% 5.82/6.15 ( ( ord_less_set_nat @ T4 @ S )
% 5.82/6.15 => ( ( P @ T4 )
% 5.82/6.15 => ? [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ ( minus_minus_set_nat @ S @ T4 ) )
% 5.82/6.15 & ( P @ ( insert_nat @ X8 @ T4 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_induct_select
% 5.82/6.15 thf(fact_6773_finite__Collect__disjI,axiom,
% 5.82/6.15 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.82/6.15 ( ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 | ( Q @ X3 ) ) ) )
% 5.82/6.15 = ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.82/6.15 & ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_disjI
% 5.82/6.15 thf(fact_6774_finite__Collect__disjI,axiom,
% 5.82/6.15 ! [P: nat > $o,Q: nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 | ( Q @ X3 ) ) ) )
% 5.82/6.15 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.15 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_disjI
% 5.82/6.15 thf(fact_6775_finite__Collect__disjI,axiom,
% 5.82/6.15 ! [P: int > $o,Q: int > $o] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 | ( Q @ X3 ) ) ) )
% 5.82/6.15 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.82/6.15 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_disjI
% 5.82/6.15 thf(fact_6776_finite__Collect__disjI,axiom,
% 5.82/6.15 ! [P: code_integer > $o,Q: code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 | ( Q @ X3 ) ) ) )
% 5.82/6.15 = ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.82/6.15 & ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_disjI
% 5.82/6.15 thf(fact_6777_finite__Collect__disjI,axiom,
% 5.82/6.15 ! [P: complex > $o,Q: complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 | ( Q @ X3 ) ) ) )
% 5.82/6.15 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.82/6.15 & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_disjI
% 5.82/6.15 thf(fact_6778_finite__Collect__conjI,axiom,
% 5.82/6.15 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.82/6.15 ( ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.82/6.15 | ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) )
% 5.82/6.15 => ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 & ( Q @ X3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_conjI
% 5.82/6.15 thf(fact_6779_finite__Collect__conjI,axiom,
% 5.82/6.15 ! [P: nat > $o,Q: nat > $o] :
% 5.82/6.15 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.15 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 & ( Q @ X3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_conjI
% 5.82/6.15 thf(fact_6780_finite__Collect__conjI,axiom,
% 5.82/6.15 ! [P: int > $o,Q: int > $o] :
% 5.82/6.15 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.82/6.15 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 & ( Q @ X3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_conjI
% 5.82/6.15 thf(fact_6781_finite__Collect__conjI,axiom,
% 5.82/6.15 ! [P: code_integer > $o,Q: code_integer > $o] :
% 5.82/6.15 ( ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.82/6.15 | ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q ) ) )
% 5.82/6.15 => ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 & ( Q @ X3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_conjI
% 5.82/6.15 thf(fact_6782_finite__Collect__conjI,axiom,
% 5.82/6.15 ! [P: complex > $o,Q: complex > $o] :
% 5.82/6.15 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.82/6.15 | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] :
% 5.82/6.15 ( ( P @ X3 )
% 5.82/6.15 & ( Q @ X3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Collect_conjI
% 5.82/6.15 thf(fact_6783_finite__interval__int1,axiom,
% 5.82/6.15 ! [A2: int,B2: int] :
% 5.82/6.15 ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( ord_less_eq_int @ A2 @ I4 )
% 5.82/6.15 & ( ord_less_eq_int @ I4 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_interval_int1
% 5.82/6.15 thf(fact_6784_finite__interval__int4,axiom,
% 5.82/6.15 ! [A2: int,B2: int] :
% 5.82/6.15 ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( ord_less_int @ A2 @ I4 )
% 5.82/6.15 & ( ord_less_int @ I4 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_interval_int4
% 5.82/6.15 thf(fact_6785_finite__atLeastLessThan__integer,axiom,
% 5.82/6.15 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_atLeastLessThan_integer
% 5.82/6.15 thf(fact_6786_finite__atLeastAtMost__integer,axiom,
% 5.82/6.15 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_atLeastAtMost_integer
% 5.82/6.15 thf(fact_6787_finite__Diff,axiom,
% 5.82/6.15 ! [A: set_int,B: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( finite_finite_int @ ( minus_minus_set_int @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff
% 5.82/6.15 thf(fact_6788_finite__Diff,axiom,
% 5.82/6.15 ! [A: set_Code_integer,B: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff
% 5.82/6.15 thf(fact_6789_finite__Diff,axiom,
% 5.82/6.15 ! [A: set_complex,B: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff
% 5.82/6.15 thf(fact_6790_finite__Diff,axiom,
% 5.82/6.15 ! [A: set_nat,B: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( finite_finite_nat @ ( minus_minus_set_nat @ A @ B ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff
% 5.82/6.15 thf(fact_6791_finite__Diff2,axiom,
% 5.82/6.15 ! [B: set_int,A: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ B )
% 5.82/6.15 => ( ( finite_finite_int @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.15 = ( finite_finite_int @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff2
% 5.82/6.15 thf(fact_6792_finite__Diff2,axiom,
% 5.82/6.15 ! [B: set_Code_integer,A: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A @ B ) )
% 5.82/6.15 = ( finite6017078050557962740nteger @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff2
% 5.82/6.15 thf(fact_6793_finite__Diff2,axiom,
% 5.82/6.15 ! [B: set_complex,A: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A @ B ) )
% 5.82/6.15 = ( finite3207457112153483333omplex @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff2
% 5.82/6.15 thf(fact_6794_finite__Diff2,axiom,
% 5.82/6.15 ! [B: set_nat,A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.15 = ( finite_finite_nat @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_Diff2
% 5.82/6.15 thf(fact_6795_finite__interval__int2,axiom,
% 5.82/6.15 ! [A2: int,B2: int] :
% 5.82/6.15 ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( ord_less_eq_int @ A2 @ I4 )
% 5.82/6.15 & ( ord_less_int @ I4 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_interval_int2
% 5.82/6.15 thf(fact_6796_finite__interval__int3,axiom,
% 5.82/6.15 ! [A2: int,B2: int] :
% 5.82/6.15 ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( ord_less_int @ A2 @ I4 )
% 5.82/6.15 & ( ord_less_eq_int @ I4 @ B2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_interval_int3
% 5.82/6.15 thf(fact_6797_finite__atLeastZeroLessThan__integer,axiom,
% 5.82/6.15 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_atLeastZeroLessThan_integer
% 5.82/6.15 thf(fact_6798_finite__maxlen,axiom,
% 5.82/6.15 ! [M8: set_list_VEBT_VEBT] :
% 5.82/6.15 ( ( finite3004134309566078307T_VEBT @ M8 )
% 5.82/6.15 => ? [N3: nat] :
% 5.82/6.15 ! [X8: list_VEBT_VEBT] :
% 5.82/6.15 ( ( member2936631157270082147T_VEBT @ X8 @ M8 )
% 5.82/6.15 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X8 ) @ N3 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_maxlen
% 5.82/6.15 thf(fact_6799_finite__maxlen,axiom,
% 5.82/6.15 ! [M8: set_list_real] :
% 5.82/6.15 ( ( finite306553202115118035t_real @ M8 )
% 5.82/6.15 => ? [N3: nat] :
% 5.82/6.15 ! [X8: list_real] :
% 5.82/6.15 ( ( member_list_real @ X8 @ M8 )
% 5.82/6.15 => ( ord_less_nat @ ( size_size_list_real @ X8 ) @ N3 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_maxlen
% 5.82/6.15 thf(fact_6800_finite__maxlen,axiom,
% 5.82/6.15 ! [M8: set_list_o] :
% 5.82/6.15 ( ( finite_finite_list_o @ M8 )
% 5.82/6.15 => ? [N3: nat] :
% 5.82/6.15 ! [X8: list_o] :
% 5.82/6.15 ( ( member_list_o @ X8 @ M8 )
% 5.82/6.15 => ( ord_less_nat @ ( size_size_list_o @ X8 ) @ N3 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_maxlen
% 5.82/6.15 thf(fact_6801_finite__maxlen,axiom,
% 5.82/6.15 ! [M8: set_list_nat] :
% 5.82/6.15 ( ( finite8100373058378681591st_nat @ M8 )
% 5.82/6.15 => ? [N3: nat] :
% 5.82/6.15 ! [X8: list_nat] :
% 5.82/6.15 ( ( member_list_nat @ X8 @ M8 )
% 5.82/6.15 => ( ord_less_nat @ ( size_size_list_nat @ X8 ) @ N3 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_maxlen
% 5.82/6.15 thf(fact_6802_finite__maxlen,axiom,
% 5.82/6.15 ! [M8: set_list_VEBT_VEBTi] :
% 5.82/6.15 ( ( finite5722435864697464412_VEBTi @ M8 )
% 5.82/6.15 => ? [N3: nat] :
% 5.82/6.15 ! [X8: list_VEBT_VEBTi] :
% 5.82/6.15 ( ( member8117914210271334748_VEBTi @ X8 @ M8 )
% 5.82/6.15 => ( ord_less_nat @ ( size_s7982070591426661849_VEBTi @ X8 ) @ N3 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_maxlen
% 5.82/6.15 thf(fact_6803_finite__divisors__int,axiom,
% 5.82/6.15 ! [I: int] :
% 5.82/6.15 ( ( I != zero_zero_int )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [D3: int] : ( dvd_dvd_int @ D3 @ I ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_divisors_int
% 5.82/6.15 thf(fact_6804_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,B: set_nat,R: vEBT_VEBT > nat > $o] :
% 5.82/6.15 ( ~ ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.15 => ? [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ B )
% 5.82/6.15 & ~ ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [A5: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6805_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_real,B: set_nat,R: real > nat > $o] :
% 5.82/6.15 ( ~ ( finite_finite_real @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ A )
% 5.82/6.15 => ? [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ B )
% 5.82/6.15 & ~ ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [A5: real] :
% 5.82/6.15 ( ( member_real @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6806_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,B: set_int,R: vEBT_VEBT > int > $o] :
% 5.82/6.15 ( ~ ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( finite_finite_int @ B )
% 5.82/6.15 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.15 => ? [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ B )
% 5.82/6.15 & ~ ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [A5: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6807_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_real,B: set_int,R: real > int > $o] :
% 5.82/6.15 ( ~ ( finite_finite_real @ A )
% 5.82/6.15 => ( ( finite_finite_int @ B )
% 5.82/6.15 => ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ A )
% 5.82/6.15 => ? [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ B )
% 5.82/6.15 & ~ ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [A5: real] :
% 5.82/6.15 ( ( member_real @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6808_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,B: set_Code_integer,R: vEBT_VEBT > code_integer > $o] :
% 5.82/6.15 ( ~ ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.15 => ? [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ B )
% 5.82/6.15 & ~ ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [A5: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6809_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_real,B: set_Code_integer,R: real > code_integer > $o] :
% 5.82/6.15 ( ~ ( finite_finite_real @ A )
% 5.82/6.15 => ( ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ A )
% 5.82/6.15 => ? [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ B )
% 5.82/6.15 & ~ ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [A5: real] :
% 5.82/6.15 ( ( member_real @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6810_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,B: set_complex,R: vEBT_VEBT > complex > $o] :
% 5.82/6.15 ( ~ ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.15 => ? [Xa2: complex] :
% 5.82/6.15 ( ( member_complex @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: complex] :
% 5.82/6.15 ( ( member_complex @ X4 @ B )
% 5.82/6.15 & ~ ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [A5: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6811_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_real,B: set_complex,R: real > complex > $o] :
% 5.82/6.15 ( ~ ( finite_finite_real @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ A )
% 5.82/6.15 => ? [Xa2: complex] :
% 5.82/6.15 ( ( member_complex @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: complex] :
% 5.82/6.15 ( ( member_complex @ X4 @ B )
% 5.82/6.15 & ~ ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [A5: real] :
% 5.82/6.15 ( ( member_real @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6812_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_nat,B: set_nat,R: nat > nat > $o] :
% 5.82/6.15 ( ~ ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ A )
% 5.82/6.15 => ? [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ B )
% 5.82/6.15 & ~ ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [A5: nat] :
% 5.82/6.15 ( ( member_nat @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6813_pigeonhole__infinite__rel,axiom,
% 5.82/6.15 ! [A: set_nat,B: set_int,R: nat > int > $o] :
% 5.82/6.15 ( ~ ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( finite_finite_int @ B )
% 5.82/6.15 => ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ A )
% 5.82/6.15 => ? [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ B )
% 5.82/6.15 & ( R @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ B )
% 5.82/6.15 & ~ ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [A5: nat] :
% 5.82/6.15 ( ( member_nat @ A5 @ A )
% 5.82/6.15 & ( R @ A5 @ X4 ) ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % pigeonhole_infinite_rel
% 5.82/6.15 thf(fact_6814_not__finite__existsD,axiom,
% 5.82/6.15 ! [P: product_prod_int_int > $o] :
% 5.82/6.15 ( ~ ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.82/6.15 => ? [X_1: product_prod_int_int] : ( P @ X_1 ) ) ).
% 5.82/6.15
% 5.82/6.15 % not_finite_existsD
% 5.82/6.15 thf(fact_6815_not__finite__existsD,axiom,
% 5.82/6.15 ! [P: nat > $o] :
% 5.82/6.15 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.15 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 5.82/6.15
% 5.82/6.15 % not_finite_existsD
% 5.82/6.15 thf(fact_6816_not__finite__existsD,axiom,
% 5.82/6.15 ! [P: int > $o] :
% 5.82/6.15 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 5.82/6.15 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 5.82/6.15
% 5.82/6.15 % not_finite_existsD
% 5.82/6.15 thf(fact_6817_not__finite__existsD,axiom,
% 5.82/6.15 ! [P: code_integer > $o] :
% 5.82/6.15 ( ~ ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.82/6.15 => ? [X_1: code_integer] : ( P @ X_1 ) ) ).
% 5.82/6.15
% 5.82/6.15 % not_finite_existsD
% 5.82/6.15 thf(fact_6818_not__finite__existsD,axiom,
% 5.82/6.15 ! [P: complex > $o] :
% 5.82/6.15 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.82/6.15 => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 5.82/6.15
% 5.82/6.15 % not_finite_existsD
% 5.82/6.15 thf(fact_6819_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_real,A2: real] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( member_real @ A2 @ A )
% 5.82/6.15 => ? [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_real @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: real] :
% 5.82/6.15 ( ( member_real @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_real @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6820_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_Code_integer,A2: code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( member_Code_integer @ A2 @ A )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.15 & ( ord_le3102999989581377725nteger @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_le3102999989581377725nteger @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6821_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_set_int,A2: set_int] :
% 5.82/6.15 ( ( finite6197958912794628473et_int @ A )
% 5.82/6.15 => ( ( member_set_int @ A2 @ A )
% 5.82/6.15 => ? [X4: set_int] :
% 5.82/6.15 ( ( member_set_int @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_set_int @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: set_int] :
% 5.82/6.15 ( ( member_set_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6822_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_rat,A2: rat] :
% 5.82/6.15 ( ( finite_finite_rat @ A )
% 5.82/6.15 => ( ( member_rat @ A2 @ A )
% 5.82/6.15 => ? [X4: rat] :
% 5.82/6.15 ( ( member_rat @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_rat @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: rat] :
% 5.82/6.15 ( ( member_rat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_rat @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6823_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_num,A2: num] :
% 5.82/6.15 ( ( finite_finite_num @ A )
% 5.82/6.15 => ( ( member_num @ A2 @ A )
% 5.82/6.15 => ? [X4: num] :
% 5.82/6.15 ( ( member_num @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_num @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: num] :
% 5.82/6.15 ( ( member_num @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_num @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6824_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_nat,A2: nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( member_nat @ A2 @ A )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_nat @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6825_finite__has__minimal2,axiom,
% 5.82/6.15 ! [A: set_int,A2: int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( member_int @ A2 @ A )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_int @ X4 @ A2 )
% 5.82/6.15 & ! [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_int @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal2
% 5.82/6.15 thf(fact_6826_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_real,A2: real] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( member_real @ A2 @ A )
% 5.82/6.15 => ? [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: real] :
% 5.82/6.15 ( ( member_real @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_real @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6827_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_Code_integer,A2: code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( member_Code_integer @ A2 @ A )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.15 & ( ord_le3102999989581377725nteger @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_le3102999989581377725nteger @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6828_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_set_int,A2: set_int] :
% 5.82/6.15 ( ( finite6197958912794628473et_int @ A )
% 5.82/6.15 => ( ( member_set_int @ A2 @ A )
% 5.82/6.15 => ? [X4: set_int] :
% 5.82/6.15 ( ( member_set_int @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_set_int @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: set_int] :
% 5.82/6.15 ( ( member_set_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6829_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_rat,A2: rat] :
% 5.82/6.15 ( ( finite_finite_rat @ A )
% 5.82/6.15 => ( ( member_rat @ A2 @ A )
% 5.82/6.15 => ? [X4: rat] :
% 5.82/6.15 ( ( member_rat @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_rat @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: rat] :
% 5.82/6.15 ( ( member_rat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_rat @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6830_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_num,A2: num] :
% 5.82/6.15 ( ( finite_finite_num @ A )
% 5.82/6.15 => ( ( member_num @ A2 @ A )
% 5.82/6.15 => ? [X4: num] :
% 5.82/6.15 ( ( member_num @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_num @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: num] :
% 5.82/6.15 ( ( member_num @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_num @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6831_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_nat,A2: nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( member_nat @ A2 @ A )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_nat @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_nat @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6832_finite__has__maximal2,axiom,
% 5.82/6.15 ! [A: set_int,A2: int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( member_int @ A2 @ A )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ A )
% 5.82/6.15 & ( ord_less_eq_int @ A2 @ X4 )
% 5.82/6.15 & ! [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_int @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal2
% 5.82/6.15 thf(fact_6833_finite__subset,axiom,
% 5.82/6.15 ! [A: set_nat,B: set_nat] :
% 5.82/6.15 ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( finite_finite_nat @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset
% 5.82/6.15 thf(fact_6834_finite__subset,axiom,
% 5.82/6.15 ! [A: set_Code_integer,B: set_Code_integer] :
% 5.82/6.15 ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.15 => ( ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( finite6017078050557962740nteger @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset
% 5.82/6.15 thf(fact_6835_finite__subset,axiom,
% 5.82/6.15 ! [A: set_complex,B: set_complex] :
% 5.82/6.15 ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( finite3207457112153483333omplex @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset
% 5.82/6.15 thf(fact_6836_finite__subset,axiom,
% 5.82/6.15 ! [A: set_int,B: set_int] :
% 5.82/6.15 ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.15 => ( ( finite_finite_int @ B )
% 5.82/6.15 => ( finite_finite_int @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset
% 5.82/6.15 thf(fact_6837_infinite__super,axiom,
% 5.82/6.15 ! [S: set_nat,T5: set_nat] :
% 5.82/6.15 ( ( ord_less_eq_set_nat @ S @ T5 )
% 5.82/6.15 => ( ~ ( finite_finite_nat @ S )
% 5.82/6.15 => ~ ( finite_finite_nat @ T5 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_super
% 5.82/6.15 thf(fact_6838_infinite__super,axiom,
% 5.82/6.15 ! [S: set_Code_integer,T5: set_Code_integer] :
% 5.82/6.15 ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.15 => ( ~ ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ~ ( finite6017078050557962740nteger @ T5 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_super
% 5.82/6.15 thf(fact_6839_infinite__super,axiom,
% 5.82/6.15 ! [S: set_complex,T5: set_complex] :
% 5.82/6.15 ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.15 => ( ~ ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ~ ( finite3207457112153483333omplex @ T5 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_super
% 5.82/6.15 thf(fact_6840_infinite__super,axiom,
% 5.82/6.15 ! [S: set_int,T5: set_int] :
% 5.82/6.15 ( ( ord_less_eq_set_int @ S @ T5 )
% 5.82/6.15 => ( ~ ( finite_finite_int @ S )
% 5.82/6.15 => ~ ( finite_finite_int @ T5 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_super
% 5.82/6.15 thf(fact_6841_rev__finite__subset,axiom,
% 5.82/6.15 ! [B: set_nat,A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.15 => ( finite_finite_nat @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % rev_finite_subset
% 5.82/6.15 thf(fact_6842_rev__finite__subset,axiom,
% 5.82/6.15 ! [B: set_Code_integer,A: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.15 => ( finite6017078050557962740nteger @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % rev_finite_subset
% 5.82/6.15 thf(fact_6843_rev__finite__subset,axiom,
% 5.82/6.15 ! [B: set_complex,A: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.15 => ( finite3207457112153483333omplex @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % rev_finite_subset
% 5.82/6.15 thf(fact_6844_rev__finite__subset,axiom,
% 5.82/6.15 ! [B: set_int,A: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ B )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.15 => ( finite_finite_int @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % rev_finite_subset
% 5.82/6.15 thf(fact_6845_Diff__infinite__finite,axiom,
% 5.82/6.15 ! [T5: set_int,S: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ T5 )
% 5.82/6.15 => ( ~ ( finite_finite_int @ S )
% 5.82/6.15 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ T5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Diff_infinite_finite
% 5.82/6.15 thf(fact_6846_Diff__infinite__finite,axiom,
% 5.82/6.15 ! [T5: set_Code_integer,S: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.15 => ( ~ ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S @ T5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Diff_infinite_finite
% 5.82/6.15 thf(fact_6847_Diff__infinite__finite,axiom,
% 5.82/6.15 ! [T5: set_complex,S: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.15 => ( ~ ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S @ T5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Diff_infinite_finite
% 5.82/6.15 thf(fact_6848_Diff__infinite__finite,axiom,
% 5.82/6.15 ! [T5: set_nat,S: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ T5 )
% 5.82/6.15 => ( ~ ( finite_finite_nat @ S )
% 5.82/6.15 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ T5 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % Diff_infinite_finite
% 5.82/6.15 thf(fact_6849_finite__has__maximal,axiom,
% 5.82/6.15 ! [A: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( A != bot_bo3990330152332043303nteger )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.15 & ! [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_le3102999989581377725nteger @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal
% 5.82/6.15 thf(fact_6850_finite__has__maximal,axiom,
% 5.82/6.15 ! [A: set_set_int] :
% 5.82/6.15 ( ( finite6197958912794628473et_int @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_set_int )
% 5.82/6.15 => ? [X4: set_int] :
% 5.82/6.15 ( ( member_set_int @ X4 @ A )
% 5.82/6.15 & ! [Xa2: set_int] :
% 5.82/6.15 ( ( member_set_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal
% 5.82/6.15 thf(fact_6851_finite__has__maximal,axiom,
% 5.82/6.15 ! [A: set_rat] :
% 5.82/6.15 ( ( finite_finite_rat @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_rat )
% 5.82/6.15 => ? [X4: rat] :
% 5.82/6.15 ( ( member_rat @ X4 @ A )
% 5.82/6.15 & ! [Xa2: rat] :
% 5.82/6.15 ( ( member_rat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_rat @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal
% 5.82/6.15 thf(fact_6852_finite__has__maximal,axiom,
% 5.82/6.15 ! [A: set_num] :
% 5.82/6.15 ( ( finite_finite_num @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_num )
% 5.82/6.15 => ? [X4: num] :
% 5.82/6.15 ( ( member_num @ X4 @ A )
% 5.82/6.15 & ! [Xa2: num] :
% 5.82/6.15 ( ( member_num @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_num @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal
% 5.82/6.15 thf(fact_6853_finite__has__maximal,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_nat )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ A )
% 5.82/6.15 & ! [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_nat @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal
% 5.82/6.15 thf(fact_6854_finite__has__maximal,axiom,
% 5.82/6.15 ! [A: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_int )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ A )
% 5.82/6.15 & ! [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_int @ X4 @ Xa2 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_maximal
% 5.82/6.15 thf(fact_6855_finite__has__minimal,axiom,
% 5.82/6.15 ! [A: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( A != bot_bo3990330152332043303nteger )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.15 & ! [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_le3102999989581377725nteger @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal
% 5.82/6.15 thf(fact_6856_finite__has__minimal,axiom,
% 5.82/6.15 ! [A: set_set_int] :
% 5.82/6.15 ( ( finite6197958912794628473et_int @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_set_int )
% 5.82/6.15 => ? [X4: set_int] :
% 5.82/6.15 ( ( member_set_int @ X4 @ A )
% 5.82/6.15 & ! [Xa2: set_int] :
% 5.82/6.15 ( ( member_set_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal
% 5.82/6.15 thf(fact_6857_finite__has__minimal,axiom,
% 5.82/6.15 ! [A: set_rat] :
% 5.82/6.15 ( ( finite_finite_rat @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_rat )
% 5.82/6.15 => ? [X4: rat] :
% 5.82/6.15 ( ( member_rat @ X4 @ A )
% 5.82/6.15 & ! [Xa2: rat] :
% 5.82/6.15 ( ( member_rat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_rat @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal
% 5.82/6.15 thf(fact_6858_finite__has__minimal,axiom,
% 5.82/6.15 ! [A: set_num] :
% 5.82/6.15 ( ( finite_finite_num @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_num )
% 5.82/6.15 => ? [X4: num] :
% 5.82/6.15 ( ( member_num @ X4 @ A )
% 5.82/6.15 & ! [Xa2: num] :
% 5.82/6.15 ( ( member_num @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_num @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal
% 5.82/6.15 thf(fact_6859_finite__has__minimal,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_nat )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ A )
% 5.82/6.15 & ! [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_nat @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal
% 5.82/6.15 thf(fact_6860_finite__has__minimal,axiom,
% 5.82/6.15 ! [A: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( A != bot_bot_set_int )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ A )
% 5.82/6.15 & ! [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ A )
% 5.82/6.15 => ( ( ord_less_eq_int @ Xa2 @ X4 )
% 5.82/6.15 => ( X4 = Xa2 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_has_minimal
% 5.82/6.15 thf(fact_6861_finite__subset__induct_H,axiom,
% 5.82/6.15 ! [F3: set_VEBT_VEBT,A: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ F3 )
% 5.82/6.15 => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ! [A3: vEBT_VEBT,F6: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ F6 )
% 5.82/6.15 => ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.15 => ( ( ord_le4337996190870823476T_VEBT @ F6 @ A )
% 5.82/6.15 => ( ~ ( member_VEBT_VEBT @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_VEBT_VEBT @ A3 @ F6 ) ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct'
% 5.82/6.15 thf(fact_6862_finite__subset__induct_H,axiom,
% 5.82/6.15 ! [F3: set_real,A: set_real,P: set_real > $o] :
% 5.82/6.15 ( ( finite_finite_real @ F3 )
% 5.82/6.15 => ( ( ord_less_eq_set_real @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [A3: real,F6: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ F6 )
% 5.82/6.15 => ( ( member_real @ A3 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_real @ F6 @ A )
% 5.82/6.15 => ( ~ ( member_real @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_real @ A3 @ F6 ) ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct'
% 5.82/6.15 thf(fact_6863_finite__subset__induct_H,axiom,
% 5.82/6.15 ! [F3: set_Code_integer,A: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ F3 )
% 5.82/6.15 => ( ( ord_le7084787975880047091nteger @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [A3: code_integer,F6: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ F6 )
% 5.82/6.15 => ( ( member_Code_integer @ A3 @ A )
% 5.82/6.15 => ( ( ord_le7084787975880047091nteger @ F6 @ A )
% 5.82/6.15 => ( ~ ( member_Code_integer @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_Code_integer @ A3 @ F6 ) ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct'
% 5.82/6.15 thf(fact_6864_finite__subset__induct_H,axiom,
% 5.82/6.15 ! [F3: set_complex,A: set_complex,P: set_complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ F3 )
% 5.82/6.15 => ( ( ord_le211207098394363844omplex @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ! [A3: complex,F6: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ F6 )
% 5.82/6.15 => ( ( member_complex @ A3 @ A )
% 5.82/6.15 => ( ( ord_le211207098394363844omplex @ F6 @ A )
% 5.82/6.15 => ( ~ ( member_complex @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_complex @ A3 @ F6 ) ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct'
% 5.82/6.15 thf(fact_6865_finite__subset__induct_H,axiom,
% 5.82/6.15 ! [F3: set_nat,A: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ F3 )
% 5.82/6.15 => ( ( ord_less_eq_set_nat @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [A3: nat,F6: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ F6 )
% 5.82/6.15 => ( ( member_nat @ A3 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_nat @ F6 @ A )
% 5.82/6.15 => ( ~ ( member_nat @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_nat @ A3 @ F6 ) ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct'
% 5.82/6.15 thf(fact_6866_finite__subset__induct_H,axiom,
% 5.82/6.15 ! [F3: set_int,A: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ F3 )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [A3: int,F6: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ F6 )
% 5.82/6.15 => ( ( member_int @ A3 @ A )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ F6 @ A )
% 5.82/6.15 => ( ~ ( member_int @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_int @ A3 @ F6 ) ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct'
% 5.82/6.15 thf(fact_6867_finite__subset__induct,axiom,
% 5.82/6.15 ! [F3: set_VEBT_VEBT,A: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ F3 )
% 5.82/6.15 => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ! [A3: vEBT_VEBT,F6: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ F6 )
% 5.82/6.15 => ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.15 => ( ~ ( member_VEBT_VEBT @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_VEBT_VEBT @ A3 @ F6 ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct
% 5.82/6.15 thf(fact_6868_finite__subset__induct,axiom,
% 5.82/6.15 ! [F3: set_real,A: set_real,P: set_real > $o] :
% 5.82/6.15 ( ( finite_finite_real @ F3 )
% 5.82/6.15 => ( ( ord_less_eq_set_real @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [A3: real,F6: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ F6 )
% 5.82/6.15 => ( ( member_real @ A3 @ A )
% 5.82/6.15 => ( ~ ( member_real @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_real @ A3 @ F6 ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct
% 5.82/6.15 thf(fact_6869_finite__subset__induct,axiom,
% 5.82/6.15 ! [F3: set_Code_integer,A: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ F3 )
% 5.82/6.15 => ( ( ord_le7084787975880047091nteger @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [A3: code_integer,F6: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ F6 )
% 5.82/6.15 => ( ( member_Code_integer @ A3 @ A )
% 5.82/6.15 => ( ~ ( member_Code_integer @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_Code_integer @ A3 @ F6 ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct
% 5.82/6.15 thf(fact_6870_finite__subset__induct,axiom,
% 5.82/6.15 ! [F3: set_complex,A: set_complex,P: set_complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ F3 )
% 5.82/6.15 => ( ( ord_le211207098394363844omplex @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ! [A3: complex,F6: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ F6 )
% 5.82/6.15 => ( ( member_complex @ A3 @ A )
% 5.82/6.15 => ( ~ ( member_complex @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_complex @ A3 @ F6 ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct
% 5.82/6.15 thf(fact_6871_finite__subset__induct,axiom,
% 5.82/6.15 ! [F3: set_nat,A: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ F3 )
% 5.82/6.15 => ( ( ord_less_eq_set_nat @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [A3: nat,F6: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ F6 )
% 5.82/6.15 => ( ( member_nat @ A3 @ A )
% 5.82/6.15 => ( ~ ( member_nat @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_nat @ A3 @ F6 ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct
% 5.82/6.15 thf(fact_6872_finite__subset__induct,axiom,
% 5.82/6.15 ! [F3: set_int,A: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ F3 )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ F3 @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [A3: int,F6: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ F6 )
% 5.82/6.15 => ( ( member_int @ A3 @ A )
% 5.82/6.15 => ( ~ ( member_int @ A3 @ F6 )
% 5.82/6.15 => ( ( P @ F6 )
% 5.82/6.15 => ( P @ ( insert_int @ A3 @ F6 ) ) ) ) ) )
% 5.82/6.15 => ( P @ F3 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_subset_induct
% 5.82/6.15 thf(fact_6873_infinite__remove,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT] :
% 5.82/6.15 ( ~ ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_remove
% 5.82/6.15 thf(fact_6874_infinite__remove,axiom,
% 5.82/6.15 ! [S: set_Code_integer,A2: code_integer] :
% 5.82/6.15 ( ~ ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_remove
% 5.82/6.15 thf(fact_6875_infinite__remove,axiom,
% 5.82/6.15 ! [S: set_complex,A2: complex] :
% 5.82/6.15 ( ~ ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_remove
% 5.82/6.15 thf(fact_6876_infinite__remove,axiom,
% 5.82/6.15 ! [S: set_int,A2: int] :
% 5.82/6.15 ( ~ ( finite_finite_int @ S )
% 5.82/6.15 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_remove
% 5.82/6.15 thf(fact_6877_infinite__remove,axiom,
% 5.82/6.15 ! [S: set_nat,A2: nat] :
% 5.82/6.15 ( ~ ( finite_finite_nat @ S )
% 5.82/6.15 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_remove
% 5.82/6.15 thf(fact_6878_infinite__coinduct,axiom,
% 5.82/6.15 ! [X: set_VEBT_VEBT > $o,A: set_VEBT_VEBT] :
% 5.82/6.15 ( ( X @ A )
% 5.82/6.15 => ( ! [A8: set_VEBT_VEBT] :
% 5.82/6.15 ( ( X @ A8 )
% 5.82/6.15 => ? [X8: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X8 @ A8 )
% 5.82/6.15 & ( ( X @ ( minus_5127226145743854075T_VEBT @ A8 @ ( insert_VEBT_VEBT @ X8 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.15 | ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A8 @ ( insert_VEBT_VEBT @ X8 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.15 => ~ ( finite5795047828879050333T_VEBT @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_coinduct
% 5.82/6.15 thf(fact_6879_infinite__coinduct,axiom,
% 5.82/6.15 ! [X: set_Code_integer > $o,A: set_Code_integer] :
% 5.82/6.15 ( ( X @ A )
% 5.82/6.15 => ( ! [A8: set_Code_integer] :
% 5.82/6.15 ( ( X @ A8 )
% 5.82/6.15 => ? [X8: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X8 @ A8 )
% 5.82/6.15 & ( ( X @ ( minus_2355218937544613996nteger @ A8 @ ( insert_Code_integer @ X8 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.15 | ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A8 @ ( insert_Code_integer @ X8 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 5.82/6.15 => ~ ( finite6017078050557962740nteger @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_coinduct
% 5.82/6.15 thf(fact_6880_infinite__coinduct,axiom,
% 5.82/6.15 ! [X: set_complex > $o,A: set_complex] :
% 5.82/6.15 ( ( X @ A )
% 5.82/6.15 => ( ! [A8: set_complex] :
% 5.82/6.15 ( ( X @ A8 )
% 5.82/6.15 => ? [X8: complex] :
% 5.82/6.15 ( ( member_complex @ X8 @ A8 )
% 5.82/6.15 & ( ( X @ ( minus_811609699411566653omplex @ A8 @ ( insert_complex @ X8 @ bot_bot_set_complex ) ) )
% 5.82/6.15 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A8 @ ( insert_complex @ X8 @ bot_bot_set_complex ) ) ) ) ) )
% 5.82/6.15 => ~ ( finite3207457112153483333omplex @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_coinduct
% 5.82/6.15 thf(fact_6881_infinite__coinduct,axiom,
% 5.82/6.15 ! [X: set_int > $o,A: set_int] :
% 5.82/6.15 ( ( X @ A )
% 5.82/6.15 => ( ! [A8: set_int] :
% 5.82/6.15 ( ( X @ A8 )
% 5.82/6.15 => ? [X8: int] :
% 5.82/6.15 ( ( member_int @ X8 @ A8 )
% 5.82/6.15 & ( ( X @ ( minus_minus_set_int @ A8 @ ( insert_int @ X8 @ bot_bot_set_int ) ) )
% 5.82/6.15 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A8 @ ( insert_int @ X8 @ bot_bot_set_int ) ) ) ) ) )
% 5.82/6.15 => ~ ( finite_finite_int @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_coinduct
% 5.82/6.15 thf(fact_6882_infinite__coinduct,axiom,
% 5.82/6.15 ! [X: set_nat > $o,A: set_nat] :
% 5.82/6.15 ( ( X @ A )
% 5.82/6.15 => ( ! [A8: set_nat] :
% 5.82/6.15 ( ( X @ A8 )
% 5.82/6.15 => ? [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ A8 )
% 5.82/6.15 & ( ( X @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X8 @ bot_bot_set_nat ) ) )
% 5.82/6.15 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X8 @ bot_bot_set_nat ) ) ) ) ) )
% 5.82/6.15 => ~ ( finite_finite_nat @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_coinduct
% 5.82/6.15 thf(fact_6883_finite__empty__induct,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( P @ A )
% 5.82/6.15 => ( ! [A3: vEBT_VEBT,A8: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A8 )
% 5.82/6.15 => ( ( member_VEBT_VEBT @ A3 @ A8 )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( minus_5127226145743854075T_VEBT @ A8 @ ( insert_VEBT_VEBT @ A3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.15 => ( P @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_empty_induct
% 5.82/6.15 thf(fact_6884_finite__empty__induct,axiom,
% 5.82/6.15 ! [A: set_real,P: set_real > $o] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( P @ A )
% 5.82/6.15 => ( ! [A3: real,A8: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ A8 )
% 5.82/6.15 => ( ( member_real @ A3 @ A8 )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_real @ A8 @ ( insert_real @ A3 @ bot_bot_set_real ) ) ) ) ) )
% 5.82/6.15 => ( P @ bot_bot_set_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_empty_induct
% 5.82/6.15 thf(fact_6885_finite__empty__induct,axiom,
% 5.82/6.15 ! [A: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( P @ A )
% 5.82/6.15 => ( ! [A3: code_integer,A8: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A8 )
% 5.82/6.15 => ( ( member_Code_integer @ A3 @ A8 )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( minus_2355218937544613996nteger @ A8 @ ( insert_Code_integer @ A3 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 5.82/6.15 => ( P @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_empty_induct
% 5.82/6.15 thf(fact_6886_finite__empty__induct,axiom,
% 5.82/6.15 ! [A: set_complex,P: set_complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( ( P @ A )
% 5.82/6.15 => ( ! [A3: complex,A8: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A8 )
% 5.82/6.15 => ( ( member_complex @ A3 @ A8 )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( minus_811609699411566653omplex @ A8 @ ( insert_complex @ A3 @ bot_bot_set_complex ) ) ) ) ) )
% 5.82/6.15 => ( P @ bot_bot_set_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_empty_induct
% 5.82/6.15 thf(fact_6887_finite__empty__induct,axiom,
% 5.82/6.15 ! [A: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( P @ A )
% 5.82/6.15 => ( ! [A3: int,A8: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A8 )
% 5.82/6.15 => ( ( member_int @ A3 @ A8 )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ A3 @ bot_bot_set_int ) ) ) ) ) )
% 5.82/6.15 => ( P @ bot_bot_set_int ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_empty_induct
% 5.82/6.15 thf(fact_6888_finite__empty__induct,axiom,
% 5.82/6.15 ! [A: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( P @ A )
% 5.82/6.15 => ( ! [A3: nat,A8: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A8 )
% 5.82/6.15 => ( ( member_nat @ A3 @ A8 )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ) )
% 5.82/6.15 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_empty_induct
% 5.82/6.15 thf(fact_6889_finite__remove__induct,axiom,
% 5.82/6.15 ! [B: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.15 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ! [A8: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ( ord_le4337996190870823476T_VEBT @ A8 @ B )
% 5.82/6.15 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_5127226145743854075T_VEBT @ A8 @ ( insert_VEBT_VEBT @ X8 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_remove_induct
% 5.82/6.15 thf(fact_6890_finite__remove__induct,axiom,
% 5.82/6.15 ! [B: set_real,P: set_real > $o] :
% 5.82/6.15 ( ( finite_finite_real @ B )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [A8: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_real )
% 5.82/6.15 => ( ( ord_less_eq_set_real @ A8 @ B )
% 5.82/6.15 => ( ! [X8: real] :
% 5.82/6.15 ( ( member_real @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_real @ A8 @ ( insert_real @ X8 @ bot_bot_set_real ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_remove_induct
% 5.82/6.15 thf(fact_6891_finite__remove__induct,axiom,
% 5.82/6.15 ! [B: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [A8: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ( ord_le7084787975880047091nteger @ A8 @ B )
% 5.82/6.15 => ( ! [X8: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_2355218937544613996nteger @ A8 @ ( insert_Code_integer @ X8 @ bot_bo3990330152332043303nteger ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_remove_induct
% 5.82/6.15 thf(fact_6892_finite__remove__induct,axiom,
% 5.82/6.15 ! [B: set_complex,P: set_complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ! [A8: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_complex )
% 5.82/6.15 => ( ( ord_le211207098394363844omplex @ A8 @ B )
% 5.82/6.15 => ( ! [X8: complex] :
% 5.82/6.15 ( ( member_complex @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_811609699411566653omplex @ A8 @ ( insert_complex @ X8 @ bot_bot_set_complex ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_remove_induct
% 5.82/6.15 thf(fact_6893_finite__remove__induct,axiom,
% 5.82/6.15 ! [B: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [A8: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_nat )
% 5.82/6.15 => ( ( ord_less_eq_set_nat @ A8 @ B )
% 5.82/6.15 => ( ! [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X8 @ bot_bot_set_nat ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_remove_induct
% 5.82/6.15 thf(fact_6894_finite__remove__induct,axiom,
% 5.82/6.15 ! [B: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ B )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [A8: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_int )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ A8 @ B )
% 5.82/6.15 => ( ! [X8: int] :
% 5.82/6.15 ( ( member_int @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ X8 @ bot_bot_set_int ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_remove_induct
% 5.82/6.15 thf(fact_6895_remove__induct,axiom,
% 5.82/6.15 ! [P: set_VEBT_VEBT > $o,B: set_VEBT_VEBT] :
% 5.82/6.15 ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ( ~ ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.15 => ( P @ B ) )
% 5.82/6.15 => ( ! [A8: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ( ord_le4337996190870823476T_VEBT @ A8 @ B )
% 5.82/6.15 => ( ! [X8: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_5127226145743854075T_VEBT @ A8 @ ( insert_VEBT_VEBT @ X8 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % remove_induct
% 5.82/6.15 thf(fact_6896_remove__induct,axiom,
% 5.82/6.15 ! [P: set_real > $o,B: set_real] :
% 5.82/6.15 ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ( ~ ( finite_finite_real @ B )
% 5.82/6.15 => ( P @ B ) )
% 5.82/6.15 => ( ! [A8: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_real )
% 5.82/6.15 => ( ( ord_less_eq_set_real @ A8 @ B )
% 5.82/6.15 => ( ! [X8: real] :
% 5.82/6.15 ( ( member_real @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_real @ A8 @ ( insert_real @ X8 @ bot_bot_set_real ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % remove_induct
% 5.82/6.15 thf(fact_6897_remove__induct,axiom,
% 5.82/6.15 ! [P: set_Code_integer > $o,B: set_Code_integer] :
% 5.82/6.15 ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ( ~ ( finite6017078050557962740nteger @ B )
% 5.82/6.15 => ( P @ B ) )
% 5.82/6.15 => ( ! [A8: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ( ord_le7084787975880047091nteger @ A8 @ B )
% 5.82/6.15 => ( ! [X8: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_2355218937544613996nteger @ A8 @ ( insert_Code_integer @ X8 @ bot_bo3990330152332043303nteger ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % remove_induct
% 5.82/6.15 thf(fact_6898_remove__induct,axiom,
% 5.82/6.15 ! [P: set_complex > $o,B: set_complex] :
% 5.82/6.15 ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ( ~ ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( P @ B ) )
% 5.82/6.15 => ( ! [A8: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_complex )
% 5.82/6.15 => ( ( ord_le211207098394363844omplex @ A8 @ B )
% 5.82/6.15 => ( ! [X8: complex] :
% 5.82/6.15 ( ( member_complex @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_811609699411566653omplex @ A8 @ ( insert_complex @ X8 @ bot_bot_set_complex ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % remove_induct
% 5.82/6.15 thf(fact_6899_remove__induct,axiom,
% 5.82/6.15 ! [P: set_nat > $o,B: set_nat] :
% 5.82/6.15 ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ( ~ ( finite_finite_nat @ B )
% 5.82/6.15 => ( P @ B ) )
% 5.82/6.15 => ( ! [A8: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_nat )
% 5.82/6.15 => ( ( ord_less_eq_set_nat @ A8 @ B )
% 5.82/6.15 => ( ! [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X8 @ bot_bot_set_nat ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % remove_induct
% 5.82/6.15 thf(fact_6900_remove__induct,axiom,
% 5.82/6.15 ! [P: set_int > $o,B: set_int] :
% 5.82/6.15 ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ( ~ ( finite_finite_int @ B )
% 5.82/6.15 => ( P @ B ) )
% 5.82/6.15 => ( ! [A8: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A8 )
% 5.82/6.15 => ( ( A8 != bot_bot_set_int )
% 5.82/6.15 => ( ( ord_less_eq_set_int @ A8 @ B )
% 5.82/6.15 => ( ! [X8: int] :
% 5.82/6.15 ( ( member_int @ X8 @ A8 )
% 5.82/6.15 => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ X8 @ bot_bot_set_int ) ) ) )
% 5.82/6.15 => ( P @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % remove_induct
% 5.82/6.15 thf(fact_6901_finite__nth__roots,axiom,
% 5.82/6.15 ! [N: nat,C2: complex] :
% 5.82/6.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Z4: complex] :
% 5.82/6.15 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.15 = C2 ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_nth_roots
% 5.82/6.15 thf(fact_6902_set__encode__insert,axiom,
% 5.82/6.15 ! [A: set_nat,N: nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ~ ( member_nat @ N @ A )
% 5.82/6.15 => ( ( nat_set_encode @ ( insert_nat @ N @ A ) )
% 5.82/6.15 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % set_encode_insert
% 5.82/6.15 thf(fact_6903_diff__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: product_prod_int_int > nat,N7: product_prod_int_int > nat] :
% 5.82/6.15 ( ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M8 @ X3 ) @ ( N7 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % diff_preserves_multiset
% 5.82/6.15 thf(fact_6904_diff__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: nat > nat,N7: nat > nat] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M8 @ X3 ) @ ( N7 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % diff_preserves_multiset
% 5.82/6.15 thf(fact_6905_diff__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: int > nat,N7: int > nat] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M8 @ X3 ) @ ( N7 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % diff_preserves_multiset
% 5.82/6.15 thf(fact_6906_diff__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: code_integer > nat,N7: code_integer > nat] :
% 5.82/6.15 ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M8 @ X3 ) @ ( N7 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % diff_preserves_multiset
% 5.82/6.15 thf(fact_6907_diff__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: complex > nat,N7: complex > nat] :
% 5.82/6.15 ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M8 @ X3 ) @ ( N7 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % diff_preserves_multiset
% 5.82/6.15 thf(fact_6908_add__mset__in__multiset,axiom,
% 5.82/6.15 ! [M8: product_prod_int_int > nat,A2: product_prod_int_int] :
% 5.82/6.15 ( ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A2 ) @ ( suc @ ( M8 @ X3 ) ) @ ( M8 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % add_mset_in_multiset
% 5.82/6.15 thf(fact_6909_add__mset__in__multiset,axiom,
% 5.82/6.15 ! [M8: nat > nat,A2: nat] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A2 ) @ ( suc @ ( M8 @ X3 ) ) @ ( M8 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % add_mset_in_multiset
% 5.82/6.15 thf(fact_6910_add__mset__in__multiset,axiom,
% 5.82/6.15 ! [M8: int > nat,A2: int] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A2 ) @ ( suc @ ( M8 @ X3 ) ) @ ( M8 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % add_mset_in_multiset
% 5.82/6.15 thf(fact_6911_add__mset__in__multiset,axiom,
% 5.82/6.15 ! [M8: code_integer > nat,A2: code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A2 ) @ ( suc @ ( M8 @ X3 ) ) @ ( M8 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % add_mset_in_multiset
% 5.82/6.15 thf(fact_6912_add__mset__in__multiset,axiom,
% 5.82/6.15 ! [M8: complex > nat,A2: complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A2 ) @ ( suc @ ( M8 @ X3 ) ) @ ( M8 @ X3 ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % add_mset_in_multiset
% 5.82/6.15 thf(fact_6913_finite__linorder__max__induct,axiom,
% 5.82/6.15 ! [A: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [B3: code_integer,A8: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A8 )
% 5.82/6.15 => ( ! [X8: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X8 @ A8 )
% 5.82/6.15 => ( ord_le6747313008572928689nteger @ X8 @ B3 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_Code_integer @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_max_induct
% 5.82/6.15 thf(fact_6914_finite__linorder__max__induct,axiom,
% 5.82/6.15 ! [A: set_real,P: set_real > $o] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [B3: real,A8: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ A8 )
% 5.82/6.15 => ( ! [X8: real] :
% 5.82/6.15 ( ( member_real @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_real @ X8 @ B3 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_real @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_max_induct
% 5.82/6.15 thf(fact_6915_finite__linorder__max__induct,axiom,
% 5.82/6.15 ! [A: set_rat,P: set_rat > $o] :
% 5.82/6.15 ( ( finite_finite_rat @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_rat )
% 5.82/6.15 => ( ! [B3: rat,A8: set_rat] :
% 5.82/6.15 ( ( finite_finite_rat @ A8 )
% 5.82/6.15 => ( ! [X8: rat] :
% 5.82/6.15 ( ( member_rat @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_rat @ X8 @ B3 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_rat @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_max_induct
% 5.82/6.15 thf(fact_6916_finite__linorder__max__induct,axiom,
% 5.82/6.15 ! [A: set_num,P: set_num > $o] :
% 5.82/6.15 ( ( finite_finite_num @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_num )
% 5.82/6.15 => ( ! [B3: num,A8: set_num] :
% 5.82/6.15 ( ( finite_finite_num @ A8 )
% 5.82/6.15 => ( ! [X8: num] :
% 5.82/6.15 ( ( member_num @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_num @ X8 @ B3 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_num @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_max_induct
% 5.82/6.15 thf(fact_6917_finite__linorder__max__induct,axiom,
% 5.82/6.15 ! [A: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [B3: nat,A8: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A8 )
% 5.82/6.15 => ( ! [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_nat @ X8 @ B3 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_nat @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_max_induct
% 5.82/6.15 thf(fact_6918_finite__linorder__max__induct,axiom,
% 5.82/6.15 ! [A: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [B3: int,A8: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A8 )
% 5.82/6.15 => ( ! [X8: int] :
% 5.82/6.15 ( ( member_int @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_int @ X8 @ B3 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_int @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_max_induct
% 5.82/6.15 thf(fact_6919_complex__mod__triangle__ineq2,axiom,
% 5.82/6.15 ! [B2: complex,A2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B2 @ A2 ) ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ A2 ) ) ).
% 5.82/6.15
% 5.82/6.15 % complex_mod_triangle_ineq2
% 5.82/6.15 thf(fact_6920_even__set__encode__iff,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A ) )
% 5.82/6.15 = ( ~ ( member_nat @ zero_zero_nat @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % even_set_encode_iff
% 5.82/6.15 thf(fact_6921_infinite__growing,axiom,
% 5.82/6.15 ! [X: set_Code_integer] :
% 5.82/6.15 ( ( X != bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ X )
% 5.82/6.15 => ? [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ X )
% 5.82/6.15 & ( ord_le6747313008572928689nteger @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ~ ( finite6017078050557962740nteger @ X ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_growing
% 5.82/6.15 thf(fact_6922_infinite__growing,axiom,
% 5.82/6.15 ! [X: set_real] :
% 5.82/6.15 ( ( X != bot_bot_set_real )
% 5.82/6.15 => ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ X )
% 5.82/6.15 => ? [Xa2: real] :
% 5.82/6.15 ( ( member_real @ Xa2 @ X )
% 5.82/6.15 & ( ord_less_real @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ~ ( finite_finite_real @ X ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_growing
% 5.82/6.15 thf(fact_6923_infinite__growing,axiom,
% 5.82/6.15 ! [X: set_rat] :
% 5.82/6.15 ( ( X != bot_bot_set_rat )
% 5.82/6.15 => ( ! [X4: rat] :
% 5.82/6.15 ( ( member_rat @ X4 @ X )
% 5.82/6.15 => ? [Xa2: rat] :
% 5.82/6.15 ( ( member_rat @ Xa2 @ X )
% 5.82/6.15 & ( ord_less_rat @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ~ ( finite_finite_rat @ X ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_growing
% 5.82/6.15 thf(fact_6924_infinite__growing,axiom,
% 5.82/6.15 ! [X: set_num] :
% 5.82/6.15 ( ( X != bot_bot_set_num )
% 5.82/6.15 => ( ! [X4: num] :
% 5.82/6.15 ( ( member_num @ X4 @ X )
% 5.82/6.15 => ? [Xa2: num] :
% 5.82/6.15 ( ( member_num @ Xa2 @ X )
% 5.82/6.15 & ( ord_less_num @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ~ ( finite_finite_num @ X ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_growing
% 5.82/6.15 thf(fact_6925_infinite__growing,axiom,
% 5.82/6.15 ! [X: set_nat] :
% 5.82/6.15 ( ( X != bot_bot_set_nat )
% 5.82/6.15 => ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ X )
% 5.82/6.15 => ? [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ X )
% 5.82/6.15 & ( ord_less_nat @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ~ ( finite_finite_nat @ X ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_growing
% 5.82/6.15 thf(fact_6926_infinite__growing,axiom,
% 5.82/6.15 ! [X: set_int] :
% 5.82/6.15 ( ( X != bot_bot_set_int )
% 5.82/6.15 => ( ! [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ X )
% 5.82/6.15 => ? [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ X )
% 5.82/6.15 & ( ord_less_int @ X4 @ Xa2 ) ) )
% 5.82/6.15 => ~ ( finite_finite_int @ X ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % infinite_growing
% 5.82/6.15 thf(fact_6927_ex__min__if__finite,axiom,
% 5.82/6.15 ! [S: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( S != bot_bo3990330152332043303nteger )
% 5.82/6.15 => ? [X4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.15 & ~ ? [Xa2: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Xa2 @ S )
% 5.82/6.15 & ( ord_le6747313008572928689nteger @ Xa2 @ X4 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ex_min_if_finite
% 5.82/6.15 thf(fact_6928_ex__min__if__finite,axiom,
% 5.82/6.15 ! [S: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( S != bot_bot_set_real )
% 5.82/6.15 => ? [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ S )
% 5.82/6.15 & ~ ? [Xa2: real] :
% 5.82/6.15 ( ( member_real @ Xa2 @ S )
% 5.82/6.15 & ( ord_less_real @ Xa2 @ X4 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ex_min_if_finite
% 5.82/6.15 thf(fact_6929_ex__min__if__finite,axiom,
% 5.82/6.15 ! [S: set_rat] :
% 5.82/6.15 ( ( finite_finite_rat @ S )
% 5.82/6.15 => ( ( S != bot_bot_set_rat )
% 5.82/6.15 => ? [X4: rat] :
% 5.82/6.15 ( ( member_rat @ X4 @ S )
% 5.82/6.15 & ~ ? [Xa2: rat] :
% 5.82/6.15 ( ( member_rat @ Xa2 @ S )
% 5.82/6.15 & ( ord_less_rat @ Xa2 @ X4 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ex_min_if_finite
% 5.82/6.15 thf(fact_6930_ex__min__if__finite,axiom,
% 5.82/6.15 ! [S: set_num] :
% 5.82/6.15 ( ( finite_finite_num @ S )
% 5.82/6.15 => ( ( S != bot_bot_set_num )
% 5.82/6.15 => ? [X4: num] :
% 5.82/6.15 ( ( member_num @ X4 @ S )
% 5.82/6.15 & ~ ? [Xa2: num] :
% 5.82/6.15 ( ( member_num @ Xa2 @ S )
% 5.82/6.15 & ( ord_less_num @ Xa2 @ X4 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ex_min_if_finite
% 5.82/6.15 thf(fact_6931_ex__min__if__finite,axiom,
% 5.82/6.15 ! [S: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ S )
% 5.82/6.15 => ( ( S != bot_bot_set_nat )
% 5.82/6.15 => ? [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ S )
% 5.82/6.15 & ~ ? [Xa2: nat] :
% 5.82/6.15 ( ( member_nat @ Xa2 @ S )
% 5.82/6.15 & ( ord_less_nat @ Xa2 @ X4 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ex_min_if_finite
% 5.82/6.15 thf(fact_6932_ex__min__if__finite,axiom,
% 5.82/6.15 ! [S: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( S != bot_bot_set_int )
% 5.82/6.15 => ? [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ S )
% 5.82/6.15 & ~ ? [Xa2: int] :
% 5.82/6.15 ( ( member_int @ Xa2 @ S )
% 5.82/6.15 & ( ord_less_int @ Xa2 @ X4 ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % ex_min_if_finite
% 5.82/6.15 thf(fact_6933_filter__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: product_prod_int_int > nat,P: product_prod_int_int > $o] :
% 5.82/6.15 ( ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite2998713641127702882nt_int
% 5.82/6.15 @ ( collec213857154873943460nt_int
% 5.82/6.15 @ ^ [X3: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M8 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % filter_preserves_multiset
% 5.82/6.15 thf(fact_6934_filter__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: nat > nat,P: nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M8 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % filter_preserves_multiset
% 5.82/6.15 thf(fact_6935_filter__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: int > nat,P: int > $o] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M8 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % filter_preserves_multiset
% 5.82/6.15 thf(fact_6936_filter__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: code_integer > nat,P: code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M8 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % filter_preserves_multiset
% 5.82/6.15 thf(fact_6937_filter__preserves__multiset,axiom,
% 5.82/6.15 ! [M8: complex > nat,P: complex > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] : ( ord_less_nat @ zero_zero_nat @ ( M8 @ X3 ) ) ) )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M8 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % filter_preserves_multiset
% 5.82/6.15 thf(fact_6938_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ! [X4: vEBT_VEBT,S6: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S6 )
% 5.82/6.15 => ( ! [Y5: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_VEBT_VEBT @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6939_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_real,P: set_real > $o,F: real > rat] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [X4: real,S6: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ S6 )
% 5.82/6.15 => ( ! [Y5: real] :
% 5.82/6.15 ( ( member_real @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_real @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6940_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_Code_integer,P: set_Code_integer > $o,F: code_integer > rat] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [X4: code_integer,S6: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S6 )
% 5.82/6.15 => ( ! [Y5: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_Code_integer @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6941_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ! [X4: complex,S6: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S6 )
% 5.82/6.15 => ( ! [Y5: complex] :
% 5.82/6.15 ( ( member_complex @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_complex @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6942_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.82/6.15 ( ( finite_finite_nat @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [X4: nat,S6: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ S6 )
% 5.82/6.15 => ( ! [Y5: nat] :
% 5.82/6.15 ( ( member_nat @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_nat @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6943_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_int,P: set_int > $o,F: int > rat] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [X4: int,S6: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ S6 )
% 5.82/6.15 => ( ! [Y5: int] :
% 5.82/6.15 ( ( member_int @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_int @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6944_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.82/6.15 => ( ! [X4: vEBT_VEBT,S6: set_VEBT_VEBT] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S6 )
% 5.82/6.15 => ( ! [Y5: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_VEBT_VEBT @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6945_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_real,P: set_real > $o,F: real > num] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [X4: real,S6: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ S6 )
% 5.82/6.15 => ( ! [Y5: real] :
% 5.82/6.15 ( ( member_real @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_real @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6946_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_Code_integer,P: set_Code_integer > $o,F: code_integer > num] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [X4: code_integer,S6: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S6 )
% 5.82/6.15 => ( ! [Y5: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_Code_integer @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6947_finite__ranking__induct,axiom,
% 5.82/6.15 ! [S: set_complex,P: set_complex > $o,F: complex > num] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ( ( P @ bot_bot_set_complex )
% 5.82/6.15 => ( ! [X4: complex,S6: set_complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S6 )
% 5.82/6.15 => ( ! [Y5: complex] :
% 5.82/6.15 ( ( member_complex @ Y5 @ S6 )
% 5.82/6.15 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.82/6.15 => ( ( P @ S6 )
% 5.82/6.15 => ( P @ ( insert_complex @ X4 @ S6 ) ) ) ) )
% 5.82/6.15 => ( P @ S ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_ranking_induct
% 5.82/6.15 thf(fact_6948_finite__linorder__min__induct,axiom,
% 5.82/6.15 ! [A: set_Code_integer,P: set_Code_integer > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( P @ bot_bo3990330152332043303nteger )
% 5.82/6.15 => ( ! [B3: code_integer,A8: set_Code_integer] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A8 )
% 5.82/6.15 => ( ! [X8: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X8 @ A8 )
% 5.82/6.15 => ( ord_le6747313008572928689nteger @ B3 @ X8 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_Code_integer @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_min_induct
% 5.82/6.15 thf(fact_6949_finite__linorder__min__induct,axiom,
% 5.82/6.15 ! [A: set_real,P: set_real > $o] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_real )
% 5.82/6.15 => ( ! [B3: real,A8: set_real] :
% 5.82/6.15 ( ( finite_finite_real @ A8 )
% 5.82/6.15 => ( ! [X8: real] :
% 5.82/6.15 ( ( member_real @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_real @ B3 @ X8 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_real @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_min_induct
% 5.82/6.15 thf(fact_6950_finite__linorder__min__induct,axiom,
% 5.82/6.15 ! [A: set_rat,P: set_rat > $o] :
% 5.82/6.15 ( ( finite_finite_rat @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_rat )
% 5.82/6.15 => ( ! [B3: rat,A8: set_rat] :
% 5.82/6.15 ( ( finite_finite_rat @ A8 )
% 5.82/6.15 => ( ! [X8: rat] :
% 5.82/6.15 ( ( member_rat @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_rat @ B3 @ X8 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_rat @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_min_induct
% 5.82/6.15 thf(fact_6951_finite__linorder__min__induct,axiom,
% 5.82/6.15 ! [A: set_num,P: set_num > $o] :
% 5.82/6.15 ( ( finite_finite_num @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_num )
% 5.82/6.15 => ( ! [B3: num,A8: set_num] :
% 5.82/6.15 ( ( finite_finite_num @ A8 )
% 5.82/6.15 => ( ! [X8: num] :
% 5.82/6.15 ( ( member_num @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_num @ B3 @ X8 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_num @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_min_induct
% 5.82/6.15 thf(fact_6952_finite__linorder__min__induct,axiom,
% 5.82/6.15 ! [A: set_nat,P: set_nat > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_nat )
% 5.82/6.15 => ( ! [B3: nat,A8: set_nat] :
% 5.82/6.15 ( ( finite_finite_nat @ A8 )
% 5.82/6.15 => ( ! [X8: nat] :
% 5.82/6.15 ( ( member_nat @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_nat @ B3 @ X8 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_nat @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_min_induct
% 5.82/6.15 thf(fact_6953_finite__linorder__min__induct,axiom,
% 5.82/6.15 ! [A: set_int,P: set_int > $o] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( P @ bot_bot_set_int )
% 5.82/6.15 => ( ! [B3: int,A8: set_int] :
% 5.82/6.15 ( ( finite_finite_int @ A8 )
% 5.82/6.15 => ( ! [X8: int] :
% 5.82/6.15 ( ( member_int @ X8 @ A8 )
% 5.82/6.15 => ( ord_less_int @ B3 @ X8 ) )
% 5.82/6.15 => ( ( P @ A8 )
% 5.82/6.15 => ( P @ ( insert_int @ B3 @ A8 ) ) ) ) )
% 5.82/6.15 => ( P @ A ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % finite_linorder_min_induct
% 5.82/6.15 thf(fact_6954_freeze__rule,axiom,
% 5.82/6.15 ! [A2: array_VEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 5.82/6.15 ( hoare_3904069481286416050_VEBTi @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs ) @ ( array_8141364883501958055_VEBTi @ A2 )
% 5.82/6.15 @ ^ [R5: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs ) @ ( pure_assn @ ( R5 = Xs ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % freeze_rule
% 5.82/6.15 thf(fact_6955_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_VEBT_VEBT,X2: vEBT_VEBT > assn,Y3: vEBT_VEBT > assn] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_assn @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_assn ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6956_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_real,X2: real > assn,Y3: real > assn] :
% 5.82/6.15 ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_assn @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_assn ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6957_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_nat,X2: nat > assn,Y3: nat > assn] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_assn @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_assn ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6958_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_int,X2: int > assn,Y3: int > assn] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_assn @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_assn ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6959_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_Code_integer,X2: code_integer > assn,Y3: code_integer > assn] :
% 5.82/6.15 ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [I4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [I4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [I4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_assn @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_assn ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6960_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_complex,X2: complex > assn,Y3: complex > assn] :
% 5.82/6.15 ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [I4: complex] :
% 5.82/6.15 ( ( member_complex @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [I4: complex] :
% 5.82/6.15 ( ( member_complex @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_assn ) ) ) )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [I4: complex] :
% 5.82/6.15 ( ( member_complex @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_assn @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_assn ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6961_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_VEBT_VEBT,X2: vEBT_VEBT > real,Y3: vEBT_VEBT > real] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6962_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_real,X2: real > real,Y3: real > real] :
% 5.82/6.15 ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6963_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_nat,X2: nat > real,Y3: nat > real] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6964_prod_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_int,X2: int > real,Y3: int > real] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != one_one_real ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != one_one_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % prod.finite_Collect_op
% 5.82/6.15 thf(fact_6965_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_VEBT_VEBT,X2: vEBT_VEBT > complex,Y3: vEBT_VEBT > complex] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_complex ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6966_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_real,X2: real > complex,Y3: real > complex] :
% 5.82/6.15 ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_complex ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6967_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_nat,X2: nat > complex,Y3: nat > complex] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_complex ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6968_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_int,X2: int > complex,Y3: int > complex] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_complex ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6969_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_Code_integer,X2: code_integer > complex,Y3: code_integer > complex] :
% 5.82/6.15 ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [I4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [I4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( finite6017078050557962740nteger
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [I4: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_complex ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6970_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_complex,X2: complex > complex,Y3: complex > complex] :
% 5.82/6.15 ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [I4: complex] :
% 5.82/6.15 ( ( member_complex @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [I4: complex] :
% 5.82/6.15 ( ( member_complex @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_complex ) ) ) )
% 5.82/6.15 => ( finite3207457112153483333omplex
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [I4: complex] :
% 5.82/6.15 ( ( member_complex @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_complex ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6971_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_VEBT_VEBT,X2: vEBT_VEBT > real,Y3: vEBT_VEBT > real] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( finite5795047828879050333T_VEBT
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [I4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6972_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_real,X2: real > real,Y3: real > real] :
% 5.82/6.15 ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( finite_finite_real
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [I4: real] :
% 5.82/6.15 ( ( member_real @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6973_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_nat,X2: nat > real,Y3: nat > real] :
% 5.82/6.15 ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( finite_finite_nat
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( ( member_nat @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6974_sum_Ofinite__Collect__op,axiom,
% 5.82/6.15 ! [I6: set_int,X2: int > real,Y3: int > real] :
% 5.82/6.15 ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( X2 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( Y3 @ I4 )
% 5.82/6.15 != zero_zero_real ) ) ) )
% 5.82/6.15 => ( finite_finite_int
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [I4: int] :
% 5.82/6.15 ( ( member_int @ I4 @ I6 )
% 5.82/6.15 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.82/6.15 != zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.finite_Collect_op
% 5.82/6.15 thf(fact_6975_sum__gp,axiom,
% 5.82/6.15 ! [N: nat,M: nat,X2: complex] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = zero_zero_complex ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( ( X2 = one_one_complex )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.82/6.15 & ( ( X2 != one_one_complex )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_gp
% 5.82/6.15 thf(fact_6976_sum__gp,axiom,
% 5.82/6.15 ! [N: nat,M: nat,X2: rat] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = zero_zero_rat ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( ( X2 = one_one_rat )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.82/6.15 & ( ( X2 != one_one_rat )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_gp
% 5.82/6.15 thf(fact_6977_sum__gp,axiom,
% 5.82/6.15 ! [N: nat,M: nat,X2: real] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = zero_zero_real ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( ( X2 = one_one_real )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.82/6.15 & ( ( X2 != one_one_real )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.15 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_gp
% 5.82/6.15 thf(fact_6978_sum_Oneutral__const,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [Uu3: nat] : zero_zero_nat
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_nat ) ).
% 5.82/6.15
% 5.82/6.15 % sum.neutral_const
% 5.82/6.15 thf(fact_6979_sum_Oneutral__const,axiom,
% 5.82/6.15 ! [A: set_complex] :
% 5.82/6.15 ( ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [Uu3: complex] : zero_zero_complex
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_complex ) ).
% 5.82/6.15
% 5.82/6.15 % sum.neutral_const
% 5.82/6.15 thf(fact_6980_sum_Oneutral__const,axiom,
% 5.82/6.15 ! [A: set_nat] :
% 5.82/6.15 ( ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [Uu3: nat] : zero_zero_real
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_real ) ).
% 5.82/6.15
% 5.82/6.15 % sum.neutral_const
% 5.82/6.15 thf(fact_6981_sum_Oneutral__const,axiom,
% 5.82/6.15 ! [A: set_int] :
% 5.82/6.15 ( ( groups4538972089207619220nt_int
% 5.82/6.15 @ ^ [Uu3: int] : zero_zero_int
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_int ) ).
% 5.82/6.15
% 5.82/6.15 % sum.neutral_const
% 5.82/6.15 thf(fact_6982_of__nat__sum,axiom,
% 5.82/6.15 ! [F: complex > nat,A: set_complex] :
% 5.82/6.15 ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A ) )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [X3: complex] : ( semiri8010041392384452111omplex @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_nat_sum
% 5.82/6.15 thf(fact_6983_of__nat__sum,axiom,
% 5.82/6.15 ! [F: int > nat,A: set_int] :
% 5.82/6.15 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A ) )
% 5.82/6.15 = ( groups4538972089207619220nt_int
% 5.82/6.15 @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_nat_sum
% 5.82/6.15 thf(fact_6984_of__nat__sum,axiom,
% 5.82/6.15 ! [F: nat > nat,A: set_nat] :
% 5.82/6.15 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.15 = ( groups3539618377306564664at_int
% 5.82/6.15 @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_nat_sum
% 5.82/6.15 thf(fact_6985_of__nat__sum,axiom,
% 5.82/6.15 ! [F: nat > nat,A: set_nat] :
% 5.82/6.15 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [X3: nat] : ( semiri1316708129612266289at_nat @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_nat_sum
% 5.82/6.15 thf(fact_6986_of__nat__sum,axiom,
% 5.82/6.15 ! [F: nat > nat,A: set_nat] :
% 5.82/6.15 ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.15 = ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [X3: nat] : ( semiri5074537144036343181t_real @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_nat_sum
% 5.82/6.15 thf(fact_6987_of__int__sum,axiom,
% 5.82/6.15 ! [F: complex > int,A: set_complex] :
% 5.82/6.15 ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A ) )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [X3: complex] : ( ring_17405671764205052669omplex @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_int_sum
% 5.82/6.15 thf(fact_6988_of__int__sum,axiom,
% 5.82/6.15 ! [F: nat > int,A: set_nat] :
% 5.82/6.15 ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A ) )
% 5.82/6.15 = ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [X3: nat] : ( ring_1_of_int_real @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_int_sum
% 5.82/6.15 thf(fact_6989_of__int__sum,axiom,
% 5.82/6.15 ! [F: int > int,A: set_int] :
% 5.82/6.15 ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A ) )
% 5.82/6.15 = ( groups8778361861064173332t_real
% 5.82/6.15 @ ^ [X3: int] : ( ring_1_of_int_real @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_int_sum
% 5.82/6.15 thf(fact_6990_of__int__sum,axiom,
% 5.82/6.15 ! [F: int > int,A: set_int] :
% 5.82/6.15 ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A ) )
% 5.82/6.15 = ( groups3906332499630173760nt_rat
% 5.82/6.15 @ ^ [X3: int] : ( ring_1_of_int_rat @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_int_sum
% 5.82/6.15 thf(fact_6991_of__int__sum,axiom,
% 5.82/6.15 ! [F: int > int,A: set_int] :
% 5.82/6.15 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A ) )
% 5.82/6.15 = ( groups4538972089207619220nt_int
% 5.82/6.15 @ ^ [X3: int] : ( ring_1_of_int_int @ ( F @ X3 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % of_int_sum
% 5.82/6.15 thf(fact_6992_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > complex] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups1794756597179926696omplex
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups1794756597179926696omplex
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6993_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_real,A2: real,B2: real > complex] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups5754745047067104278omplex
% 5.82/6.15 @ ^ [K3: real] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups5754745047067104278omplex
% 5.82/6.15 @ ^ [K3: real] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6994_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_nat,A2: nat,B2: nat > complex] :
% 5.82/6.15 ( ( finite_finite_nat @ S )
% 5.82/6.15 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [K3: nat] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [K3: nat] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6995_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_int,A2: int,B2: int > complex] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups3049146728041665814omplex
% 5.82/6.15 @ ^ [K3: int] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups3049146728041665814omplex
% 5.82/6.15 @ ^ [K3: int] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6996_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > complex] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups8024822376189712711omplex
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups8024822376189712711omplex
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_complex @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6997_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > real] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups2240296850493347238T_real
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups2240296850493347238T_real
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6998_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_real,A2: real,B2: real > real] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups8097168146408367636l_real
% 5.82/6.15 @ ^ [K3: real] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups8097168146408367636l_real
% 5.82/6.15 @ ^ [K3: real] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_6999_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_int,A2: int,B2: int > real] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups8778361861064173332t_real
% 5.82/6.15 @ ^ [K3: int] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups8778361861064173332t_real
% 5.82/6.15 @ ^ [K3: int] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_7000_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > real] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups1270011288395367621r_real
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups1270011288395367621r_real
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_7001_sum_Odelta_H,axiom,
% 5.82/6.15 ! [S: set_complex,A2: complex,B2: complex > real] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.15 => ( ( groups5808333547571424918x_real
% 5.82/6.15 @ ^ [K3: complex] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.15 => ( ( groups5808333547571424918x_real
% 5.82/6.15 @ ^ [K3: complex] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta'
% 5.82/6.15 thf(fact_7002_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > complex] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups1794756597179926696omplex
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups1794756597179926696omplex
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7003_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_real,A2: real,B2: real > complex] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups5754745047067104278omplex
% 5.82/6.15 @ ^ [K3: real] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups5754745047067104278omplex
% 5.82/6.15 @ ^ [K3: real] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7004_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_nat,A2: nat,B2: nat > complex] :
% 5.82/6.15 ( ( finite_finite_nat @ S )
% 5.82/6.15 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [K3: nat] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [K3: nat] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7005_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_int,A2: int,B2: int > complex] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups3049146728041665814omplex
% 5.82/6.15 @ ^ [K3: int] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups3049146728041665814omplex
% 5.82/6.15 @ ^ [K3: int] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7006_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > complex] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups8024822376189712711omplex
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups8024822376189712711omplex
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_complex @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_complex )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_complex ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7007_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > real] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.15 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups2240296850493347238T_real
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.15 => ( ( groups2240296850493347238T_real
% 5.82/6.15 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7008_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_real,A2: real,B2: real > real] :
% 5.82/6.15 ( ( finite_finite_real @ S )
% 5.82/6.15 => ( ( ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups8097168146408367636l_real
% 5.82/6.15 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.15 => ( ( groups8097168146408367636l_real
% 5.82/6.15 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7009_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_int,A2: int,B2: int > real] :
% 5.82/6.15 ( ( finite_finite_int @ S )
% 5.82/6.15 => ( ( ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups8778361861064173332t_real
% 5.82/6.15 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.15 => ( ( groups8778361861064173332t_real
% 5.82/6.15 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7010_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > real] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.15 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups1270011288395367621r_real
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.15 => ( ( groups1270011288395367621r_real
% 5.82/6.15 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7011_sum_Odelta,axiom,
% 5.82/6.15 ! [S: set_complex,A2: complex,B2: complex > real] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.15 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.15 => ( ( groups5808333547571424918x_real
% 5.82/6.15 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = ( B2 @ A2 ) ) )
% 5.82/6.15 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.15 => ( ( groups5808333547571424918x_real
% 5.82/6.15 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ zero_zero_real )
% 5.82/6.15 @ S )
% 5.82/6.15 = zero_zero_real ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.delta
% 5.82/6.15 thf(fact_7012_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.15 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7013_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_real,X2: real,G: real > real] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ~ ( member_real @ X2 @ A )
% 5.82/6.15 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7014_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_int,X2: int,G: int > real] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ~ ( member_int @ X2 @ A )
% 5.82/6.15 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7015_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_Code_integer,X2: code_integer,G: code_integer > real] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ~ ( member_Code_integer @ X2 @ A )
% 5.82/6.15 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1270011288395367621r_real @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7016_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_complex,X2: complex,G: complex > real] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( ~ ( member_complex @ X2 @ A )
% 5.82/6.15 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7017_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.15 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7018_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_real,X2: real,G: real > rat] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ~ ( member_real @ X2 @ A )
% 5.82/6.15 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7019_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_nat,X2: nat,G: nat > rat] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ~ ( member_nat @ X2 @ A )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7020_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_int,X2: int,G: int > rat] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ~ ( member_int @ X2 @ A )
% 5.82/6.15 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7021_sum_Oinsert,axiom,
% 5.82/6.15 ! [A: set_Code_integer,X2: code_integer,G: code_integer > rat] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ~ ( member_Code_integer @ X2 @ A )
% 5.82/6.15 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.15 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups6602215022474089585er_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.insert
% 5.82/6.15 thf(fact_7022_sum_Oop__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > complex] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_complex ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.op_ivl_Suc
% 5.82/6.15 thf(fact_7023_sum_Oop__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > rat] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_rat ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.op_ivl_Suc
% 5.82/6.15 thf(fact_7024_sum_Oop__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > int] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_int ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.op_ivl_Suc
% 5.82/6.15 thf(fact_7025_sum_Oop__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > nat] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_nat ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.op_ivl_Suc
% 5.82/6.15 thf(fact_7026_sum_Oop__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > real] :
% 5.82/6.15 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_real ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.op_ivl_Suc
% 5.82/6.15 thf(fact_7027_sum_Ocl__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > complex] :
% 5.82/6.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_complex ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.cl_ivl_Suc
% 5.82/6.15 thf(fact_7028_sum_Ocl__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > rat] :
% 5.82/6.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_rat ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.cl_ivl_Suc
% 5.82/6.15 thf(fact_7029_sum_Ocl__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > int] :
% 5.82/6.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_int ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.cl_ivl_Suc
% 5.82/6.15 thf(fact_7030_sum_Ocl__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > nat] :
% 5.82/6.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_nat ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.cl_ivl_Suc
% 5.82/6.15 thf(fact_7031_sum_Ocl__ivl__Suc,axiom,
% 5.82/6.15 ! [N: nat,M: nat,G: nat > real] :
% 5.82/6.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = zero_zero_real ) )
% 5.82/6.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.15 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.15 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.cl_ivl_Suc
% 5.82/6.15 thf(fact_7032_sum__zero__power,axiom,
% 5.82/6.15 ! [A: set_nat,C2: nat > complex] :
% 5.82/6.15 ( ( ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( C2 @ zero_zero_nat ) ) )
% 5.82/6.15 & ( ~ ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_complex ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_zero_power
% 5.82/6.15 thf(fact_7033_sum__zero__power,axiom,
% 5.82/6.15 ! [A: set_nat,C2: nat > rat] :
% 5.82/6.15 ( ( ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat
% 5.82/6.15 @ ^ [I4: nat] : ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( C2 @ zero_zero_nat ) ) )
% 5.82/6.15 & ( ~ ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat
% 5.82/6.15 @ ^ [I4: nat] : ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_rat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_zero_power
% 5.82/6.15 thf(fact_7034_sum__zero__power,axiom,
% 5.82/6.15 ! [A: set_nat,C2: nat > real] :
% 5.82/6.15 ( ( ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( C2 @ zero_zero_nat ) ) )
% 5.82/6.15 & ( ~ ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_real ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_zero_power
% 5.82/6.15 thf(fact_7035_sum__zero__power_H,axiom,
% 5.82/6.15 ! [A: set_nat,C2: nat > complex,D2: nat > complex] :
% 5.82/6.15 ( ( ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D2 @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( divide1717551699836669952omplex @ ( C2 @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.82/6.15 & ( ~ ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D2 @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_complex ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_zero_power'
% 5.82/6.15 thf(fact_7036_sum__zero__power_H,axiom,
% 5.82/6.15 ! [A: set_nat,C2: nat > rat,D2: nat > rat] :
% 5.82/6.15 ( ( ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat
% 5.82/6.15 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( divide_divide_rat @ ( C2 @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.82/6.15 & ( ~ ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups2906978787729119204at_rat
% 5.82/6.15 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_rat ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_zero_power'
% 5.82/6.15 thf(fact_7037_sum__zero__power_H,axiom,
% 5.82/6.15 ! [A: set_nat,C2: nat > real,D2: nat > real] :
% 5.82/6.15 ( ( ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D2 @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( divide_divide_real @ ( C2 @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.82/6.15 & ( ~ ( ( finite_finite_nat @ A )
% 5.82/6.15 & ( member_nat @ zero_zero_nat @ A ) )
% 5.82/6.15 => ( ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D2 @ I4 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = zero_zero_real ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_zero_power'
% 5.82/6.15 thf(fact_7038_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,B: set_nat,G: vEBT_VEBT > nat > nat,R: vEBT_VEBT > nat > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( groups771621172384141258BT_nat
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.15 ( groups3542108847815614940at_nat @ ( G @ X3 )
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( ( member_nat @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( groups771621172384141258BT_nat
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7039_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_real,B: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( groups1935376822645274424al_nat
% 5.82/6.15 @ ^ [X3: real] :
% 5.82/6.15 ( groups3542108847815614940at_nat @ ( G @ X3 )
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( ( member_nat @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( groups1935376822645274424al_nat
% 5.82/6.15 @ ^ [X3: real] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [X3: real] :
% 5.82/6.15 ( ( member_real @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7040_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_int,B: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( groups4541462559716669496nt_nat
% 5.82/6.15 @ ^ [X3: int] :
% 5.82/6.15 ( groups3542108847815614940at_nat @ ( G @ X3 )
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( ( member_nat @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( groups4541462559716669496nt_nat
% 5.82/6.15 @ ^ [X3: int] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] :
% 5.82/6.15 ( ( member_int @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7041_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_Code_integer,B: set_nat,G: code_integer > nat > nat,R: code_integer > nat > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( groups7237345082560585321er_nat
% 5.82/6.15 @ ^ [X3: code_integer] :
% 5.82/6.15 ( groups3542108847815614940at_nat @ ( G @ X3 )
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( ( member_nat @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( groups7237345082560585321er_nat
% 5.82/6.15 @ ^ [X3: code_integer] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7042_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_complex,B: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 5.82/6.15 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.15 => ( ( finite_finite_nat @ B )
% 5.82/6.15 => ( ( groups5693394587270226106ex_nat
% 5.82/6.15 @ ^ [X3: complex] :
% 5.82/6.15 ( groups3542108847815614940at_nat @ ( G @ X3 )
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( ( member_nat @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [Y: nat] :
% 5.82/6.15 ( groups5693394587270226106ex_nat
% 5.82/6.15 @ ^ [X3: complex] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [X3: complex] :
% 5.82/6.15 ( ( member_complex @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7043_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_VEBT_VEBT,B: set_complex,G: vEBT_VEBT > complex > complex,R: vEBT_VEBT > complex > $o] :
% 5.82/6.15 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( groups1794756597179926696omplex
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.15 ( groups7754918857620584856omplex @ ( G @ X3 )
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( ( member_complex @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( groups1794756597179926696omplex
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_VEBT_VEBT
% 5.82/6.15 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7044_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_real,B: set_complex,G: real > complex > complex,R: real > complex > $o] :
% 5.82/6.15 ( ( finite_finite_real @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( groups5754745047067104278omplex
% 5.82/6.15 @ ^ [X3: real] :
% 5.82/6.15 ( groups7754918857620584856omplex @ ( G @ X3 )
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( ( member_complex @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( groups5754745047067104278omplex
% 5.82/6.15 @ ^ [X3: real] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_real
% 5.82/6.15 @ ^ [X3: real] :
% 5.82/6.15 ( ( member_real @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7045_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_nat,B: set_complex,G: nat > complex > complex,R: nat > complex > $o] :
% 5.82/6.15 ( ( finite_finite_nat @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [X3: nat] :
% 5.82/6.15 ( groups7754918857620584856omplex @ ( G @ X3 )
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( ( member_complex @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( groups2073611262835488442omplex
% 5.82/6.15 @ ^ [X3: nat] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_nat
% 5.82/6.15 @ ^ [X3: nat] :
% 5.82/6.15 ( ( member_nat @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7046_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_int,B: set_complex,G: int > complex > complex,R: int > complex > $o] :
% 5.82/6.15 ( ( finite_finite_int @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( groups3049146728041665814omplex
% 5.82/6.15 @ ^ [X3: int] :
% 5.82/6.15 ( groups7754918857620584856omplex @ ( G @ X3 )
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( ( member_complex @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( groups3049146728041665814omplex
% 5.82/6.15 @ ^ [X3: int] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_int
% 5.82/6.15 @ ^ [X3: int] :
% 5.82/6.15 ( ( member_int @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7047_sum_Oswap__restrict,axiom,
% 5.82/6.15 ! [A: set_Code_integer,B: set_complex,G: code_integer > complex > complex,R: code_integer > complex > $o] :
% 5.82/6.15 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.15 => ( ( finite3207457112153483333omplex @ B )
% 5.82/6.15 => ( ( groups8024822376189712711omplex
% 5.82/6.15 @ ^ [X3: code_integer] :
% 5.82/6.15 ( groups7754918857620584856omplex @ ( G @ X3 )
% 5.82/6.15 @ ( collect_complex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( ( member_complex @ Y @ B )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [Y: complex] :
% 5.82/6.15 ( groups8024822376189712711omplex
% 5.82/6.15 @ ^ [X3: code_integer] : ( G @ X3 @ Y )
% 5.82/6.15 @ ( collect_Code_integer
% 5.82/6.15 @ ^ [X3: code_integer] :
% 5.82/6.15 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.15 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.15 @ B ) ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum.swap_restrict
% 5.82/6.15 thf(fact_7048_sum__subtractf,axiom,
% 5.82/6.15 ! [F: complex > complex,G: complex > complex,A: set_complex] :
% 5.82/6.15 ( ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [X3: complex] : ( minus_minus_complex @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A ) @ ( groups7754918857620584856omplex @ G @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_subtractf
% 5.82/6.15 thf(fact_7049_sum__subtractf,axiom,
% 5.82/6.15 ! [F: nat > real,G: nat > real,A: set_nat] :
% 5.82/6.15 ( ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [X3: nat] : ( minus_minus_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A ) @ ( groups6591440286371151544t_real @ G @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_subtractf
% 5.82/6.15 thf(fact_7050_sum__subtractf,axiom,
% 5.82/6.15 ! [F: int > int,G: int > int,A: set_int] :
% 5.82/6.15 ( ( groups4538972089207619220nt_int
% 5.82/6.15 @ ^ [X3: int] : ( minus_minus_int @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.15 @ A )
% 5.82/6.15 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A ) @ ( groups4538972089207619220nt_int @ G @ A ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_subtractf
% 5.82/6.15 thf(fact_7051_sum__norm__le,axiom,
% 5.82/6.15 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > complex,G: vEBT_VEBT > real] :
% 5.82/6.15 ( ! [X4: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups1794756597179926696omplex @ F @ S ) ) @ ( groups2240296850493347238T_real @ G @ S ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_norm_le
% 5.82/6.15 thf(fact_7052_sum__norm__le,axiom,
% 5.82/6.15 ! [S: set_real,F: real > complex,G: real > real] :
% 5.82/6.15 ( ! [X4: real] :
% 5.82/6.15 ( ( member_real @ X4 @ S )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S ) ) @ ( groups8097168146408367636l_real @ G @ S ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_norm_le
% 5.82/6.15 thf(fact_7053_sum__norm__le,axiom,
% 5.82/6.15 ! [S: set_int,F: int > complex,G: int > real] :
% 5.82/6.15 ( ! [X4: int] :
% 5.82/6.15 ( ( member_int @ X4 @ S )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S ) ) @ ( groups8778361861064173332t_real @ G @ S ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_norm_le
% 5.82/6.15 thf(fact_7054_sum__norm__le,axiom,
% 5.82/6.15 ! [S: set_nat,F: nat > complex,G: nat > real] :
% 5.82/6.15 ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ S )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S ) ) @ ( groups6591440286371151544t_real @ G @ S ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_norm_le
% 5.82/6.15 thf(fact_7055_sum__norm__le,axiom,
% 5.82/6.15 ! [S: set_complex,F: complex > complex,G: complex > real] :
% 5.82/6.15 ( ! [X4: complex] :
% 5.82/6.15 ( ( member_complex @ X4 @ S )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S ) ) @ ( groups5808333547571424918x_real @ G @ S ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_norm_le
% 5.82/6.15 thf(fact_7056_sum__norm__le,axiom,
% 5.82/6.15 ! [S: set_nat,F: nat > real,G: nat > real] :
% 5.82/6.15 ( ! [X4: nat] :
% 5.82/6.15 ( ( member_nat @ X4 @ S )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X4 ) ) @ ( G @ X4 ) ) )
% 5.82/6.15 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S ) ) @ ( groups6591440286371151544t_real @ G @ S ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_norm_le
% 5.82/6.15 thf(fact_7057_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_nat,F: nat > rat,G: nat > rat] :
% 5.82/6.15 ( ! [I2: nat] :
% 5.82/6.15 ( ( member_nat @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K6 ) @ ( groups2906978787729119204at_rat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7058_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 5.82/6.15 ( ! [I2: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ K6 ) @ ( groups136491112297645522BT_rat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7059_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_real,F: real > rat,G: real > rat] :
% 5.82/6.15 ( ! [I2: real] :
% 5.82/6.15 ( ( member_real @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K6 ) @ ( groups1300246762558778688al_rat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7060_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_int,F: int > rat,G: int > rat] :
% 5.82/6.15 ( ! [I2: int] :
% 5.82/6.15 ( ( member_int @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K6 ) @ ( groups3906332499630173760nt_rat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7061_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.15 ( ! [I2: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ K6 ) @ ( groups771621172384141258BT_nat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7062_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_real,F: real > nat,G: real > nat] :
% 5.82/6.15 ( ! [I2: real] :
% 5.82/6.15 ( ( member_real @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K6 ) @ ( groups1935376822645274424al_nat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7063_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_int,F: int > nat,G: int > nat] :
% 5.82/6.15 ( ! [I2: int] :
% 5.82/6.15 ( ( member_int @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K6 ) @ ( groups4541462559716669496nt_nat @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7064_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_nat,F: nat > int,G: nat > int] :
% 5.82/6.15 ( ! [I2: nat] :
% 5.82/6.15 ( ( member_nat @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K6 ) @ ( groups3539618377306564664at_int @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7065_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 5.82/6.15 ( ! [I2: vEBT_VEBT] :
% 5.82/6.15 ( ( member_VEBT_VEBT @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_int @ ( groups769130701875090982BT_int @ F @ K6 ) @ ( groups769130701875090982BT_int @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7066_sum__mono,axiom,
% 5.82/6.15 ! [K6: set_real,F: real > int,G: real > int] :
% 5.82/6.15 ( ! [I2: real] :
% 5.82/6.15 ( ( member_real @ I2 @ K6 )
% 5.82/6.15 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.15 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K6 ) @ ( groups1932886352136224148al_int @ G @ K6 ) ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_mono
% 5.82/6.15 thf(fact_7067_sum__distrib__left,axiom,
% 5.82/6.15 ! [R2: nat,F: nat > nat,A: set_nat] :
% 5.82/6.15 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [N4: nat] : ( times_times_nat @ R2 @ ( F @ N4 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_left
% 5.82/6.15 thf(fact_7068_sum__distrib__left,axiom,
% 5.82/6.15 ! [R2: complex,F: complex > complex,A: set_complex] :
% 5.82/6.15 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A ) )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [N4: complex] : ( times_times_complex @ R2 @ ( F @ N4 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_left
% 5.82/6.15 thf(fact_7069_sum__distrib__left,axiom,
% 5.82/6.15 ! [R2: real,F: nat > real,A: set_nat] :
% 5.82/6.15 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A ) )
% 5.82/6.15 = ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [N4: nat] : ( times_times_real @ R2 @ ( F @ N4 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_left
% 5.82/6.15 thf(fact_7070_sum__distrib__left,axiom,
% 5.82/6.15 ! [R2: int,F: int > int,A: set_int] :
% 5.82/6.15 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A ) )
% 5.82/6.15 = ( groups4538972089207619220nt_int
% 5.82/6.15 @ ^ [N4: int] : ( times_times_int @ R2 @ ( F @ N4 ) )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_left
% 5.82/6.15 thf(fact_7071_sum__distrib__right,axiom,
% 5.82/6.15 ! [F: nat > nat,A: set_nat,R2: nat] :
% 5.82/6.15 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ R2 )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [N4: nat] : ( times_times_nat @ ( F @ N4 ) @ R2 )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_right
% 5.82/6.15 thf(fact_7072_sum__distrib__right,axiom,
% 5.82/6.15 ! [F: complex > complex,A: set_complex,R2: complex] :
% 5.82/6.15 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A ) @ R2 )
% 5.82/6.15 = ( groups7754918857620584856omplex
% 5.82/6.15 @ ^ [N4: complex] : ( times_times_complex @ ( F @ N4 ) @ R2 )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_right
% 5.82/6.15 thf(fact_7073_sum__distrib__right,axiom,
% 5.82/6.15 ! [F: nat > real,A: set_nat,R2: real] :
% 5.82/6.15 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A ) @ R2 )
% 5.82/6.15 = ( groups6591440286371151544t_real
% 5.82/6.15 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ R2 )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_right
% 5.82/6.15 thf(fact_7074_sum__distrib__right,axiom,
% 5.82/6.15 ! [F: int > int,A: set_int,R2: int] :
% 5.82/6.15 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A ) @ R2 )
% 5.82/6.15 = ( groups4538972089207619220nt_int
% 5.82/6.15 @ ^ [N4: int] : ( times_times_int @ ( F @ N4 ) @ R2 )
% 5.82/6.15 @ A ) ) ).
% 5.82/6.15
% 5.82/6.15 % sum_distrib_right
% 5.82/6.15 thf(fact_7075_sum__product,axiom,
% 5.82/6.15 ! [F: nat > nat,A: set_nat,G: nat > nat,B: set_nat] :
% 5.82/6.15 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ ( groups3542108847815614940at_nat @ G @ B ) )
% 5.82/6.15 = ( groups3542108847815614940at_nat
% 5.82/6.15 @ ^ [I4: nat] :
% 5.82/6.15 ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.82/6.16 @ B )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_product
% 5.82/6.16 thf(fact_7076_sum__product,axiom,
% 5.82/6.16 ! [F: complex > complex,A: set_complex,G: complex > complex,B: set_complex] :
% 5.82/6.16 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A ) @ ( groups7754918857620584856omplex @ G @ B ) )
% 5.82/6.16 = ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [I4: complex] :
% 5.82/6.16 ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.82/6.16 @ B )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_product
% 5.82/6.16 thf(fact_7077_sum__product,axiom,
% 5.82/6.16 ! [F: nat > real,A: set_nat,G: nat > real,B: set_nat] :
% 5.82/6.16 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A ) @ ( groups6591440286371151544t_real @ G @ B ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] :
% 5.82/6.16 ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [J3: nat] : ( times_times_real @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.82/6.16 @ B )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_product
% 5.82/6.16 thf(fact_7078_sum__product,axiom,
% 5.82/6.16 ! [F: int > int,A: set_int,G: int > int,B: set_int] :
% 5.82/6.16 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A ) @ ( groups4538972089207619220nt_int @ G @ B ) )
% 5.82/6.16 = ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [I4: int] :
% 5.82/6.16 ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [J3: int] : ( times_times_int @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.82/6.16 @ B )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_product
% 5.82/6.16 thf(fact_7079_sum_Oswap,axiom,
% 5.82/6.16 ! [G: nat > nat > nat,B: set_nat,A: set_nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( G @ I4 ) @ B )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [J3: nat] :
% 5.82/6.16 ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.82/6.16 @ A )
% 5.82/6.16 @ B ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.swap
% 5.82/6.16 thf(fact_7080_sum_Oswap,axiom,
% 5.82/6.16 ! [G: complex > complex > complex,B: set_complex,A: set_complex] :
% 5.82/6.16 ( ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [I4: complex] : ( groups7754918857620584856omplex @ ( G @ I4 ) @ B )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [J3: complex] :
% 5.82/6.16 ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [I4: complex] : ( G @ I4 @ J3 )
% 5.82/6.16 @ A )
% 5.82/6.16 @ B ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.swap
% 5.82/6.16 thf(fact_7081_sum_Oswap,axiom,
% 5.82/6.16 ! [G: nat > nat > real,B: set_nat,A: set_nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ ( G @ I4 ) @ B )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [J3: nat] :
% 5.82/6.16 ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.82/6.16 @ A )
% 5.82/6.16 @ B ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.swap
% 5.82/6.16 thf(fact_7082_sum_Oswap,axiom,
% 5.82/6.16 ! [G: int > int > int,B: set_int,A: set_int] :
% 5.82/6.16 ( ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [I4: int] : ( groups4538972089207619220nt_int @ ( G @ I4 ) @ B )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [J3: int] :
% 5.82/6.16 ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [I4: int] : ( G @ I4 @ J3 )
% 5.82/6.16 @ A )
% 5.82/6.16 @ B ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.swap
% 5.82/6.16 thf(fact_7083_sum__divide__distrib,axiom,
% 5.82/6.16 ! [F: complex > complex,A: set_complex,R2: complex] :
% 5.82/6.16 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A ) @ R2 )
% 5.82/6.16 = ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [N4: complex] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ R2 )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_divide_distrib
% 5.82/6.16 thf(fact_7084_sum__divide__distrib,axiom,
% 5.82/6.16 ! [F: nat > real,A: set_nat,R2: real] :
% 5.82/6.16 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A ) @ R2 )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ R2 )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_divide_distrib
% 5.82/6.16 thf(fact_7085_norm__sum,axiom,
% 5.82/6.16 ! [F: nat > complex,A: set_nat] :
% 5.82/6.16 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A ) )
% 5.82/6.16 @ ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % norm_sum
% 5.82/6.16 thf(fact_7086_norm__sum,axiom,
% 5.82/6.16 ! [F: complex > complex,A: set_complex] :
% 5.82/6.16 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A ) )
% 5.82/6.16 @ ( groups5808333547571424918x_real
% 5.82/6.16 @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % norm_sum
% 5.82/6.16 thf(fact_7087_norm__sum,axiom,
% 5.82/6.16 ! [F: nat > real,A: set_nat] :
% 5.82/6.16 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A ) )
% 5.82/6.16 @ ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( F @ I4 ) )
% 5.82/6.16 @ A ) ) ).
% 5.82/6.16
% 5.82/6.16 % norm_sum
% 5.82/6.16 thf(fact_7088_sum_Odistrib,axiom,
% 5.82/6.16 ! [G: nat > nat,H2: nat > nat,A: set_nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [X3: nat] : ( plus_plus_nat @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A ) @ ( groups3542108847815614940at_nat @ H2 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.distrib
% 5.82/6.16 thf(fact_7089_sum_Odistrib,axiom,
% 5.82/6.16 ! [G: complex > complex,H2: complex > complex,A: set_complex] :
% 5.82/6.16 ( ( groups7754918857620584856omplex
% 5.82/6.16 @ ^ [X3: complex] : ( plus_plus_complex @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A ) @ ( groups7754918857620584856omplex @ H2 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.distrib
% 5.82/6.16 thf(fact_7090_sum_Odistrib,axiom,
% 5.82/6.16 ! [G: nat > real,H2: nat > real,A: set_nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [X3: nat] : ( plus_plus_real @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A ) @ ( groups6591440286371151544t_real @ H2 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.distrib
% 5.82/6.16 thf(fact_7091_sum_Odistrib,axiom,
% 5.82/6.16 ! [G: int > int,H2: int > int,A: set_int] :
% 5.82/6.16 ( ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [X3: int] : ( plus_plus_int @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.16 @ A )
% 5.82/6.16 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A ) @ ( groups4538972089207619220nt_int @ H2 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.distrib
% 5.82/6.16 thf(fact_7092_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A ) @ zero_zero_real ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7093_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_real,F: real > real] :
% 5.82/6.16 ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A ) @ zero_zero_real ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7094_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_int,F: int > real] :
% 5.82/6.16 ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A ) @ zero_zero_real ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7095_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > rat] :
% 5.82/6.16 ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ zero_zero_rat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7096_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A ) @ zero_zero_rat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7097_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_real,F: real > rat] :
% 5.82/6.16 ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A ) @ zero_zero_rat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7098_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_int,F: int > rat] :
% 5.82/6.16 ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ zero_zero_rat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7099_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.16 ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.82/6.16 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A ) @ zero_zero_nat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7100_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_real,F: real > nat] :
% 5.82/6.16 ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.82/6.16 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A ) @ zero_zero_nat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7101_sum__nonpos,axiom,
% 5.82/6.16 ! [A: set_int,F: int > nat] :
% 5.82/6.16 ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.82/6.16 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ zero_zero_nat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonpos
% 5.82/6.16 thf(fact_7102_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7103_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_real,F: real > real] :
% 5.82/6.16 ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7104_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_int,F: int > real] :
% 5.82/6.16 ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7105_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > rat] :
% 5.82/6.16 ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7106_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7107_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_real,F: real > rat] :
% 5.82/6.16 ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7108_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_int,F: int > rat] :
% 5.82/6.16 ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7109_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.16 ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7110_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_real,F: real > nat] :
% 5.82/6.16 ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7111_sum__nonneg,axiom,
% 5.82/6.16 ! [A: set_int,F: int > nat] :
% 5.82/6.16 ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg
% 5.82/6.16 thf(fact_7112_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: vEBT_VEBT > rat,I6: set_VEBT_VEBT,G: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 5.82/6.16 ( ( ( groups136491112297645522BT_rat @ F @ I6 )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ I6 )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7113_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: real > rat,I6: set_real,G: real > rat,I: real] :
% 5.82/6.16 ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_real @ I @ I6 )
% 5.82/6.16 => ( ( finite_finite_real @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7114_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: nat > rat,I6: set_nat,G: nat > rat,I: nat] :
% 5.82/6.16 ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 5.82/6.16 = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: nat] :
% 5.82/6.16 ( ( member_nat @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_nat @ I @ I6 )
% 5.82/6.16 => ( ( finite_finite_nat @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7115_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: int > rat,I6: set_int,G: int > rat,I: int] :
% 5.82/6.16 ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 5.82/6.16 = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_int @ I @ I6 )
% 5.82/6.16 => ( ( finite_finite_int @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7116_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: code_integer > rat,I6: set_Code_integer,G: code_integer > rat,I: code_integer] :
% 5.82/6.16 ( ( ( groups6602215022474089585er_rat @ F @ I6 )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_Code_integer @ I @ I6 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7117_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: complex > rat,I6: set_complex,G: complex > rat,I: complex] :
% 5.82/6.16 ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 5.82/6.16 = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: complex] :
% 5.82/6.16 ( ( member_complex @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_complex @ I @ I6 )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7118_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: vEBT_VEBT > nat,I6: set_VEBT_VEBT,G: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 5.82/6.16 ( ( ( groups771621172384141258BT_nat @ F @ I6 )
% 5.82/6.16 = ( groups771621172384141258BT_nat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ I6 )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7119_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 5.82/6.16 ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 5.82/6.16 = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_real @ I @ I6 )
% 5.82/6.16 => ( ( finite_finite_real @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7120_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 5.82/6.16 ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 5.82/6.16 = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_int @ I @ I6 )
% 5.82/6.16 => ( ( finite_finite_int @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7121_sum__mono__inv,axiom,
% 5.82/6.16 ! [F: code_integer > nat,I6: set_Code_integer,G: code_integer > nat,I: code_integer] :
% 5.82/6.16 ( ( ( groups7237345082560585321er_nat @ F @ I6 )
% 5.82/6.16 = ( groups7237345082560585321er_nat @ G @ I6 ) )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.82/6.16 => ( ( member_Code_integer @ I @ I6 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = ( G @ I ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono_inv
% 5.82/6.16 thf(fact_7122_sum__cong__Suc,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > nat,G: nat > nat] :
% 5.82/6.16 ( ~ ( member_nat @ zero_zero_nat @ A )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ ( suc @ X4 ) @ A )
% 5.82/6.16 => ( ( F @ ( suc @ X4 ) )
% 5.82/6.16 = ( G @ ( suc @ X4 ) ) ) )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ F @ A )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ G @ A ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_cong_Suc
% 5.82/6.16 thf(fact_7123_sum__cong__Suc,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > real,G: nat > real] :
% 5.82/6.16 ( ~ ( member_nat @ zero_zero_nat @ A )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ ( suc @ X4 ) @ A )
% 5.82/6.16 => ( ( F @ ( suc @ X4 ) )
% 5.82/6.16 = ( G @ ( suc @ X4 ) ) ) )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ F @ A )
% 5.82/6.16 = ( groups6591440286371151544t_real @ G @ A ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_cong_Suc
% 5.82/6.16 thf(fact_7124_mod__sum__eq,axiom,
% 5.82/6.16 ! [F: nat > nat,A2: nat,A: set_nat] :
% 5.82/6.16 ( ( modulo_modulo_nat
% 5.82/6.16 @ ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A2 )
% 5.82/6.16 @ A )
% 5.82/6.16 @ A2 )
% 5.82/6.16 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ A2 ) ) ).
% 5.82/6.16
% 5.82/6.16 % mod_sum_eq
% 5.82/6.16 thf(fact_7125_mod__sum__eq,axiom,
% 5.82/6.16 ! [F: int > int,A2: int,A: set_int] :
% 5.82/6.16 ( ( modulo_modulo_int
% 5.82/6.16 @ ( groups4538972089207619220nt_int
% 5.82/6.16 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A2 )
% 5.82/6.16 @ A )
% 5.82/6.16 @ A2 )
% 5.82/6.16 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A ) @ A2 ) ) ).
% 5.82/6.16
% 5.82/6.16 % mod_sum_eq
% 5.82/6.16 thf(fact_7126_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > complex,P: vEBT_VEBT > $o] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G
% 5.82/6.16 @ ( collect_VEBT_VEBT
% 5.82/6.16 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups1794756597179926696omplex
% 5.82/6.16 @ ^ [X3: vEBT_VEBT] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7127_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_real,G: real > complex,P: real > $o] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G
% 5.82/6.16 @ ( collect_real
% 5.82/6.16 @ ^ [X3: real] :
% 5.82/6.16 ( ( member_real @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups5754745047067104278omplex
% 5.82/6.16 @ ^ [X3: real] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7128_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_nat,G: nat > complex,P: nat > $o] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ G
% 5.82/6.16 @ ( collect_nat
% 5.82/6.16 @ ^ [X3: nat] :
% 5.82/6.16 ( ( member_nat @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups2073611262835488442omplex
% 5.82/6.16 @ ^ [X3: nat] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7129_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_int,G: int > complex,P: int > $o] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( groups3049146728041665814omplex @ G
% 5.82/6.16 @ ( collect_int
% 5.82/6.16 @ ^ [X3: int] :
% 5.82/6.16 ( ( member_int @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups3049146728041665814omplex
% 5.82/6.16 @ ^ [X3: int] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7130_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > complex,P: code_integer > $o] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G
% 5.82/6.16 @ ( collect_Code_integer
% 5.82/6.16 @ ^ [X3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups8024822376189712711omplex
% 5.82/6.16 @ ^ [X3: code_integer] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7131_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G
% 5.82/6.16 @ ( collect_VEBT_VEBT
% 5.82/6.16 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups2240296850493347238T_real
% 5.82/6.16 @ ^ [X3: vEBT_VEBT] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7132_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_real,G: real > real,P: real > $o] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G
% 5.82/6.16 @ ( collect_real
% 5.82/6.16 @ ^ [X3: real] :
% 5.82/6.16 ( ( member_real @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups8097168146408367636l_real
% 5.82/6.16 @ ^ [X3: real] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7133_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_int,G: int > real,P: int > $o] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ G
% 5.82/6.16 @ ( collect_int
% 5.82/6.16 @ ^ [X3: int] :
% 5.82/6.16 ( ( member_int @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups8778361861064173332t_real
% 5.82/6.16 @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7134_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > real,P: code_integer > $o] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G
% 5.82/6.16 @ ( collect_Code_integer
% 5.82/6.16 @ ^ [X3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups1270011288395367621r_real
% 5.82/6.16 @ ^ [X3: code_integer] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7135_sum_Ointer__filter,axiom,
% 5.82/6.16 ! [A: set_complex,G: complex > real,P: complex > $o] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G
% 5.82/6.16 @ ( collect_complex
% 5.82/6.16 @ ^ [X3: complex] :
% 5.82/6.16 ( ( member_complex @ X3 @ A )
% 5.82/6.16 & ( P @ X3 ) ) ) )
% 5.82/6.16 = ( groups5808333547571424918x_real
% 5.82/6.16 @ ^ [X3: complex] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.82/6.16 @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.inter_filter
% 5.82/6.16 thf(fact_7136_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ( finite_finite_int @ T )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: int] :
% 5.82/6.16 ( ( member_int @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7137_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_int,T: set_Code_integer,G: code_integer > real,I: code_integer > int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ T )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7138_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ T )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: complex] :
% 5.82/6.16 ( ( member_complex @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7139_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,T: set_int,G: int > real,I: int > code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ( finite_finite_int @ T )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: int] :
% 5.82/6.16 ( ( member_int @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7140_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,T: set_Code_integer,G: code_integer > real,I: code_integer > code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ T )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S2 ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7141_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,T: set_complex,G: complex > real,I: complex > code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ T )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: complex] :
% 5.82/6.16 ( ( member_complex @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7142_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S2 )
% 5.82/6.16 => ( ( finite_finite_int @ T )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: int] :
% 5.82/6.16 ( ( member_int @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7143_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_complex,T: set_Code_integer,G: code_integer > real,I: code_integer > complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S2 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ T )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7144_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S2 )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ T )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: complex] :
% 5.82/6.16 ( ( member_complex @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7145_sum__le__included,axiom,
% 5.82/6.16 ! [S2: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ S2 )
% 5.82/6.16 => ( ( finite_finite_nat @ T )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ T )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ S2 )
% 5.82/6.16 => ? [Xa2: nat] :
% 5.82/6.16 ( ( member_nat @ Xa2 @ T )
% 5.82/6.16 & ( ( I @ Xa2 )
% 5.82/6.16 = X4 )
% 5.82/6.16 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa2 ) ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_le_included
% 5.82/6.16 thf(fact_7146_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups2240296850493347238T_real @ F @ A )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 = ( ! [X3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7147_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_real,F: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups8097168146408367636l_real @ F @ A )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 = ( ! [X3: real] :
% 5.82/6.16 ( ( member_real @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7148_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups8778361861064173332t_real @ F @ A )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 = ( ! [X3: int] :
% 5.82/6.16 ( ( member_int @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7149_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups1270011288395367621r_real @ F @ A )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 = ( ! [X3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7150_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups5808333547571424918x_real @ F @ A )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 = ( ! [X3: complex] :
% 5.82/6.16 ( ( member_complex @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7151_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups136491112297645522BT_rat @ F @ A )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 = ( ! [X3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7152_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_real,F: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups1300246762558778688al_rat @ F @ A )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 = ( ! [X3: real] :
% 5.82/6.16 ( ( member_real @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7153_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups2906978787729119204at_rat @ F @ A )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 = ( ! [X3: nat] :
% 5.82/6.16 ( ( member_nat @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7154_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_int,F: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups3906332499630173760nt_rat @ F @ A )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 = ( ! [X3: int] :
% 5.82/6.16 ( ( member_int @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7155_sum__nonneg__eq__0__iff,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( ( groups6602215022474089585er_rat @ F @ A )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 = ( ! [X3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.16 => ( ( F @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_eq_0_iff
% 5.82/6.16 thf(fact_7156_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_int,F: int > real,G: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: int] :
% 5.82/6.16 ( ( member_int @ X8 @ A )
% 5.82/6.16 & ( ord_less_real @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A ) @ ( groups8778361861064173332t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7157_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X8 @ A )
% 5.82/6.16 & ( ord_less_real @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A ) @ ( groups1270011288395367621r_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7158_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_complex,F: complex > real,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: complex] :
% 5.82/6.16 ( ( member_complex @ X8 @ A )
% 5.82/6.16 & ( ord_less_real @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A ) @ ( groups5808333547571424918x_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7159_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > rat,G: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: nat] :
% 5.82/6.16 ( ( member_nat @ X8 @ A )
% 5.82/6.16 & ( ord_less_rat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( groups2906978787729119204at_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7160_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_int,F: int > rat,G: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: int] :
% 5.82/6.16 ( ( member_int @ X8 @ A )
% 5.82/6.16 & ( ord_less_rat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ ( groups3906332499630173760nt_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7161_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X8 @ A )
% 5.82/6.16 & ( ord_less_rat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( groups6602215022474089585er_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7162_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_complex,F: complex > rat,G: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: complex] :
% 5.82/6.16 ( ( member_complex @ X8 @ A )
% 5.82/6.16 & ( ord_less_rat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A ) @ ( groups5058264527183730370ex_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7163_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_int,F: int > nat,G: int > nat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: int] :
% 5.82/6.16 ( ( member_int @ X8 @ A )
% 5.82/6.16 & ( ord_less_nat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( groups4541462559716669496nt_nat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7164_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X8 @ A )
% 5.82/6.16 & ( ord_less_nat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A ) @ ( groups7237345082560585321er_nat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7165_sum__strict__mono__ex1,axiom,
% 5.82/6.16 ! [A: set_complex,F: complex > nat,G: complex > nat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ A )
% 5.82/6.16 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ? [X8: complex] :
% 5.82/6.16 ( ( member_complex @ X8 @ A )
% 5.82/6.16 & ( ord_less_nat @ ( F @ X8 ) @ ( G @ X8 ) ) )
% 5.82/6.16 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A ) @ ( groups5693394587270226106ex_nat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono_ex1
% 5.82/6.16 thf(fact_7166_sum_Orelated,axiom,
% 5.82/6.16 ! [R: complex > complex > $o,S: set_nat,H2: nat > complex,G: nat > complex] :
% 5.82/6.16 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.82/6.16 => ( ! [X15: complex,Y1: complex,X23: complex,Y22: complex] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_complex @ X15 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite_finite_nat @ S )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups2073611262835488442omplex @ H2 @ S ) @ ( groups2073611262835488442omplex @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7167_sum_Orelated,axiom,
% 5.82/6.16 ! [R: complex > complex > $o,S: set_int,H2: int > complex,G: int > complex] :
% 5.82/6.16 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.82/6.16 => ( ! [X15: complex,Y1: complex,X23: complex,Y22: complex] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_complex @ X15 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite_finite_int @ S )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups3049146728041665814omplex @ H2 @ S ) @ ( groups3049146728041665814omplex @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7168_sum_Orelated,axiom,
% 5.82/6.16 ! [R: complex > complex > $o,S: set_Code_integer,H2: code_integer > complex,G: code_integer > complex] :
% 5.82/6.16 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.82/6.16 => ( ! [X15: complex,Y1: complex,X23: complex,Y22: complex] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_complex @ X15 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ S )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups8024822376189712711omplex @ H2 @ S ) @ ( groups8024822376189712711omplex @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7169_sum_Orelated,axiom,
% 5.82/6.16 ! [R: real > real > $o,S: set_int,H2: int > real,G: int > real] :
% 5.82/6.16 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.82/6.16 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_real @ X15 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite_finite_int @ S )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups8778361861064173332t_real @ H2 @ S ) @ ( groups8778361861064173332t_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7170_sum_Orelated,axiom,
% 5.82/6.16 ! [R: real > real > $o,S: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 5.82/6.16 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.82/6.16 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_real @ X15 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ S )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups1270011288395367621r_real @ H2 @ S ) @ ( groups1270011288395367621r_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7171_sum_Orelated,axiom,
% 5.82/6.16 ! [R: real > real > $o,S: set_complex,H2: complex > real,G: complex > real] :
% 5.82/6.16 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.82/6.16 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_real @ X15 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ S )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups5808333547571424918x_real @ H2 @ S ) @ ( groups5808333547571424918x_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7172_sum_Orelated,axiom,
% 5.82/6.16 ! [R: rat > rat > $o,S: set_nat,H2: nat > rat,G: nat > rat] :
% 5.82/6.16 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.82/6.16 => ( ! [X15: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_rat @ X15 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite_finite_nat @ S )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S ) @ ( groups2906978787729119204at_rat @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7173_sum_Orelated,axiom,
% 5.82/6.16 ! [R: rat > rat > $o,S: set_int,H2: int > rat,G: int > rat] :
% 5.82/6.16 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.82/6.16 => ( ! [X15: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_rat @ X15 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite_finite_int @ S )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S ) @ ( groups3906332499630173760nt_rat @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7174_sum_Orelated,axiom,
% 5.82/6.16 ! [R: rat > rat > $o,S: set_Code_integer,H2: code_integer > rat,G: code_integer > rat] :
% 5.82/6.16 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.82/6.16 => ( ! [X15: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_rat @ X15 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ S )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups6602215022474089585er_rat @ H2 @ S ) @ ( groups6602215022474089585er_rat @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7175_sum_Orelated,axiom,
% 5.82/6.16 ! [R: rat > rat > $o,S: set_complex,H2: complex > rat,G: complex > rat] :
% 5.82/6.16 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.82/6.16 => ( ! [X15: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.82/6.16 ( ( ( R @ X15 @ X23 )
% 5.82/6.16 & ( R @ Y1 @ Y22 ) )
% 5.82/6.16 => ( R @ ( plus_plus_rat @ X15 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ S )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S )
% 5.82/6.16 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S ) @ ( groups5058264527183730370ex_rat @ G @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.related
% 5.82/6.16 thf(fact_7176_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( A != bot_bo8194388402131092736T_VEBT )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A ) @ ( groups2240296850493347238T_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7177_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_real,F: real > real,G: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( A != bot_bot_set_real )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A ) @ ( groups8097168146408367636l_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7178_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( A != bot_bo3990330152332043303nteger )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A ) @ ( groups1270011288395367621r_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7179_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_complex,F: complex > real,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( A != bot_bot_set_complex )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ A )
% 5.82/6.16 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A ) @ ( groups5808333547571424918x_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7180_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_int,F: int > real,G: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( A != bot_bot_set_int )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ A )
% 5.82/6.16 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A ) @ ( groups8778361861064173332t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7181_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( A != bot_bo8194388402131092736T_VEBT )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.16 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A ) @ ( groups136491112297645522BT_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7182_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_real,F: real > rat,G: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( A != bot_bot_set_real )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ A )
% 5.82/6.16 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A ) @ ( groups1300246762558778688al_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7183_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( A != bot_bo3990330152332043303nteger )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ A )
% 5.82/6.16 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( groups6602215022474089585er_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7184_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_complex,F: complex > rat,G: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( A != bot_bot_set_complex )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ A )
% 5.82/6.16 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A ) @ ( groups5058264527183730370ex_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7185_sum__strict__mono,axiom,
% 5.82/6.16 ! [A: set_nat,F: nat > rat,G: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( A != bot_bot_set_nat )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ A )
% 5.82/6.16 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( groups2906978787729119204at_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono
% 5.82/6.16 thf(fact_7186_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( groups2240296850493347238T_real @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7187_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_real,X2: real,G: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.16 = ( groups8097168146408367636l_real @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7188_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_int,X2: int,G: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( ( member_int @ X2 @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.16 = ( groups8778361861064173332t_real @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_int @ X2 @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7189_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_Code_integer,X2: code_integer,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ( member_Code_integer @ X2 @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( groups1270011288395367621r_real @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_Code_integer @ X2 @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1270011288395367621r_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7190_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_complex,X2: complex,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( ( member_complex @ X2 @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.16 = ( groups5808333547571424918x_real @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_complex @ X2 @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7191_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7192_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_real,X2: real,G: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7193_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_nat,X2: nat,G: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( ( member_nat @ X2 @ A )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.16 = ( groups2906978787729119204at_rat @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_nat @ X2 @ A )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7194_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_int,X2: int,G: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( ( member_int @ X2 @ A )
% 5.82/6.16 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.16 = ( groups3906332499630173760nt_rat @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_int @ X2 @ A )
% 5.82/6.16 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7195_sum_Oinsert__if,axiom,
% 5.82/6.16 ! [A: set_Code_integer,X2: code_integer,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ( member_Code_integer @ X2 @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ G @ A ) ) )
% 5.82/6.16 & ( ~ ( member_Code_integer @ X2 @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups6602215022474089585er_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_if
% 5.82/6.16 thf(fact_7196_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_VEBT_VEBT,T6: set_VEBT_VEBT,S: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T5: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ T6 )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ S )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7197_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_VEBT_VEBT,T6: set_real,S: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T5: set_real,G: vEBT_VEBT > complex,H2: real > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.16 => ( ( finite_finite_real @ T6 )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ S )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7198_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_real,T6: set_VEBT_VEBT,S: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T5: set_VEBT_VEBT,G: real > complex,H2: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite_finite_real @ S7 )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ T6 )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.16 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7199_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_real,T6: set_real,S: set_real,I: real > real,J: real > real,T5: set_real,G: real > complex,H2: real > complex] :
% 5.82/6.16 ( ( finite_finite_real @ S7 )
% 5.82/6.16 => ( ( finite_finite_real @ T6 )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.16 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7200_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_VEBT_VEBT,T6: set_int,S: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T5: set_int,G: vEBT_VEBT > complex,H2: int > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.16 => ( ( finite_finite_int @ T6 )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: int] :
% 5.82/6.16 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: int] :
% 5.82/6.16 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: int] :
% 5.82/6.16 ( ( member_int @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ S )
% 5.82/6.16 = ( groups3049146728041665814omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7201_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_real,T6: set_int,S: set_real,I: int > real,J: real > int,T5: set_int,G: real > complex,H2: int > complex] :
% 5.82/6.16 ( ( finite_finite_real @ S7 )
% 5.82/6.16 => ( ( finite_finite_int @ T6 )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: int] :
% 5.82/6.16 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: int] :
% 5.82/6.16 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.16 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: int] :
% 5.82/6.16 ( ( member_int @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.82/6.16 = ( groups3049146728041665814omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7202_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_VEBT_VEBT,T6: set_Code_integer,S: set_VEBT_VEBT,I: code_integer > vEBT_VEBT,J: vEBT_VEBT > code_integer,T5: set_Code_integer,G: vEBT_VEBT > complex,H2: code_integer > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ T6 )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.16 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ S )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7203_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_real,T6: set_Code_integer,S: set_real,I: code_integer > real,J: real > code_integer,T5: set_Code_integer,G: real > complex,H2: code_integer > complex] :
% 5.82/6.16 ( ( finite_finite_real @ S7 )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ T6 )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.16 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.16 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7204_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_int,T6: set_VEBT_VEBT,S: set_int,I: vEBT_VEBT > int,J: int > vEBT_VEBT,T5: set_VEBT_VEBT,G: int > complex,H2: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite_finite_int @ S7 )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ T6 )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S7 ) )
% 5.82/6.16 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.16 => ( member_int @ ( I @ B3 ) @ ( minus_minus_set_int @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups3049146728041665814omplex @ G @ S )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7205_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.16 ! [S7: set_int,T6: set_real,S: set_int,I: real > int,J: int > real,T5: set_real,G: int > complex,H2: real > complex] :
% 5.82/6.16 ( ( finite_finite_int @ S7 )
% 5.82/6.16 => ( ( finite_finite_real @ T6 )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S7 ) )
% 5.82/6.16 => ( ( I @ ( J @ A3 ) )
% 5.82/6.16 = A3 ) )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S7 ) )
% 5.82/6.16 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T6 ) ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.16 => ( ( J @ ( I @ B3 ) )
% 5.82/6.16 = B3 ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.16 => ( member_int @ ( I @ B3 ) @ ( minus_minus_set_int @ S @ S7 ) ) )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ S7 )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ T6 )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [A3: int] :
% 5.82/6.16 ( ( member_int @ A3 @ S )
% 5.82/6.16 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.16 = ( G @ A3 ) ) )
% 5.82/6.16 => ( ( groups3049146728041665814omplex @ G @ S )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.reindex_bij_witness_not_neutral
% 5.82/6.16 thf(fact_7206_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_VEBT_VEBT,F: vEBT_VEBT > real,I: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups2240296850493347238T_real @ F @ S2 )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7207_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_real,F: real > real,I: real] :
% 5.82/6.16 ( ( finite_finite_real @ S2 )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( member_real @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7208_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_int,F: int > real,I: int] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( member_int @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7209_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,F: code_integer > real,I: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups1270011288395367621r_real @ F @ S2 )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( member_Code_integer @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7210_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_complex,F: complex > real,I: complex] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S2 )
% 5.82/6.16 => ( ! [I2: complex] :
% 5.82/6.16 ( ( member_complex @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( member_complex @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7211_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_VEBT_VEBT,F: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups136491112297645522BT_rat @ F @ S2 )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7212_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_real,F: real > rat,I: real] :
% 5.82/6.16 ( ( finite_finite_real @ S2 )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( member_real @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7213_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_nat,F: nat > rat,I: nat] :
% 5.82/6.16 ( ( finite_finite_nat @ S2 )
% 5.82/6.16 => ( ! [I2: nat] :
% 5.82/6.16 ( ( member_nat @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( member_nat @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7214_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_int,F: int > rat,I: int] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( member_int @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7215_sum__nonneg__0,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,F: code_integer > rat,I: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups6602215022474089585er_rat @ F @ S2 )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( member_Code_integer @ I @ S2 )
% 5.82/6.16 => ( ( F @ I )
% 5.82/6.16 = zero_zero_rat ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_0
% 5.82/6.16 thf(fact_7216_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_VEBT_VEBT,F: vEBT_VEBT > real,B: real,I: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups2240296850493347238T_real @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7217_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_real,F: real > real,B: real,I: real] :
% 5.82/6.16 ( ( finite_finite_real @ S2 )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_real @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7218_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_int,F: int > real,B: real,I: int] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_int @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7219_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,F: code_integer > real,B: real,I: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups1270011288395367621r_real @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_Code_integer @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7220_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_complex,F: complex > real,B: real,I: complex] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S2 )
% 5.82/6.16 => ( ! [I2: complex] :
% 5.82/6.16 ( ( member_complex @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_complex @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7221_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_VEBT_VEBT,F: vEBT_VEBT > rat,B: rat,I: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups136491112297645522BT_rat @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7222_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_real,F: real > rat,B: rat,I: real] :
% 5.82/6.16 ( ( finite_finite_real @ S2 )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_real @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7223_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_nat,F: nat > rat,B: rat,I: nat] :
% 5.82/6.16 ( ( finite_finite_nat @ S2 )
% 5.82/6.16 => ( ! [I2: nat] :
% 5.82/6.16 ( ( member_nat @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_nat @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7224_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_int,F: int > rat,B: rat,I: int] :
% 5.82/6.16 ( ( finite_finite_int @ S2 )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_int @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7225_sum__nonneg__leq__bound,axiom,
% 5.82/6.16 ! [S2: set_Code_integer,F: code_integer > rat,B: rat,I: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S2 )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ( ( groups6602215022474089585er_rat @ F @ S2 )
% 5.82/6.16 = B )
% 5.82/6.16 => ( ( member_Code_integer @ I @ S2 )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_nonneg_leq_bound
% 5.82/6.16 thf(fact_7226_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_int,G: int > complex] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( groups3049146728041665814omplex @ G
% 5.82/6.16 @ ( minus_minus_set_int @ A
% 5.82/6.16 @ ( collect_int
% 5.82/6.16 @ ^ [X3: int] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_complex ) ) ) )
% 5.82/6.16 = ( groups3049146728041665814omplex @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7227_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G
% 5.82/6.16 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.16 @ ( collect_Code_integer
% 5.82/6.16 @ ^ [X3: code_integer] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_complex ) ) ) )
% 5.82/6.16 = ( groups8024822376189712711omplex @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7228_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_int,G: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ G
% 5.82/6.16 @ ( minus_minus_set_int @ A
% 5.82/6.16 @ ( collect_int
% 5.82/6.16 @ ^ [X3: int] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) )
% 5.82/6.16 = ( groups8778361861064173332t_real @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7229_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G
% 5.82/6.16 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.16 @ ( collect_Code_integer
% 5.82/6.16 @ ^ [X3: code_integer] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) )
% 5.82/6.16 = ( groups1270011288395367621r_real @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7230_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_complex,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G
% 5.82/6.16 @ ( minus_811609699411566653omplex @ A
% 5.82/6.16 @ ( collect_complex
% 5.82/6.16 @ ^ [X3: complex] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_real ) ) ) )
% 5.82/6.16 = ( groups5808333547571424918x_real @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7231_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_int,G: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( groups3906332499630173760nt_rat @ G
% 5.82/6.16 @ ( minus_minus_set_int @ A
% 5.82/6.16 @ ( collect_int
% 5.82/6.16 @ ^ [X3: int] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) )
% 5.82/6.16 = ( groups3906332499630173760nt_rat @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7232_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G
% 5.82/6.16 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.16 @ ( collect_Code_integer
% 5.82/6.16 @ ^ [X3: code_integer] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7233_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_complex,G: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ G
% 5.82/6.16 @ ( minus_811609699411566653omplex @ A
% 5.82/6.16 @ ( collect_complex
% 5.82/6.16 @ ^ [X3: complex] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_rat ) ) ) )
% 5.82/6.16 = ( groups5058264527183730370ex_rat @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7234_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_int,G: int > nat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( groups4541462559716669496nt_nat @ G
% 5.82/6.16 @ ( minus_minus_set_int @ A
% 5.82/6.16 @ ( collect_int
% 5.82/6.16 @ ^ [X3: int] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_nat ) ) ) )
% 5.82/6.16 = ( groups4541462559716669496nt_nat @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7235_sum_Osetdiff__irrelevant,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > nat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups7237345082560585321er_nat @ G
% 5.82/6.16 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.16 @ ( collect_Code_integer
% 5.82/6.16 @ ^ [X3: code_integer] :
% 5.82/6.16 ( ( G @ X3 )
% 5.82/6.16 = zero_zero_nat ) ) ) )
% 5.82/6.16 = ( groups7237345082560585321er_nat @ G @ A ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.setdiff_irrelevant
% 5.82/6.16 thf(fact_7236_sum_Oshift__bounds__Suc__ivl,axiom,
% 5.82/6.16 ! [G: nat > nat,M: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_Suc_ivl
% 5.82/6.16 thf(fact_7237_sum_Oshift__bounds__Suc__ivl,axiom,
% 5.82/6.16 ! [G: nat > real,M: nat,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_Suc_ivl
% 5.82/6.16 thf(fact_7238_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.82/6.16 ! [G: nat > nat,M: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_cl_Suc_ivl
% 5.82/6.16 thf(fact_7239_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.82/6.16 ! [G: nat > real,M: nat,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_cl_Suc_ivl
% 5.82/6.16 thf(fact_7240_sum_Oshift__bounds__nat__ivl,axiom,
% 5.82/6.16 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_nat_ivl
% 5.82/6.16 thf(fact_7241_sum_Oshift__bounds__nat__ivl,axiom,
% 5.82/6.16 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_nat_ivl
% 5.82/6.16 thf(fact_7242_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.82/6.16 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_cl_nat_ivl
% 5.82/6.16 thf(fact_7243_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.82/6.16 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.shift_bounds_cl_nat_ivl
% 5.82/6.16 thf(fact_7244_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7245_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_real,I: real,F: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ I6 )
% 5.82/6.16 => ( ( member_real @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7246_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_int,I: int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ I6 )
% 5.82/6.16 => ( ( member_int @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7247_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_Code_integer,I: code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.16 => ( ( member_Code_integer @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups1270011288395367621r_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7248_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_complex,I: complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.16 => ( ( member_complex @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: complex] :
% 5.82/6.16 ( ( member_complex @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7249_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7250_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_real,I: real,F: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ I6 )
% 5.82/6.16 => ( ( member_real @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7251_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_nat,I: nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ I6 )
% 5.82/6.16 => ( ( member_nat @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: nat] :
% 5.82/6.16 ( ( member_nat @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7252_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_int,I: int,F: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ I6 )
% 5.82/6.16 => ( ( member_int @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7253_sum__pos2,axiom,
% 5.82/6.16 ! [I6: set_Code_integer,I: code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.16 => ( ( member_Code_integer @ I @ I6 )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos2
% 5.82/6.16 thf(fact_7254_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7255_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_real,F: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bot_set_real )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7256_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_Code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bo3990330152332043303nteger )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups1270011288395367621r_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7257_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bot_set_complex )
% 5.82/6.16 => ( ! [I2: complex] :
% 5.82/6.16 ( ( member_complex @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7258_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bot_set_int )
% 5.82/6.16 => ( ! [I2: int] :
% 5.82/6.16 ( ( member_int @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7259_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 5.82/6.16 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7260_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_real,F: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bot_set_real )
% 5.82/6.16 => ( ! [I2: real] :
% 5.82/6.16 ( ( member_real @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7261_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_Code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bo3990330152332043303nteger )
% 5.82/6.16 => ( ! [I2: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7262_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_complex,F: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bot_set_complex )
% 5.82/6.16 => ( ! [I2: complex] :
% 5.82/6.16 ( ( member_complex @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7263_sum__pos,axiom,
% 5.82/6.16 ! [I6: set_nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ I6 )
% 5.82/6.16 => ( ( I6 != bot_bot_set_nat )
% 5.82/6.16 => ( ! [I2: nat] :
% 5.82/6.16 ( ( member_nat @ I2 @ I6 )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.82/6.16 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_pos
% 5.82/6.16 thf(fact_7264_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( ( groups1794756597179926696omplex @ G @ A )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ B ) )
% 5.82/6.16 = ( ( groups1794756597179926696omplex @ G @ C )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7265_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_real,A: set_real,B: set_real,G: real > complex,H2: real > complex] :
% 5.82/6.16 ( ( finite_finite_real @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( ( groups5754745047067104278omplex @ G @ A )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ B ) )
% 5.82/6.16 = ( ( groups5754745047067104278omplex @ G @ C )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7266_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > complex,H2: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.16 => ( ! [A3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( ( groups8024822376189712711omplex @ G @ A )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ B ) )
% 5.82/6.16 = ( ( groups8024822376189712711omplex @ G @ C )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7267_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups2240296850493347238T_real @ G @ A )
% 5.82/6.16 = ( groups2240296850493347238T_real @ H2 @ B ) )
% 5.82/6.16 = ( ( groups2240296850493347238T_real @ G @ C )
% 5.82/6.16 = ( groups2240296850493347238T_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7268_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_real,A: set_real,B: set_real,G: real > real,H2: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups8097168146408367636l_real @ G @ A )
% 5.82/6.16 = ( groups8097168146408367636l_real @ H2 @ B ) )
% 5.82/6.16 = ( ( groups8097168146408367636l_real @ G @ C )
% 5.82/6.16 = ( groups8097168146408367636l_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7269_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.16 => ( ! [A3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups1270011288395367621r_real @ G @ A )
% 5.82/6.16 = ( groups1270011288395367621r_real @ H2 @ B ) )
% 5.82/6.16 = ( ( groups1270011288395367621r_real @ G @ C )
% 5.82/6.16 = ( groups1270011288395367621r_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7270_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_complex,A: set_complex,B: set_complex,G: complex > real,H2: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ C )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ A @ C )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ B @ C )
% 5.82/6.16 => ( ! [A3: complex] :
% 5.82/6.16 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: complex] :
% 5.82/6.16 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups5808333547571424918x_real @ G @ A )
% 5.82/6.16 = ( groups5808333547571424918x_real @ H2 @ B ) )
% 5.82/6.16 = ( ( groups5808333547571424918x_real @ G @ C )
% 5.82/6.16 = ( groups5808333547571424918x_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7271_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( ( groups136491112297645522BT_rat @ G @ A )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ H2 @ B ) )
% 5.82/6.16 = ( ( groups136491112297645522BT_rat @ G @ C )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7272_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_real,A: set_real,B: set_real,G: real > rat,H2: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( ( groups1300246762558778688al_rat @ G @ A )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ H2 @ B ) )
% 5.82/6.16 = ( ( groups1300246762558778688al_rat @ G @ C )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7273_sum_Osame__carrier,axiom,
% 5.82/6.16 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > rat,H2: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.16 => ( ! [A3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( ( groups6602215022474089585er_rat @ G @ A )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ H2 @ B ) )
% 5.82/6.16 = ( ( groups6602215022474089585er_rat @ G @ C )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrier
% 5.82/6.16 thf(fact_7274_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( ( groups1794756597179926696omplex @ G @ C )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ C ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ A )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7275_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_real,A: set_real,B: set_real,G: real > complex,H2: real > complex] :
% 5.82/6.16 ( ( finite_finite_real @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( ( groups5754745047067104278omplex @ G @ C )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ C ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ A )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7276_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > complex,H2: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.16 => ( ! [A3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( ( groups8024822376189712711omplex @ G @ C )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ C ) )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G @ A )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7277_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups2240296850493347238T_real @ G @ C )
% 5.82/6.16 = ( groups2240296850493347238T_real @ H2 @ C ) )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ A )
% 5.82/6.16 = ( groups2240296850493347238T_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7278_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_real,A: set_real,B: set_real,G: real > real,H2: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups8097168146408367636l_real @ G @ C )
% 5.82/6.16 = ( groups8097168146408367636l_real @ H2 @ C ) )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G @ A )
% 5.82/6.16 = ( groups8097168146408367636l_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7279_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.16 => ( ! [A3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups1270011288395367621r_real @ G @ C )
% 5.82/6.16 = ( groups1270011288395367621r_real @ H2 @ C ) )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ A )
% 5.82/6.16 = ( groups1270011288395367621r_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7280_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_complex,A: set_complex,B: set_complex,G: complex > real,H2: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ C )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ A @ C )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ B @ C )
% 5.82/6.16 => ( ! [A3: complex] :
% 5.82/6.16 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [B3: complex] :
% 5.82/6.16 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( ( groups5808333547571424918x_real @ G @ C )
% 5.82/6.16 = ( groups5808333547571424918x_real @ H2 @ C ) )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ A )
% 5.82/6.16 = ( groups5808333547571424918x_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7281_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.16 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( ( groups136491112297645522BT_rat @ G @ C )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ H2 @ C ) )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ A )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7282_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_real,A: set_real,B: set_real,G: real > rat,H2: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.16 => ( ! [A3: real] :
% 5.82/6.16 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( ( groups1300246762558778688al_rat @ G @ C )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ H2 @ C ) )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ G @ A )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7283_sum_Osame__carrierI,axiom,
% 5.82/6.16 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > rat,H2: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.16 => ( ! [A3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.16 => ( ( G @ A3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.16 => ( ( H2 @ B3 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( ( groups6602215022474089585er_rat @ G @ C )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ H2 @ C ) )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ A )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.same_carrierI
% 5.82/6.16 thf(fact_7284_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G @ S )
% 5.82/6.16 = ( groups8024822376189712711omplex @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7285_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ S )
% 5.82/6.16 = ( groups1270011288395367621r_real @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7286_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ S )
% 5.82/6.16 = ( groups5808333547571424918x_real @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7287_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ S )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7288_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ G @ S )
% 5.82/6.16 = ( groups5058264527183730370ex_rat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7289_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_nat ) )
% 5.82/6.16 => ( ( groups7237345082560585321er_nat @ G @ S )
% 5.82/6.16 = ( groups7237345082560585321er_nat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7290_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > nat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_nat ) )
% 5.82/6.16 => ( ( groups5693394587270226106ex_nat @ G @ S )
% 5.82/6.16 = ( groups5693394587270226106ex_nat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7291_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_int ) )
% 5.82/6.16 => ( ( groups7234854612051535045er_int @ G @ S )
% 5.82/6.16 = ( groups7234854612051535045er_int @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7292_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > int] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_int ) )
% 5.82/6.16 => ( ( groups5690904116761175830ex_int @ G @ S )
% 5.82/6.16 = ( groups5690904116761175830ex_int @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7293_sum_Omono__neutral__left,axiom,
% 5.82/6.16 ! [T5: set_nat,S: set_nat,G: nat > complex] :
% 5.82/6.16 ( ( finite_finite_nat @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_nat @ S @ T5 )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ G @ S )
% 5.82/6.16 = ( groups2073611262835488442omplex @ G @ T5 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_left
% 5.82/6.16 thf(fact_7294_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G @ T5 )
% 5.82/6.16 = ( groups8024822376189712711omplex @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7295_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ T5 )
% 5.82/6.16 = ( groups1270011288395367621r_real @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7296_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ T5 )
% 5.82/6.16 = ( groups5808333547571424918x_real @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7297_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ T5 )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7298_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ G @ T5 )
% 5.82/6.16 = ( groups5058264527183730370ex_rat @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7299_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_nat ) )
% 5.82/6.16 => ( ( groups7237345082560585321er_nat @ G @ T5 )
% 5.82/6.16 = ( groups7237345082560585321er_nat @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7300_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > nat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_nat ) )
% 5.82/6.16 => ( ( groups5693394587270226106ex_nat @ G @ T5 )
% 5.82/6.16 = ( groups5693394587270226106ex_nat @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7301_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_int ) )
% 5.82/6.16 => ( ( groups7234854612051535045er_int @ G @ T5 )
% 5.82/6.16 = ( groups7234854612051535045er_int @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7302_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > int] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_int ) )
% 5.82/6.16 => ( ( groups5690904116761175830ex_int @ G @ T5 )
% 5.82/6.16 = ( groups5690904116761175830ex_int @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7303_sum_Omono__neutral__right,axiom,
% 5.82/6.16 ! [T5: set_nat,S: set_nat,G: nat > complex] :
% 5.82/6.16 ( ( finite_finite_nat @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_nat @ S @ T5 )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ G @ T5 )
% 5.82/6.16 = ( groups2073611262835488442omplex @ G @ S ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_right
% 5.82/6.16 thf(fact_7304_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ S )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7305_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_real,S: set_real,H2: real > complex,G: real > complex] :
% 5.82/6.16 ( ( finite_finite_real @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7306_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,H2: code_integer > complex,G: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G @ S )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7307_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ S )
% 5.82/6.16 = ( groups2240296850493347238T_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7308_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_real,S: set_real,H2: real > real,G: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G @ S )
% 5.82/6.16 = ( groups8097168146408367636l_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7309_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ S )
% 5.82/6.16 = ( groups1270011288395367621r_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7310_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,H2: complex > real,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ S )
% 5.82/6.16 = ( groups5808333547571424918x_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7311_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ S )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7312_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_real,S: set_real,H2: real > rat,G: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ G @ S )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7313_sum_Omono__neutral__cong__left,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,H2: code_integer > rat,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( H2 @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ S )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_left
% 5.82/6.16 thf(fact_7314_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,G: vEBT_VEBT > complex,H2: vEBT_VEBT > complex] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups1794756597179926696omplex @ G @ T5 )
% 5.82/6.16 = ( groups1794756597179926696omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7315_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_real,S: set_real,G: real > complex,H2: real > complex] :
% 5.82/6.16 ( ( finite_finite_real @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups5754745047067104278omplex @ G @ T5 )
% 5.82/6.16 = ( groups5754745047067104278omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7316_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > complex,H2: code_integer > complex] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups8024822376189712711omplex @ G @ T5 )
% 5.82/6.16 = ( groups8024822376189712711omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7317_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ T5 )
% 5.82/6.16 = ( groups2240296850493347238T_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7318_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_real,S: set_real,G: real > real,H2: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G @ T5 )
% 5.82/6.16 = ( groups8097168146408367636l_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7319_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ T5 )
% 5.82/6.16 = ( groups1270011288395367621r_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7320_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_complex,S: set_complex,G: complex > real,H2: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ T5 )
% 5.82/6.16 = ( groups5808333547571424918x_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7321_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ T5 )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7322_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_real,S: set_real,G: real > rat,H2: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ T5 )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ G @ T5 )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7323_sum_Omono__neutral__cong__right,axiom,
% 5.82/6.16 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > rat,H2: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ T5 )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.mono_neutral_cong_right
% 5.82/6.16 thf(fact_7324_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > real] :
% 5.82/6.16 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ A )
% 5.82/6.16 = ( plus_plus_real @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups1270011288395367621r_real @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7325_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,G: complex > real] :
% 5.82/6.16 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ A )
% 5.82/6.16 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups5808333547571424918x_real @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7326_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > rat] :
% 5.82/6.16 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups6602215022474089585er_rat @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7327_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,G: complex > rat] :
% 5.82/6.16 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups5058264527183730370ex_rat @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7328_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > nat] :
% 5.82/6.16 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups7237345082560585321er_nat @ G @ A )
% 5.82/6.16 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups7237345082560585321er_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7329_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,G: complex > nat] :
% 5.82/6.16 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5693394587270226106ex_nat @ G @ A )
% 5.82/6.16 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups5693394587270226106ex_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7330_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > int] :
% 5.82/6.16 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups7234854612051535045er_int @ G @ A )
% 5.82/6.16 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups7234854612051535045er_int @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7331_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,G: complex > int] :
% 5.82/6.16 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5690904116761175830ex_int @ G @ A )
% 5.82/6.16 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups5690904116761175830ex_int @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7332_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_nat,A: set_nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.16 => ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A @ B ) ) @ ( groups2906978787729119204at_rat @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7333_sum_Osubset__diff,axiom,
% 5.82/6.16 ! [B: set_nat,A: set_nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.16 => ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ A )
% 5.82/6.16 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A @ B ) ) @ ( groups3539618377306564664at_int @ G @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.subset_diff
% 5.82/6.16 thf(fact_7334_sum__diff,axiom,
% 5.82/6.16 ! [A: set_Code_integer,B: set_Code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A @ B ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups1270011288395367621r_real @ F @ A ) @ ( groups1270011288395367621r_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7335_sum__diff,axiom,
% 5.82/6.16 ! [A: set_complex,B: set_complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A @ B ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A ) @ ( groups5808333547571424918x_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7336_sum__diff,axiom,
% 5.82/6.16 ! [A: set_Code_integer,B: set_Code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A @ B ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( groups6602215022474089585er_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7337_sum__diff,axiom,
% 5.82/6.16 ! [A: set_complex,B: set_complex,F: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A @ B ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A ) @ ( groups5058264527183730370ex_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7338_sum__diff,axiom,
% 5.82/6.16 ! [A: set_Code_integer,B: set_Code_integer,F: code_integer > int] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.16 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A @ B ) )
% 5.82/6.16 = ( minus_minus_int @ ( groups7234854612051535045er_int @ F @ A ) @ ( groups7234854612051535045er_int @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7339_sum__diff,axiom,
% 5.82/6.16 ! [A: set_complex,B: set_complex,F: complex > int] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.16 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A @ B ) )
% 5.82/6.16 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A ) @ ( groups5690904116761175830ex_int @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7340_sum__diff,axiom,
% 5.82/6.16 ! [A: set_nat,B: set_nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( groups2906978787729119204at_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7341_sum__diff,axiom,
% 5.82/6.16 ! [A: set_nat,B: set_nat,F: nat > int] :
% 5.82/6.16 ( ( finite_finite_nat @ A )
% 5.82/6.16 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.16 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A ) @ ( groups3539618377306564664at_int @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7342_sum__diff,axiom,
% 5.82/6.16 ! [A: set_int,B: set_int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( ord_less_eq_set_int @ B @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A ) @ ( groups8778361861064173332t_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7343_sum__diff,axiom,
% 5.82/6.16 ! [A: set_int,B: set_int,F: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( ord_less_eq_set_int @ B @ A )
% 5.82/6.16 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ ( groups3906332499630173760nt_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff
% 5.82/6.16 thf(fact_7344_sum_Oivl__cong,axiom,
% 5.82/6.16 ! [A2: nat,C2: nat,B2: nat,D2: nat,G: nat > nat,H2: nat > nat] :
% 5.82/6.16 ( ( A2 = C2 )
% 5.82/6.16 => ( ( B2 = D2 )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ C2 @ X4 )
% 5.82/6.16 => ( ( ord_less_nat @ X4 @ D2 )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) ) )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ivl_cong
% 5.82/6.16 thf(fact_7345_sum_Oivl__cong,axiom,
% 5.82/6.16 ! [A2: nat,C2: nat,B2: nat,D2: nat,G: nat > real,H2: nat > real] :
% 5.82/6.16 ( ( A2 = C2 )
% 5.82/6.16 => ( ( B2 = D2 )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ C2 @ X4 )
% 5.82/6.16 => ( ( ord_less_nat @ X4 @ D2 )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) ) )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) )
% 5.82/6.16 = ( groups6591440286371151544t_real @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ivl_cong
% 5.82/6.16 thf(fact_7346_sum_Oivl__cong,axiom,
% 5.82/6.16 ! [A2: int,C2: int,B2: int,D2: int,G: int > int,H2: int > int] :
% 5.82/6.16 ( ( A2 = C2 )
% 5.82/6.16 => ( ( B2 = D2 )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( ord_less_eq_int @ C2 @ X4 )
% 5.82/6.16 => ( ( ord_less_int @ X4 @ D2 )
% 5.82/6.16 => ( ( G @ X4 )
% 5.82/6.16 = ( H2 @ X4 ) ) ) )
% 5.82/6.16 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A2 @ B2 ) )
% 5.82/6.16 = ( groups4538972089207619220nt_int @ H2 @ ( set_or4662586982721622107an_int @ C2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ivl_cong
% 5.82/6.16 thf(fact_7347_sum_OatLeastLessThan__concat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_concat
% 5.82/6.16 thf(fact_7348_sum_OatLeastLessThan__concat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_concat
% 5.82/6.16 thf(fact_7349_sum_OatLeastLessThan__concat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_concat
% 5.82/6.16 thf(fact_7350_sum_OatLeastLessThan__concat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_concat
% 5.82/6.16 thf(fact_7351_sum__diff__nat__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,F: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 5.82/6.16 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff_nat_ivl
% 5.82/6.16 thf(fact_7352_sum__diff__nat__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,F: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 5.82/6.16 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff_nat_ivl
% 5.82/6.16 thf(fact_7353_sum__diff__nat__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,P6: nat,F: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.16 => ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff_nat_ivl
% 5.82/6.16 thf(fact_7354_sum__power__add,axiom,
% 5.82/6.16 ! [X2: complex,M: nat,I6: set_nat] :
% 5.82/6.16 ( ( groups2073611262835488442omplex
% 5.82/6.16 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.82/6.16 @ I6 )
% 5.82/6.16 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ I6 ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_power_add
% 5.82/6.16 thf(fact_7355_sum__power__add,axiom,
% 5.82/6.16 ! [X2: code_integer,M: nat,I6: set_nat] :
% 5.82/6.16 ( ( groups7501900531339628137nteger
% 5.82/6.16 @ ^ [I4: nat] : ( power_8256067586552552935nteger @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.82/6.16 @ I6 )
% 5.82/6.16 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ I6 ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_power_add
% 5.82/6.16 thf(fact_7356_sum__power__add,axiom,
% 5.82/6.16 ! [X2: rat,M: nat,I6: set_nat] :
% 5.82/6.16 ( ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.82/6.16 @ I6 )
% 5.82/6.16 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ I6 ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_power_add
% 5.82/6.16 thf(fact_7357_sum__power__add,axiom,
% 5.82/6.16 ! [X2: int,M: nat,I6: set_nat] :
% 5.82/6.16 ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.82/6.16 @ I6 )
% 5.82/6.16 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ I6 ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_power_add
% 5.82/6.16 thf(fact_7358_sum__power__add,axiom,
% 5.82/6.16 ! [X2: real,M: nat,I6: set_nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.82/6.16 @ I6 )
% 5.82/6.16 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ I6 ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_power_add
% 5.82/6.16 thf(fact_7359_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A ) @ ( groups2240296850493347238T_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7360_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_real,A: set_real,F: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ B )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A ) @ ( groups8097168146408367636l_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7361_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ A ) @ ( groups1270011288395367621r_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7362_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.16 => ( ! [B3: complex] :
% 5.82/6.16 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A ) @ ( groups5808333547571424918x_real @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7363_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A ) @ ( groups136491112297645522BT_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7364_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_real,A: set_real,F: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ B )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.16 => ( ! [B3: real] :
% 5.82/6.16 ( ( member_real @ B3 @ ( minus_minus_set_real @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A ) @ ( groups1300246762558778688al_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7365_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.16 => ( ! [B3: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( groups6602215022474089585er_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7366_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,F: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.16 => ( ! [B3: complex] :
% 5.82/6.16 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A ) @ ( groups5058264527183730370ex_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7367_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_nat,A: set_nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ B )
% 5.82/6.16 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.16 => ( ! [B3: nat] :
% 5.82/6.16 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( groups2906978787729119204at_rat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7368_sum__mono2,axiom,
% 5.82/6.16 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.16 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 5.82/6.16 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A ) @ ( groups771621172384141258BT_nat @ F @ B ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_mono2
% 5.82/6.16 thf(fact_7369_sum_OatLeastAtMost__rev,axiom,
% 5.82/6.16 ! [G: nat > nat,N: nat,M: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastAtMost_rev
% 5.82/6.16 thf(fact_7370_sum_OatLeastAtMost__rev,axiom,
% 5.82/6.16 ! [G: nat > real,N: nat,M: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastAtMost_rev
% 5.82/6.16 thf(fact_7371_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7372_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > real,X2: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7373_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_complex,G: complex > real,X2: complex] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7374_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > rat,X2: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7375_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > rat,X2: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7376_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_complex,G: complex > rat,X2: complex] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7377_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > nat,X2: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7378_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_Code_integer,G: code_integer > nat,X2: code_integer] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7379_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_complex,G: complex > nat,X2: complex] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7380_sum_Oinsert__remove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > int,X2: vEBT_VEBT] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.16 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.insert_remove
% 5.82/6.16 thf(fact_7381_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ G @ A )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7382_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_real,X2: real,G: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ G @ A )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7383_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_Code_integer,X2: code_integer,G: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( member_Code_integer @ X2 @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ G @ A )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7384_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_complex,X2: complex,G: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( member_complex @ X2 @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ G @ A )
% 5.82/6.16 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7385_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7386_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_real,X2: real,G: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7387_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_Code_integer,X2: code_integer,G: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( member_Code_integer @ X2 @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7388_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_complex,X2: complex,G: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( member_complex @ X2 @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ G @ A )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7389_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.16 => ( ( groups771621172384141258BT_nat @ G @ A )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7390_sum_Oremove,axiom,
% 5.82/6.16 ! [A: set_real,X2: real,G: real > nat] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( member_real @ X2 @ A )
% 5.82/6.16 => ( ( groups1935376822645274424al_nat @ G @ A )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.remove
% 5.82/6.16 thf(fact_7391_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,A2: vEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups2240296850493347238T_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.16 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.16 = ( groups2240296850493347238T_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7392_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_real,A2: real,F: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( ( member_real @ A2 @ A )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_real @ A2 @ A )
% 5.82/6.16 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.16 = ( groups8097168146408367636l_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7393_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_Code_integer,A2: code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ( member_Code_integer @ A2 @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups1270011288395367621r_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_Code_integer @ A2 @ A )
% 5.82/6.16 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.16 = ( groups1270011288395367621r_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7394_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_complex,A2: complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( ( member_complex @ A2 @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_complex @ A2 @ A )
% 5.82/6.16 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.16 = ( groups5808333547571424918x_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7395_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_int,A2: int,F: int > real] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( ( member_int @ A2 @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.16 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_int @ A2 @ A )
% 5.82/6.16 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.16 = ( groups8778361861064173332t_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7396_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_VEBT_VEBT,A2: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7397_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_real,A2: real,F: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ( ( member_real @ A2 @ A )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_real @ A2 @ A )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7398_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_Code_integer,A2: code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ( ( member_Code_integer @ A2 @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_Code_integer @ A2 @ A )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7399_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_complex,A2: complex,F: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ( ( member_complex @ A2 @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_complex @ A2 @ A )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.16 = ( groups5058264527183730370ex_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7400_sum__diff1,axiom,
% 5.82/6.16 ! [A: set_int,A2: int,F: int > rat] :
% 5.82/6.16 ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ( ( member_int @ A2 @ A )
% 5.82/6.16 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.16 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.16 & ( ~ ( member_int @ A2 @ A )
% 5.82/6.16 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.16 = ( groups3906332499630173760nt_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_diff1
% 5.82/6.16 thf(fact_7401_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > real,C2: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.16 => ( ( groups2240296850493347238T_real
% 5.82/6.16 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_real @ ( B2 @ A2 ) @ ( groups2240296850493347238T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.16 => ( ( groups2240296850493347238T_real
% 5.82/6.16 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups2240296850493347238T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7402_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_real,A2: real,B2: real > real,C2: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ S )
% 5.82/6.16 => ( ( ( member_real @ A2 @ S )
% 5.82/6.16 => ( ( groups8097168146408367636l_real
% 5.82/6.16 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_real @ ( B2 @ A2 ) @ ( groups8097168146408367636l_real @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.16 => ( ( groups8097168146408367636l_real
% 5.82/6.16 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups8097168146408367636l_real @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7403_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > real,C2: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.16 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.16 => ( ( groups1270011288395367621r_real
% 5.82/6.16 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_real @ ( B2 @ A2 ) @ ( groups1270011288395367621r_real @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.16 => ( ( groups1270011288395367621r_real
% 5.82/6.16 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups1270011288395367621r_real @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7404_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_complex,A2: complex,B2: complex > real,C2: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.16 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.16 => ( ( groups5808333547571424918x_real
% 5.82/6.16 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_real @ ( B2 @ A2 ) @ ( groups5808333547571424918x_real @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.16 => ( ( groups5808333547571424918x_real
% 5.82/6.16 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups5808333547571424918x_real @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7405_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > rat,C2: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat
% 5.82/6.16 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_rat @ ( B2 @ A2 ) @ ( groups136491112297645522BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.16 => ( ( groups136491112297645522BT_rat
% 5.82/6.16 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups136491112297645522BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7406_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_real,A2: real,B2: real > rat,C2: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ S )
% 5.82/6.16 => ( ( ( member_real @ A2 @ S )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat
% 5.82/6.16 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_rat @ ( B2 @ A2 ) @ ( groups1300246762558778688al_rat @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.16 => ( ( groups1300246762558778688al_rat
% 5.82/6.16 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups1300246762558778688al_rat @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7407_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > rat,C2: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.16 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat
% 5.82/6.16 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_rat @ ( B2 @ A2 ) @ ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.16 => ( ( groups6602215022474089585er_rat
% 5.82/6.16 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7408_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_complex,A2: complex,B2: complex > rat,C2: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.16 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat
% 5.82/6.16 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_rat @ ( B2 @ A2 ) @ ( groups5058264527183730370ex_rat @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.16 => ( ( groups5058264527183730370ex_rat
% 5.82/6.16 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups5058264527183730370ex_rat @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7409_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > nat,C2: vEBT_VEBT > nat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.16 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.16 => ( ( groups771621172384141258BT_nat
% 5.82/6.16 @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_nat @ ( B2 @ A2 ) @ ( groups771621172384141258BT_nat @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.16 => ( ( groups771621172384141258BT_nat
% 5.82/6.16 @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups771621172384141258BT_nat @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7410_sum_Odelta__remove,axiom,
% 5.82/6.16 ! [S: set_real,A2: real,B2: real > nat,C2: real > nat] :
% 5.82/6.16 ( ( finite_finite_real @ S )
% 5.82/6.16 => ( ( ( member_real @ A2 @ S )
% 5.82/6.16 => ( ( groups1935376822645274424al_nat
% 5.82/6.16 @ ^ [K3: real] : ( if_nat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( plus_plus_nat @ ( B2 @ A2 ) @ ( groups1935376822645274424al_nat @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.82/6.16 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.16 => ( ( groups1935376822645274424al_nat
% 5.82/6.16 @ ^ [K3: real] : ( if_nat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.16 @ S )
% 5.82/6.16 = ( groups1935376822645274424al_nat @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.delta_remove
% 5.82/6.16 thf(fact_7411_sum__shift__lb__Suc0__0__upt,axiom,
% 5.82/6.16 ! [F: nat > complex,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_complex )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups2073611262835488442omplex @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0_upt
% 5.82/6.16 thf(fact_7412_sum__shift__lb__Suc0__0__upt,axiom,
% 5.82/6.16 ! [F: nat > rat,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0_upt
% 5.82/6.16 thf(fact_7413_sum__shift__lb__Suc0__0__upt,axiom,
% 5.82/6.16 ! [F: nat > int,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_int )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0_upt
% 5.82/6.16 thf(fact_7414_sum__shift__lb__Suc0__0__upt,axiom,
% 5.82/6.16 ! [F: nat > nat,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_nat )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0_upt
% 5.82/6.16 thf(fact_7415_sum__shift__lb__Suc0__0__upt,axiom,
% 5.82/6.16 ! [F: nat > real,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0_upt
% 5.82/6.16 thf(fact_7416_sum__shift__lb__Suc0__0,axiom,
% 5.82/6.16 ! [F: nat > complex,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_complex )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0
% 5.82/6.16 thf(fact_7417_sum__shift__lb__Suc0__0,axiom,
% 5.82/6.16 ! [F: nat > rat,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_rat )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0
% 5.82/6.16 thf(fact_7418_sum__shift__lb__Suc0__0,axiom,
% 5.82/6.16 ! [F: nat > int,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_int )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0
% 5.82/6.16 thf(fact_7419_sum__shift__lb__Suc0__0,axiom,
% 5.82/6.16 ! [F: nat > nat,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_nat )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0
% 5.82/6.16 thf(fact_7420_sum__shift__lb__Suc0__0,axiom,
% 5.82/6.16 ! [F: nat > real,K: nat] :
% 5.82/6.16 ( ( ( F @ zero_zero_nat )
% 5.82/6.16 = zero_zero_real )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.82/6.16 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_shift_lb_Suc0_0
% 5.82/6.16 thf(fact_7421_sum_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.16 ! [G: nat > rat,N: nat] :
% 5.82/6.16 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_lessThan_Suc
% 5.82/6.16 thf(fact_7422_sum_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.16 ! [G: nat > int,N: nat] :
% 5.82/6.16 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_lessThan_Suc
% 5.82/6.16 thf(fact_7423_sum_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.16 ! [G: nat > nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_lessThan_Suc
% 5.82/6.16 thf(fact_7424_sum_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.16 ! [G: nat > real,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_lessThan_Suc
% 5.82/6.16 thf(fact_7425_sum_OatLeast__Suc__lessThan,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_lessThan
% 5.82/6.16 thf(fact_7426_sum_OatLeast__Suc__lessThan,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_lessThan
% 5.82/6.16 thf(fact_7427_sum_OatLeast__Suc__lessThan,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_nat @ M @ N )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_lessThan
% 5.82/6.16 thf(fact_7428_sum_OatLeast__Suc__lessThan,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_lessThan
% 5.82/6.16 thf(fact_7429_sum_OatLeast0__atMost__Suc,axiom,
% 5.82/6.16 ! [G: nat > rat,N: nat] :
% 5.82/6.16 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_atMost_Suc
% 5.82/6.16 thf(fact_7430_sum_OatLeast0__atMost__Suc,axiom,
% 5.82/6.16 ! [G: nat > int,N: nat] :
% 5.82/6.16 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_atMost_Suc
% 5.82/6.16 thf(fact_7431_sum_OatLeast0__atMost__Suc,axiom,
% 5.82/6.16 ! [G: nat > nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_atMost_Suc
% 5.82/6.16 thf(fact_7432_sum_OatLeast0__atMost__Suc,axiom,
% 5.82/6.16 ! [G: nat > real,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast0_atMost_Suc
% 5.82/6.16 thf(fact_7433_sum_OatLeastLessThan__Suc,axiom,
% 5.82/6.16 ! [A2: nat,B2: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.16 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_Suc
% 5.82/6.16 thf(fact_7434_sum_OatLeastLessThan__Suc,axiom,
% 5.82/6.16 ! [A2: nat,B2: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.16 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_Suc
% 5.82/6.16 thf(fact_7435_sum_OatLeastLessThan__Suc,axiom,
% 5.82/6.16 ! [A2: nat,B2: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.16 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_Suc
% 5.82/6.16 thf(fact_7436_sum_OatLeastLessThan__Suc,axiom,
% 5.82/6.16 ! [A2: nat,B2: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.16 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_Suc
% 5.82/6.16 thf(fact_7437_sum_OatLeast__Suc__atMost,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_atMost
% 5.82/6.16 thf(fact_7438_sum_OatLeast__Suc__atMost,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_atMost
% 5.82/6.16 thf(fact_7439_sum_OatLeast__Suc__atMost,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_atMost
% 5.82/6.16 thf(fact_7440_sum_OatLeast__Suc__atMost,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeast_Suc_atMost
% 5.82/6.16 thf(fact_7441_sum_Onat__ivl__Suc_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.nat_ivl_Suc'
% 5.82/6.16 thf(fact_7442_sum_Onat__ivl__Suc_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.nat_ivl_Suc'
% 5.82/6.16 thf(fact_7443_sum_Onat__ivl__Suc_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.nat_ivl_Suc'
% 5.82/6.16 thf(fact_7444_sum_Onat__ivl__Suc_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.nat_ivl_Suc'
% 5.82/6.16 thf(fact_7445_sum_Olast__plus,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ N ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.last_plus
% 5.82/6.16 thf(fact_7446_sum_Olast__plus,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_int @ ( G @ N ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.last_plus
% 5.82/6.16 thf(fact_7447_sum_Olast__plus,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ N ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.last_plus
% 5.82/6.16 thf(fact_7448_sum_Olast__plus,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ N ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.last_plus
% 5.82/6.16 thf(fact_7449_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,B2: vEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A ) @ ( groups2240296850493347238T_real @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7450_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_real,A: set_real,B2: real,F: real > real] :
% 5.82/6.16 ( ( finite_finite_real @ B )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.16 => ( ( member_real @ B2 @ ( minus_minus_set_real @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A ) @ ( groups8097168146408367636l_real @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7451_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,B2: code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.16 => ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A ) @ ( groups1270011288395367621r_real @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7452_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,B2: complex,F: complex > real] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.16 => ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A ) @ ( groups5808333547571424918x_real @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7453_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,B2: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A ) @ ( groups136491112297645522BT_rat @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7454_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_real,A: set_real,B2: real,F: real > rat] :
% 5.82/6.16 ( ( finite_finite_real @ B )
% 5.82/6.16 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.16 => ( ( member_real @ B2 @ ( minus_minus_set_real @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A ) @ ( groups1300246762558778688al_rat @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7455_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_Code_integer,A: set_Code_integer,B2: code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.16 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.16 => ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( groups6602215022474089585er_rat @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7456_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_complex,A: set_complex,B2: complex,F: complex > rat] :
% 5.82/6.16 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.16 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.16 => ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A ) @ ( groups5058264527183730370ex_rat @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7457_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_nat,A: set_nat,B2: nat,F: nat > rat] :
% 5.82/6.16 ( ( finite_finite_nat @ B )
% 5.82/6.16 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.16 => ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: nat] :
% 5.82/6.16 ( ( member_nat @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( groups2906978787729119204at_rat @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7458_sum__strict__mono2,axiom,
% 5.82/6.16 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,B2: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.16 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.16 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.16 => ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.16 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B2 ) )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ B )
% 5.82/6.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A ) @ ( groups771621172384141258BT_nat @ F @ B ) ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_strict_mono2
% 5.82/6.16 thf(fact_7459_member__le__sum,axiom,
% 5.82/6.16 ! [I: vEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I @ A )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7460_member__le__sum,axiom,
% 5.82/6.16 ! [I: real,A: set_real,F: real > real] :
% 5.82/6.16 ( ( member_real @ I @ A )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ A @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7461_member__le__sum,axiom,
% 5.82/6.16 ! [I: code_integer,A: set_Code_integer,F: code_integer > real] :
% 5.82/6.16 ( ( member_Code_integer @ I @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ I @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ ( groups1270011288395367621r_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7462_member__le__sum,axiom,
% 5.82/6.16 ! [I: complex,A: set_complex,F: complex > real] :
% 5.82/6.16 ( ( member_complex @ I @ A )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7463_member__le__sum,axiom,
% 5.82/6.16 ! [I: int,A: set_int,F: int > real] :
% 5.82/6.16 ( ( member_int @ I @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ ( minus_minus_set_int @ A @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.82/6.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7464_member__le__sum,axiom,
% 5.82/6.16 ! [I: vEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ I @ A )
% 5.82/6.16 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.16 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7465_member__le__sum,axiom,
% 5.82/6.16 ! [I: real,A: set_real,F: real > rat] :
% 5.82/6.16 ( ( member_real @ I @ A )
% 5.82/6.16 => ( ! [X4: real] :
% 5.82/6.16 ( ( member_real @ X4 @ ( minus_minus_set_real @ A @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite_finite_real @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7466_member__le__sum,axiom,
% 5.82/6.16 ! [I: code_integer,A: set_Code_integer,F: code_integer > rat] :
% 5.82/6.16 ( ( member_Code_integer @ I @ A )
% 5.82/6.16 => ( ! [X4: code_integer] :
% 5.82/6.16 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ I @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups6602215022474089585er_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7467_member__le__sum,axiom,
% 5.82/6.16 ! [I: complex,A: set_complex,F: complex > rat] :
% 5.82/6.16 ( ( member_complex @ I @ A )
% 5.82/6.16 => ( ! [X4: complex] :
% 5.82/6.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7468_member__le__sum,axiom,
% 5.82/6.16 ! [I: int,A: set_int,F: int > rat] :
% 5.82/6.16 ( ( member_int @ I @ A )
% 5.82/6.16 => ( ! [X4: int] :
% 5.82/6.16 ( ( member_int @ X4 @ ( minus_minus_set_int @ A @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.82/6.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.82/6.16 => ( ( finite_finite_int @ A )
% 5.82/6.16 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % member_le_sum
% 5.82/6.16 thf(fact_7469_sum_OSuc__reindex__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_rat @ ( G @ M )
% 5.82/6.16 @ ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.Suc_reindex_ivl
% 5.82/6.16 thf(fact_7470_sum_OSuc__reindex__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_int @ ( G @ M )
% 5.82/6.16 @ ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.Suc_reindex_ivl
% 5.82/6.16 thf(fact_7471_sum_OSuc__reindex__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_nat @ ( G @ M )
% 5.82/6.16 @ ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.Suc_reindex_ivl
% 5.82/6.16 thf(fact_7472_sum_OSuc__reindex__ivl,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.16 = ( plus_plus_real @ ( G @ M )
% 5.82/6.16 @ ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.Suc_reindex_ivl
% 5.82/6.16 thf(fact_7473_sum__Suc__diff_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_Suc_diff'
% 5.82/6.16 thf(fact_7474_sum__Suc__diff_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_Suc_diff'
% 5.82/6.16 thf(fact_7475_sum__Suc__diff_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_Suc_diff'
% 5.82/6.16 thf(fact_7476_sum__Suc__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_Suc_diff
% 5.82/6.16 thf(fact_7477_sum__Suc__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_Suc_diff
% 5.82/6.16 thf(fact_7478_sum__Suc__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.16 => ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_Suc_diff
% 5.82/6.16 thf(fact_7479_sum_OatLeastLessThan__rev,axiom,
% 5.82/6.16 ! [G: nat > nat,N: nat,M: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I4 ) ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_rev
% 5.82/6.16 thf(fact_7480_sum_OatLeastLessThan__rev,axiom,
% 5.82/6.16 ! [G: nat > real,N: nat,M: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I4 ) ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_rev
% 5.82/6.16 thf(fact_7481_sum_Onested__swap,axiom,
% 5.82/6.16 ! [A2: nat > nat > nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( A2 @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [J3: nat] :
% 5.82/6.16 ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.nested_swap
% 5.82/6.16 thf(fact_7482_sum_Onested__swap,axiom,
% 5.82/6.16 ! [A2: nat > nat > real,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ ( A2 @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [J3: nat] :
% 5.82/6.16 ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.nested_swap
% 5.82/6.16 thf(fact_7483_sum_Oub__add__nat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ub_add_nat
% 5.82/6.16 thf(fact_7484_sum_Oub__add__nat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ub_add_nat
% 5.82/6.16 thf(fact_7485_sum_Oub__add__nat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ub_add_nat
% 5.82/6.16 thf(fact_7486_sum_Oub__add__nat,axiom,
% 5.82/6.16 ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.16 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.ub_add_nat
% 5.82/6.16 thf(fact_7487_sum_Ohead__if,axiom,
% 5.82/6.16 ! [N: nat,M: nat,G: nat > complex] :
% 5.82/6.16 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_complex ) )
% 5.82/6.16 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.head_if
% 5.82/6.16 thf(fact_7488_sum_Ohead__if,axiom,
% 5.82/6.16 ! [N: nat,M: nat,G: nat > rat] :
% 5.82/6.16 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_rat ) )
% 5.82/6.16 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.head_if
% 5.82/6.16 thf(fact_7489_sum_Ohead__if,axiom,
% 5.82/6.16 ! [N: nat,M: nat,G: nat > int] :
% 5.82/6.16 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_int ) )
% 5.82/6.16 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.head_if
% 5.82/6.16 thf(fact_7490_sum_Ohead__if,axiom,
% 5.82/6.16 ! [N: nat,M: nat,G: nat > nat] :
% 5.82/6.16 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_nat ) )
% 5.82/6.16 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.head_if
% 5.82/6.16 thf(fact_7491_sum_Ohead__if,axiom,
% 5.82/6.16 ! [N: nat,M: nat,G: nat > real] :
% 5.82/6.16 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_real ) )
% 5.82/6.16 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.16 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.head_if
% 5.82/6.16 thf(fact_7492_set__encode__def,axiom,
% 5.82/6.16 ( nat_set_encode
% 5.82/6.16 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % set_encode_def
% 5.82/6.16 thf(fact_7493_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.82/6.16 ! [G: nat > nat,N: nat,M: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_rev_at_least_Suc_atMost
% 5.82/6.16 thf(fact_7494_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.82/6.16 ! [G: nat > real,N: nat,M: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.atLeastLessThan_rev_at_least_Suc_atMost
% 5.82/6.16 thf(fact_7495_sum__natinterval__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > complex] :
% 5.82/6.16 ( ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2073611262835488442omplex
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.82/6.16 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2073611262835488442omplex
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_complex ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_natinterval_diff
% 5.82/6.16 thf(fact_7496_sum__natinterval__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > rat] :
% 5.82/6.16 ( ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.82/6.16 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_rat ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_natinterval_diff
% 5.82/6.16 thf(fact_7497_sum__natinterval__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > int] :
% 5.82/6.16 ( ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.82/6.16 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_int ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_natinterval_diff
% 5.82/6.16 thf(fact_7498_sum__natinterval__diff,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > real] :
% 5.82/6.16 ( ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.82/6.16 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = zero_zero_real ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_natinterval_diff
% 5.82/6.16 thf(fact_7499_sum__telescope_H_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.82/6.16 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_telescope''
% 5.82/6.16 thf(fact_7500_sum__telescope_H_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.82/6.16 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_telescope''
% 5.82/6.16 thf(fact_7501_sum__telescope_H_H,axiom,
% 5.82/6.16 ! [M: nat,N: nat,F: nat > real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.82/6.16 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_telescope''
% 5.82/6.16 thf(fact_7502_mask__eq__sum__exp,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer )
% 5.82/6.16 = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.16 @ ( collect_nat
% 5.82/6.16 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % mask_eq_sum_exp
% 5.82/6.16 thf(fact_7503_mask__eq__sum__exp,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.82/6.16 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.16 @ ( collect_nat
% 5.82/6.16 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % mask_eq_sum_exp
% 5.82/6.16 thf(fact_7504_mask__eq__sum__exp,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.16 @ ( collect_nat
% 5.82/6.16 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % mask_eq_sum_exp
% 5.82/6.16 thf(fact_7505_sum_Oin__pairs,axiom,
% 5.82/6.16 ! [G: nat > rat,M: nat,N: nat] :
% 5.82/6.16 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.16 = ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.in_pairs
% 5.82/6.16 thf(fact_7506_sum_Oin__pairs,axiom,
% 5.82/6.16 ! [G: nat > int,M: nat,N: nat] :
% 5.82/6.16 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.16 = ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.in_pairs
% 5.82/6.16 thf(fact_7507_sum_Oin__pairs,axiom,
% 5.82/6.16 ! [G: nat > nat,M: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.in_pairs
% 5.82/6.16 thf(fact_7508_sum_Oin__pairs,axiom,
% 5.82/6.16 ! [G: nat > real,M: nat,N: nat] :
% 5.82/6.16 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.16 = ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum.in_pairs
% 5.82/6.16 thf(fact_7509_sum__gp__multiplied,axiom,
% 5.82/6.16 ! [M: nat,N: nat,X2: complex] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.82/6.16 = ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_gp_multiplied
% 5.82/6.16 thf(fact_7510_sum__gp__multiplied,axiom,
% 5.82/6.16 ! [M: nat,N: nat,X2: code_integer] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X2 ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.82/6.16 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_gp_multiplied
% 5.82/6.16 thf(fact_7511_sum__gp__multiplied,axiom,
% 5.82/6.16 ! [M: nat,N: nat,X2: rat] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.82/6.16 = ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_gp_multiplied
% 5.82/6.16 thf(fact_7512_sum__gp__multiplied,axiom,
% 5.82/6.16 ! [M: nat,N: nat,X2: int] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.82/6.16 = ( minus_minus_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_gp_multiplied
% 5.82/6.16 thf(fact_7513_sum__gp__multiplied,axiom,
% 5.82/6.16 ! [M: nat,N: nat,X2: real] :
% 5.82/6.16 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.16 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.82/6.16 = ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_gp_multiplied
% 5.82/6.16 thf(fact_7514_mask__eq__sum__exp__nat,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.16 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.16 @ ( collect_nat
% 5.82/6.16 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % mask_eq_sum_exp_nat
% 5.82/6.16 thf(fact_7515_gauss__sum__nat,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [X3: nat] : X3
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % gauss_sum_nat
% 5.82/6.16 thf(fact_7516_sum__power2,axiom,
% 5.82/6.16 ! [K: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.82/6.16 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.82/6.16
% 5.82/6.16 % sum_power2
% 5.82/6.16 thf(fact_7517_Sum__Ico__nat,axiom,
% 5.82/6.16 ! [M: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [X3: nat] : X3
% 5.82/6.16 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.16 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % Sum_Ico_nat
% 5.82/6.16 thf(fact_7518_double__gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum
% 5.82/6.16 thf(fact_7519_double__gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum
% 5.82/6.16 thf(fact_7520_double__gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum
% 5.82/6.16 thf(fact_7521_double__gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum
% 5.82/6.16 thf(fact_7522_double__gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum
% 5.82/6.16 thf(fact_7523_double__arith__series,axiom,
% 5.82/6.16 ! [A2: complex,D2: complex,N: nat] :
% 5.82/6.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.82/6.16 @ ( groups2073611262835488442omplex
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_complex @ A2 @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_arith_series
% 5.82/6.16 thf(fact_7524_double__arith__series,axiom,
% 5.82/6.16 ! [A2: rat,D2: rat,N: nat] :
% 5.82/6.16 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.82/6.16 @ ( groups2906978787729119204at_rat
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_rat @ A2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_arith_series
% 5.82/6.16 thf(fact_7525_double__arith__series,axiom,
% 5.82/6.16 ! [A2: int,D2: int,N: nat] :
% 5.82/6.16 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.82/6.16 @ ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_int @ A2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_arith_series
% 5.82/6.16 thf(fact_7526_double__arith__series,axiom,
% 5.82/6.16 ! [A2: nat,D2: nat,N: nat] :
% 5.82/6.16 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.82/6.16 @ ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_arith_series
% 5.82/6.16 thf(fact_7527_double__arith__series,axiom,
% 5.82/6.16 ! [A2: real,D2: real,N: nat] :
% 5.82/6.16 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.82/6.16 @ ( groups6591440286371151544t_real
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_real @ A2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.16 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D2 ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_arith_series
% 5.82/6.16 thf(fact_7528_arith__series__nat,axiom,
% 5.82/6.16 ! [A2: nat,D2: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ I4 @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % arith_series_nat
% 5.82/6.16 thf(fact_7529_Sum__Icc__nat,axiom,
% 5.82/6.16 ! [M: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [X3: nat] : X3
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.16 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % Sum_Icc_nat
% 5.82/6.16 thf(fact_7530_double__gauss__sum__from__Suc__0,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.82/6.16 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum_from_Suc_0
% 5.82/6.16 thf(fact_7531_double__gauss__sum__from__Suc__0,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.82/6.16 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum_from_Suc_0
% 5.82/6.16 thf(fact_7532_double__gauss__sum__from__Suc__0,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.82/6.16 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum_from_Suc_0
% 5.82/6.16 thf(fact_7533_double__gauss__sum__from__Suc__0,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.82/6.16 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum_from_Suc_0
% 5.82/6.16 thf(fact_7534_double__gauss__sum__from__Suc__0,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.82/6.16 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % double_gauss_sum_from_Suc_0
% 5.82/6.16 thf(fact_7535_gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % gauss_sum
% 5.82/6.16 thf(fact_7536_gauss__sum,axiom,
% 5.82/6.16 ! [N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % gauss_sum
% 5.82/6.16 thf(fact_7537_arith__series,axiom,
% 5.82/6.16 ! [A2: int,D2: int,N: nat] :
% 5.82/6.16 ( ( groups3539618377306564664at_int
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_int @ A2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % arith_series
% 5.82/6.16 thf(fact_7538_arith__series,axiom,
% 5.82/6.16 ! [A2: nat,D2: nat,N: nat] :
% 5.82/6.16 ( ( groups3542108847815614940at_nat
% 5.82/6.16 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.82/6.16 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.16 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.16
% 5.82/6.16 % arith_series
% 5.82/6.16 thf(fact_7539_sum__gp__offset,axiom,
% 5.82/6.16 ! [X2: complex,M: nat,N: nat] :
% 5.82/6.16 ( ( ( X2 = one_one_complex )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.16 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.82/6.16 & ( ( X2 != one_one_complex )
% 5.82/6.16 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.16 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_gp_offset
% 5.82/6.17 thf(fact_7540_sum__gp__offset,axiom,
% 5.82/6.17 ! [X2: rat,M: nat,N: nat] :
% 5.82/6.17 ( ( ( X2 = one_one_rat )
% 5.82/6.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.17 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.82/6.17 & ( ( X2 != one_one_rat )
% 5.82/6.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.17 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_gp_offset
% 5.82/6.17 thf(fact_7541_sum__gp__offset,axiom,
% 5.82/6.17 ! [X2: real,M: nat,N: nat] :
% 5.82/6.17 ( ( ( X2 = one_one_real )
% 5.82/6.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.17 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.82/6.17 & ( ( X2 != one_one_real )
% 5.82/6.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.17 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_gp_offset
% 5.82/6.17 thf(fact_7542_gauss__sum__from__Suc__0,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.17 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % gauss_sum_from_Suc_0
% 5.82/6.17 thf(fact_7543_gauss__sum__from__Suc__0,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.17 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % gauss_sum_from_Suc_0
% 5.82/6.17 thf(fact_7544_Chebyshev__sum__upper,axiom,
% 5.82/6.17 ! [N: nat,A2: nat > rat,B2: nat > rat] :
% 5.82/6.17 ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_rat @ ( A2 @ I2 ) @ ( A2 @ J2 ) ) ) )
% 5.82/6.17 => ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_rat @ ( B2 @ J2 ) @ ( B2 @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_rat
% 5.82/6.17 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N )
% 5.82/6.17 @ ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [K3: nat] : ( times_times_rat @ ( A2 @ K3 ) @ ( B2 @ K3 ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.17 @ ( times_times_rat @ ( groups2906978787729119204at_rat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups2906978787729119204at_rat @ B2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Chebyshev_sum_upper
% 5.82/6.17 thf(fact_7545_Chebyshev__sum__upper,axiom,
% 5.82/6.17 ! [N: nat,A2: nat > int,B2: nat > int] :
% 5.82/6.17 ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_int @ ( A2 @ I2 ) @ ( A2 @ J2 ) ) ) )
% 5.82/6.17 => ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_int @ ( B2 @ J2 ) @ ( B2 @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_int
% 5.82/6.17 @ ( times_times_int @ ( semiri1314217659103216013at_int @ N )
% 5.82/6.17 @ ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [K3: nat] : ( times_times_int @ ( A2 @ K3 ) @ ( B2 @ K3 ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.17 @ ( times_times_int @ ( groups3539618377306564664at_int @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3539618377306564664at_int @ B2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Chebyshev_sum_upper
% 5.82/6.17 thf(fact_7546_Chebyshev__sum__upper,axiom,
% 5.82/6.17 ! [N: nat,A2: nat > real,B2: nat > real] :
% 5.82/6.17 ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_real @ ( A2 @ I2 ) @ ( A2 @ J2 ) ) ) )
% 5.82/6.17 => ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_real @ ( B2 @ J2 ) @ ( B2 @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_real
% 5.82/6.17 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N )
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [K3: nat] : ( times_times_real @ ( A2 @ K3 ) @ ( B2 @ K3 ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.17 @ ( times_times_real @ ( groups6591440286371151544t_real @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups6591440286371151544t_real @ B2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Chebyshev_sum_upper
% 5.82/6.17 thf(fact_7547_Chebyshev__sum__upper__nat,axiom,
% 5.82/6.17 ! [N: nat,A2: nat > nat,B2: nat > nat] :
% 5.82/6.17 ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_nat @ ( A2 @ I2 ) @ ( A2 @ J2 ) ) ) )
% 5.82/6.17 => ( ! [I2: nat,J2: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.82/6.17 => ( ( ord_less_nat @ J2 @ N )
% 5.82/6.17 => ( ord_less_eq_nat @ ( B2 @ J2 ) @ ( B2 @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_nat
% 5.82/6.17 @ ( times_times_nat @ N
% 5.82/6.17 @ ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( times_times_nat @ ( A2 @ I4 ) @ ( B2 @ I4 ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.82/6.17 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Chebyshev_sum_upper_nat
% 5.82/6.17 thf(fact_7548_lemma__termdiff2,axiom,
% 5.82/6.17 ! [H2: complex,Z: complex,N: nat] :
% 5.82/6.17 ( ( H2 != zero_zero_complex )
% 5.82/6.17 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.17 = ( times_times_complex @ H2
% 5.82/6.17 @ ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [P4: nat] :
% 5.82/6.17 ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff2
% 5.82/6.17 thf(fact_7549_lemma__termdiff2,axiom,
% 5.82/6.17 ! [H2: rat,Z: rat,N: nat] :
% 5.82/6.17 ( ( H2 != zero_zero_rat )
% 5.82/6.17 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.17 = ( times_times_rat @ H2
% 5.82/6.17 @ ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [P4: nat] :
% 5.82/6.17 ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff2
% 5.82/6.17 thf(fact_7550_lemma__termdiff2,axiom,
% 5.82/6.17 ! [H2: real,Z: real,N: nat] :
% 5.82/6.17 ( ( H2 != zero_zero_real )
% 5.82/6.17 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.17 = ( times_times_real @ H2
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [P4: nat] :
% 5.82/6.17 ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff2
% 5.82/6.17 thf(fact_7551_length__rule,axiom,
% 5.82/6.17 ! [A2: array_o,Xs: list_o] :
% 5.82/6.17 ( hoare_3067605981109127869le_nat @ ( snga_assn_o @ A2 @ Xs ) @ ( array_len_o @ A2 )
% 5.82/6.17 @ ^ [R5: nat] :
% 5.82/6.17 ( times_times_assn @ ( snga_assn_o @ A2 @ Xs )
% 5.82/6.17 @ ( pure_assn
% 5.82/6.17 @ ( R5
% 5.82/6.17 = ( size_size_list_o @ Xs ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_rule
% 5.82/6.17 thf(fact_7552_length__rule,axiom,
% 5.82/6.17 ! [A2: array_nat,Xs: list_nat] :
% 5.82/6.17 ( hoare_3067605981109127869le_nat @ ( snga_assn_nat @ A2 @ Xs ) @ ( array_len_nat @ A2 )
% 5.82/6.17 @ ^ [R5: nat] :
% 5.82/6.17 ( times_times_assn @ ( snga_assn_nat @ A2 @ Xs )
% 5.82/6.17 @ ( pure_assn
% 5.82/6.17 @ ( R5
% 5.82/6.17 = ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_rule
% 5.82/6.17 thf(fact_7553_length__rule,axiom,
% 5.82/6.17 ! [A2: array_VEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 5.82/6.17 ( hoare_3067605981109127869le_nat @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs ) @ ( array_len_VEBT_VEBTi @ A2 )
% 5.82/6.17 @ ^ [R5: nat] :
% 5.82/6.17 ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs )
% 5.82/6.17 @ ( pure_assn
% 5.82/6.17 @ ( R5
% 5.82/6.17 = ( size_s7982070591426661849_VEBTi @ Xs ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_rule
% 5.82/6.17 thf(fact_7554_dbl__inc__simps_I3_J,axiom,
% 5.82/6.17 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.82/6.17 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(3)
% 5.82/6.17 thf(fact_7555_dbl__inc__simps_I3_J,axiom,
% 5.82/6.17 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.82/6.17 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(3)
% 5.82/6.17 thf(fact_7556_dbl__inc__simps_I3_J,axiom,
% 5.82/6.17 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.82/6.17 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(3)
% 5.82/6.17 thf(fact_7557_dbl__inc__simps_I3_J,axiom,
% 5.82/6.17 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.82/6.17 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(3)
% 5.82/6.17 thf(fact_7558_lessThan__iff,axiom,
% 5.82/6.17 ! [I: rat,K: rat] :
% 5.82/6.17 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.82/6.17 = ( ord_less_rat @ I @ K ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_iff
% 5.82/6.17 thf(fact_7559_lessThan__iff,axiom,
% 5.82/6.17 ! [I: num,K: num] :
% 5.82/6.17 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.82/6.17 = ( ord_less_num @ I @ K ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_iff
% 5.82/6.17 thf(fact_7560_lessThan__iff,axiom,
% 5.82/6.17 ! [I: nat,K: nat] :
% 5.82/6.17 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.82/6.17 = ( ord_less_nat @ I @ K ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_iff
% 5.82/6.17 thf(fact_7561_lessThan__iff,axiom,
% 5.82/6.17 ! [I: int,K: int] :
% 5.82/6.17 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.82/6.17 = ( ord_less_int @ I @ K ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_iff
% 5.82/6.17 thf(fact_7562_lessThan__iff,axiom,
% 5.82/6.17 ! [I: real,K: real] :
% 5.82/6.17 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.82/6.17 = ( ord_less_real @ I @ K ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_iff
% 5.82/6.17 thf(fact_7563_lessThan__subset__iff,axiom,
% 5.82/6.17 ! [X2: rat,Y3: rat] :
% 5.82/6.17 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X2 ) @ ( set_ord_lessThan_rat @ Y3 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_subset_iff
% 5.82/6.17 thf(fact_7564_lessThan__subset__iff,axiom,
% 5.82/6.17 ! [X2: num,Y3: num] :
% 5.82/6.17 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X2 ) @ ( set_ord_lessThan_num @ Y3 ) )
% 5.82/6.17 = ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_subset_iff
% 5.82/6.17 thf(fact_7565_lessThan__subset__iff,axiom,
% 5.82/6.17 ! [X2: nat,Y3: nat] :
% 5.82/6.17 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X2 ) @ ( set_ord_lessThan_nat @ Y3 ) )
% 5.82/6.17 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_subset_iff
% 5.82/6.17 thf(fact_7566_lessThan__subset__iff,axiom,
% 5.82/6.17 ! [X2: int,Y3: int] :
% 5.82/6.17 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X2 ) @ ( set_ord_lessThan_int @ Y3 ) )
% 5.82/6.17 = ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_subset_iff
% 5.82/6.17 thf(fact_7567_lessThan__subset__iff,axiom,
% 5.82/6.17 ! [X2: real,Y3: real] :
% 5.82/6.17 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X2 ) @ ( set_or5984915006950818249n_real @ Y3 ) )
% 5.82/6.17 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_subset_iff
% 5.82/6.17 thf(fact_7568_lessThan__minus__lessThan,axiom,
% 5.82/6.17 ! [N: real,M: real] :
% 5.82/6.17 ( ( minus_minus_set_real @ ( set_or5984915006950818249n_real @ N ) @ ( set_or5984915006950818249n_real @ M ) )
% 5.82/6.17 = ( set_or66887138388493659n_real @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_minus_lessThan
% 5.82/6.17 thf(fact_7569_lessThan__minus__lessThan,axiom,
% 5.82/6.17 ! [N: nat,M: nat] :
% 5.82/6.17 ( ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( set_or4665077453230672383an_nat @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_minus_lessThan
% 5.82/6.17 thf(fact_7570_lessThan__minus__lessThan,axiom,
% 5.82/6.17 ! [N: int,M: int] :
% 5.82/6.17 ( ( minus_minus_set_int @ ( set_ord_lessThan_int @ N ) @ ( set_ord_lessThan_int @ M ) )
% 5.82/6.17 = ( set_or4662586982721622107an_int @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_minus_lessThan
% 5.82/6.17 thf(fact_7571_lessThan__minus__lessThan,axiom,
% 5.82/6.17 ! [N: code_integer,M: code_integer] :
% 5.82/6.17 ( ( minus_2355218937544613996nteger @ ( set_or5754767410780653050nteger @ N ) @ ( set_or5754767410780653050nteger @ M ) )
% 5.82/6.17 = ( set_or8404916559141939852nteger @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_minus_lessThan
% 5.82/6.17 thf(fact_7572_dbl__inc__simps_I2_J,axiom,
% 5.82/6.17 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.82/6.17 = one_one_complex ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(2)
% 5.82/6.17 thf(fact_7573_dbl__inc__simps_I2_J,axiom,
% 5.82/6.17 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(2)
% 5.82/6.17 thf(fact_7574_dbl__inc__simps_I2_J,axiom,
% 5.82/6.17 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.82/6.17 = one_one_rat ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(2)
% 5.82/6.17 thf(fact_7575_dbl__inc__simps_I2_J,axiom,
% 5.82/6.17 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(2)
% 5.82/6.17 thf(fact_7576_dbl__inc__simps_I5_J,axiom,
% 5.82/6.17 ! [K: num] :
% 5.82/6.17 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.82/6.17 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(5)
% 5.82/6.17 thf(fact_7577_dbl__inc__simps_I5_J,axiom,
% 5.82/6.17 ! [K: num] :
% 5.82/6.17 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.82/6.17 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(5)
% 5.82/6.17 thf(fact_7578_dbl__inc__simps_I5_J,axiom,
% 5.82/6.17 ! [K: num] :
% 5.82/6.17 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.82/6.17 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(5)
% 5.82/6.17 thf(fact_7579_dbl__inc__simps_I5_J,axiom,
% 5.82/6.17 ! [K: num] :
% 5.82/6.17 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.82/6.17 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_simps(5)
% 5.82/6.17 thf(fact_7580_sum_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > rat,N: nat] :
% 5.82/6.17 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc
% 5.82/6.17 thf(fact_7581_sum_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > int,N: nat] :
% 5.82/6.17 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc
% 5.82/6.17 thf(fact_7582_sum_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > nat,N: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc
% 5.82/6.17 thf(fact_7583_sum_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > real,N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc
% 5.82/6.17 thf(fact_7584_single__Diff__lessThan,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 5.82/6.17 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % single_Diff_lessThan
% 5.82/6.17 thf(fact_7585_single__Diff__lessThan,axiom,
% 5.82/6.17 ! [K: int] :
% 5.82/6.17 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 5.82/6.17 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % single_Diff_lessThan
% 5.82/6.17 thf(fact_7586_single__Diff__lessThan,axiom,
% 5.82/6.17 ! [K: real] :
% 5.82/6.17 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 5.82/6.17 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % single_Diff_lessThan
% 5.82/6.17 thf(fact_7587_sum__diff__distrib,axiom,
% 5.82/6.17 ! [Q: int > nat,P: int > nat,N: int] :
% 5.82/6.17 ( ! [X4: int] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.82/6.17 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 5.82/6.17 = ( groups4541462559716669496nt_nat
% 5.82/6.17 @ ^ [X3: int] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 5.82/6.17 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_distrib
% 5.82/6.17 thf(fact_7588_sum__diff__distrib,axiom,
% 5.82/6.17 ! [Q: real > nat,P: real > nat,N: real] :
% 5.82/6.17 ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.82/6.17 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.82/6.17 = ( groups1935376822645274424al_nat
% 5.82/6.17 @ ^ [X3: real] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 5.82/6.17 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_distrib
% 5.82/6.17 thf(fact_7589_sum__diff__distrib,axiom,
% 5.82/6.17 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.82/6.17 ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.82/6.17 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.82/6.17 = ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_distrib
% 5.82/6.17 thf(fact_7590_int__sum,axiom,
% 5.82/6.17 ! [F: int > nat,A: set_int] :
% 5.82/6.17 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A ) )
% 5.82/6.17 = ( groups4538972089207619220nt_int
% 5.82/6.17 @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % int_sum
% 5.82/6.17 thf(fact_7591_int__sum,axiom,
% 5.82/6.17 ! [F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.17 = ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % int_sum
% 5.82/6.17 thf(fact_7592_lessThan__def,axiom,
% 5.82/6.17 ( set_ord_lessThan_rat
% 5.82/6.17 = ( ^ [U2: rat] :
% 5.82/6.17 ( collect_rat
% 5.82/6.17 @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_def
% 5.82/6.17 thf(fact_7593_lessThan__def,axiom,
% 5.82/6.17 ( set_ord_lessThan_num
% 5.82/6.17 = ( ^ [U2: num] :
% 5.82/6.17 ( collect_num
% 5.82/6.17 @ ^ [X3: num] : ( ord_less_num @ X3 @ U2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_def
% 5.82/6.17 thf(fact_7594_lessThan__def,axiom,
% 5.82/6.17 ( set_ord_lessThan_nat
% 5.82/6.17 = ( ^ [U2: nat] :
% 5.82/6.17 ( collect_nat
% 5.82/6.17 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_def
% 5.82/6.17 thf(fact_7595_lessThan__def,axiom,
% 5.82/6.17 ( set_ord_lessThan_int
% 5.82/6.17 = ( ^ [U2: int] :
% 5.82/6.17 ( collect_int
% 5.82/6.17 @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_def
% 5.82/6.17 thf(fact_7596_lessThan__def,axiom,
% 5.82/6.17 ( set_or5984915006950818249n_real
% 5.82/6.17 = ( ^ [U2: real] :
% 5.82/6.17 ( collect_real
% 5.82/6.17 @ ^ [X3: real] : ( ord_less_real @ X3 @ U2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_def
% 5.82/6.17 thf(fact_7597_lessThan__strict__subset__iff,axiom,
% 5.82/6.17 ! [M: rat,N: rat] :
% 5.82/6.17 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.82/6.17 = ( ord_less_rat @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_strict_subset_iff
% 5.82/6.17 thf(fact_7598_lessThan__strict__subset__iff,axiom,
% 5.82/6.17 ! [M: num,N: num] :
% 5.82/6.17 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.82/6.17 = ( ord_less_num @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_strict_subset_iff
% 5.82/6.17 thf(fact_7599_lessThan__strict__subset__iff,axiom,
% 5.82/6.17 ! [M: nat,N: nat] :
% 5.82/6.17 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( ord_less_nat @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_strict_subset_iff
% 5.82/6.17 thf(fact_7600_lessThan__strict__subset__iff,axiom,
% 5.82/6.17 ! [M: int,N: int] :
% 5.82/6.17 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.82/6.17 = ( ord_less_int @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_strict_subset_iff
% 5.82/6.17 thf(fact_7601_lessThan__strict__subset__iff,axiom,
% 5.82/6.17 ! [M: real,N: real] :
% 5.82/6.17 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.82/6.17 = ( ord_less_real @ M @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_strict_subset_iff
% 5.82/6.17 thf(fact_7602_lessThan__Suc,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.82/6.17 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lessThan_Suc
% 5.82/6.17 thf(fact_7603_sum__subtractf__nat,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > nat,F: vEBT_VEBT > nat] :
% 5.82/6.17 ( ! [X4: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ( groups771621172384141258BT_nat
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A ) @ ( groups771621172384141258BT_nat @ G @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_subtractf_nat
% 5.82/6.17 thf(fact_7604_sum__subtractf__nat,axiom,
% 5.82/6.17 ! [A: set_real,G: real > nat,F: real > nat] :
% 5.82/6.17 ( ! [X4: real] :
% 5.82/6.17 ( ( member_real @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ( groups1935376822645274424al_nat
% 5.82/6.17 @ ^ [X3: real] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A ) @ ( groups1935376822645274424al_nat @ G @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_subtractf_nat
% 5.82/6.17 thf(fact_7605_sum__subtractf__nat,axiom,
% 5.82/6.17 ! [A: set_int,G: int > nat,F: int > nat] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ( groups4541462559716669496nt_nat
% 5.82/6.17 @ ^ [X3: int] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( groups4541462559716669496nt_nat @ G @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_subtractf_nat
% 5.82/6.17 thf(fact_7606_sum__subtractf__nat,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > nat,F: nat > nat] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [X3: nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ ( groups3542108847815614940at_nat @ G @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_subtractf_nat
% 5.82/6.17 thf(fact_7607_sum__SucD,axiom,
% 5.82/6.17 ! [F: nat > nat,A: set_nat,N: nat] :
% 5.82/6.17 ( ( ( groups3542108847815614940at_nat @ F @ A )
% 5.82/6.17 = ( suc @ N ) )
% 5.82/6.17 => ? [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_SucD
% 5.82/6.17 thf(fact_7608_sum__eq__Suc0__iff,axiom,
% 5.82/6.17 ! [A: set_int,F: int > nat] :
% 5.82/6.17 ( ( finite_finite_int @ A )
% 5.82/6.17 => ( ( ( groups4541462559716669496nt_nat @ F @ A )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 = ( ? [X3: int] :
% 5.82/6.17 ( ( member_int @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 & ! [Y: int] :
% 5.82/6.17 ( ( member_int @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_Suc0_iff
% 5.82/6.17 thf(fact_7609_sum__eq__Suc0__iff,axiom,
% 5.82/6.17 ! [A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( ( groups7237345082560585321er_nat @ F @ A )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 = ( ? [X3: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 & ! [Y: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_Suc0_iff
% 5.82/6.17 thf(fact_7610_sum__eq__Suc0__iff,axiom,
% 5.82/6.17 ! [A: set_complex,F: complex > nat] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( ( groups5693394587270226106ex_nat @ F @ A )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 = ( ? [X3: complex] :
% 5.82/6.17 ( ( member_complex @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 & ! [Y: complex] :
% 5.82/6.17 ( ( member_complex @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_Suc0_iff
% 5.82/6.17 thf(fact_7611_sum__eq__Suc0__iff,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( ( groups3542108847815614940at_nat @ F @ A )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 = ( ? [X3: nat] :
% 5.82/6.17 ( ( member_nat @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = ( suc @ zero_zero_nat ) )
% 5.82/6.17 & ! [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_Suc0_iff
% 5.82/6.17 thf(fact_7612_sum__eq__1__iff,axiom,
% 5.82/6.17 ! [A: set_int,F: int > nat] :
% 5.82/6.17 ( ( finite_finite_int @ A )
% 5.82/6.17 => ( ( ( groups4541462559716669496nt_nat @ F @ A )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 = ( ? [X3: int] :
% 5.82/6.17 ( ( member_int @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 & ! [Y: int] :
% 5.82/6.17 ( ( member_int @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_1_iff
% 5.82/6.17 thf(fact_7613_sum__eq__1__iff,axiom,
% 5.82/6.17 ! [A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( ( groups7237345082560585321er_nat @ F @ A )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 = ( ? [X3: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 & ! [Y: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_1_iff
% 5.82/6.17 thf(fact_7614_sum__eq__1__iff,axiom,
% 5.82/6.17 ! [A: set_complex,F: complex > nat] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( ( groups5693394587270226106ex_nat @ F @ A )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 = ( ? [X3: complex] :
% 5.82/6.17 ( ( member_complex @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 & ! [Y: complex] :
% 5.82/6.17 ( ( member_complex @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_1_iff
% 5.82/6.17 thf(fact_7615_sum__eq__1__iff,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( ( groups3542108847815614940at_nat @ F @ A )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 = ( ? [X3: nat] :
% 5.82/6.17 ( ( member_nat @ X3 @ A )
% 5.82/6.17 & ( ( F @ X3 )
% 5.82/6.17 = one_one_nat )
% 5.82/6.17 & ! [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ A )
% 5.82/6.17 => ( ( X3 != Y )
% 5.82/6.17 => ( ( F @ Y )
% 5.82/6.17 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_eq_1_iff
% 5.82/6.17 thf(fact_7616_sum_Onat__diff__reindex,axiom,
% 5.82/6.17 ! [G: nat > nat,N: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.nat_diff_reindex
% 5.82/6.17 thf(fact_7617_sum_Onat__diff__reindex,axiom,
% 5.82/6.17 ! [G: nat > real,N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.nat_diff_reindex
% 5.82/6.17 thf(fact_7618_sum__nth__roots,axiom,
% 5.82/6.17 ! [N: nat,C2: complex] :
% 5.82/6.17 ( ( ord_less_nat @ one_one_nat @ N )
% 5.82/6.17 => ( ( groups7754918857620584856omplex
% 5.82/6.17 @ ^ [X3: complex] : X3
% 5.82/6.17 @ ( collect_complex
% 5.82/6.17 @ ^ [Z4: complex] :
% 5.82/6.17 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.17 = C2 ) ) )
% 5.82/6.17 = zero_zero_complex ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_nth_roots
% 5.82/6.17 thf(fact_7619_sum__roots__unity,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( ord_less_nat @ one_one_nat @ N )
% 5.82/6.17 => ( ( groups7754918857620584856omplex
% 5.82/6.17 @ ^ [X3: complex] : X3
% 5.82/6.17 @ ( collect_complex
% 5.82/6.17 @ ^ [Z4: complex] :
% 5.82/6.17 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.17 = one_one_complex ) ) )
% 5.82/6.17 = zero_zero_complex ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_roots_unity
% 5.82/6.17 thf(fact_7620_sum__diff__nat,axiom,
% 5.82/6.17 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.17 => ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.17 => ( ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A @ B ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups7237345082560585321er_nat @ F @ A ) @ ( groups7237345082560585321er_nat @ F @ B ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_nat
% 5.82/6.17 thf(fact_7621_sum__diff__nat,axiom,
% 5.82/6.17 ! [B: set_complex,A: set_complex,F: complex > nat] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.17 => ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.17 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A @ B ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A ) @ ( groups5693394587270226106ex_nat @ F @ B ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_nat
% 5.82/6.17 thf(fact_7622_sum__diff__nat,axiom,
% 5.82/6.17 ! [B: set_int,A: set_int,F: int > nat] :
% 5.82/6.17 ( ( finite_finite_int @ B )
% 5.82/6.17 => ( ( ord_less_eq_set_int @ B @ A )
% 5.82/6.17 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A @ B ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( groups4541462559716669496nt_nat @ F @ B ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_nat
% 5.82/6.17 thf(fact_7623_sum__diff__nat,axiom,
% 5.82/6.17 ! [B: set_nat,A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.17 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A @ B ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ ( groups3542108847815614940at_nat @ F @ B ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff_nat
% 5.82/6.17 thf(fact_7624_sum__diff1__nat,axiom,
% 5.82/6.17 ! [A2: vEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.17 ( ( ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.17 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.17 & ( ~ ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.17 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.17 = ( groups771621172384141258BT_nat @ F @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff1_nat
% 5.82/6.17 thf(fact_7625_sum__diff1__nat,axiom,
% 5.82/6.17 ! [A2: real,A: set_real,F: real > nat] :
% 5.82/6.17 ( ( ( member_real @ A2 @ A )
% 5.82/6.17 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.17 & ( ~ ( member_real @ A2 @ A )
% 5.82/6.17 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.17 = ( groups1935376822645274424al_nat @ F @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff1_nat
% 5.82/6.17 thf(fact_7626_sum__diff1__nat,axiom,
% 5.82/6.17 ! [A2: int,A: set_int,F: int > nat] :
% 5.82/6.17 ( ( ( member_int @ A2 @ A )
% 5.82/6.17 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.17 & ( ~ ( member_int @ A2 @ A )
% 5.82/6.17 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.17 = ( groups4541462559716669496nt_nat @ F @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff1_nat
% 5.82/6.17 thf(fact_7627_sum__diff1__nat,axiom,
% 5.82/6.17 ! [A2: nat,A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ( ( member_nat @ A2 @ A )
% 5.82/6.17 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.17 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.17 & ( ~ ( member_nat @ A2 @ A )
% 5.82/6.17 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.17 = ( groups3542108847815614940at_nat @ F @ A ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_diff1_nat
% 5.82/6.17 thf(fact_7628_dbl__inc__def,axiom,
% 5.82/6.17 ( neg_nu8295874005876285629c_real
% 5.82/6.17 = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_def
% 5.82/6.17 thf(fact_7629_dbl__inc__def,axiom,
% 5.82/6.17 ( neg_nu5219082963157363817nc_rat
% 5.82/6.17 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_def
% 5.82/6.17 thf(fact_7630_dbl__inc__def,axiom,
% 5.82/6.17 ( neg_nu5851722552734809277nc_int
% 5.82/6.17 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % dbl_inc_def
% 5.82/6.17 thf(fact_7631_sum_OlessThan__Suc__shift,axiom,
% 5.82/6.17 ! [G: nat > rat,N: nat] :
% 5.82/6.17 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.82/6.17 @ ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc_shift
% 5.82/6.17 thf(fact_7632_sum_OlessThan__Suc__shift,axiom,
% 5.82/6.17 ! [G: nat > int,N: nat] :
% 5.82/6.17 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.82/6.17 @ ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc_shift
% 5.82/6.17 thf(fact_7633_sum_OlessThan__Suc__shift,axiom,
% 5.82/6.17 ! [G: nat > nat,N: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.82/6.17 @ ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc_shift
% 5.82/6.17 thf(fact_7634_sum_OlessThan__Suc__shift,axiom,
% 5.82/6.17 ! [G: nat > real,N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.lessThan_Suc_shift
% 5.82/6.17 thf(fact_7635_sum__lessThan__telescope_H,axiom,
% 5.82/6.17 ! [F: nat > rat,M: nat] :
% 5.82/6.17 ( ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_rat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_lessThan_telescope'
% 5.82/6.17 thf(fact_7636_sum__lessThan__telescope_H,axiom,
% 5.82/6.17 ! [F: nat > int,M: nat] :
% 5.82/6.17 ( ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_lessThan_telescope'
% 5.82/6.17 thf(fact_7637_sum__lessThan__telescope_H,axiom,
% 5.82/6.17 ! [F: nat > real,M: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_lessThan_telescope'
% 5.82/6.17 thf(fact_7638_sum__lessThan__telescope,axiom,
% 5.82/6.17 ! [F: nat > rat,M: nat] :
% 5.82/6.17 ( ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_rat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_lessThan_telescope
% 5.82/6.17 thf(fact_7639_sum__lessThan__telescope,axiom,
% 5.82/6.17 ! [F: nat > int,M: nat] :
% 5.82/6.17 ( ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_int @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_lessThan_telescope
% 5.82/6.17 thf(fact_7640_sum__lessThan__telescope,axiom,
% 5.82/6.17 ! [F: nat > real,M: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_lessThan_telescope
% 5.82/6.17 thf(fact_7641_sumr__diff__mult__const2,axiom,
% 5.82/6.17 ! [F: nat > rat,N: nat,R2: rat] :
% 5.82/6.17 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 5.82/6.17 = ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R2 )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sumr_diff_mult_const2
% 5.82/6.17 thf(fact_7642_sumr__diff__mult__const2,axiom,
% 5.82/6.17 ! [F: nat > int,N: nat,R2: int] :
% 5.82/6.17 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 5.82/6.17 = ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R2 )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sumr_diff_mult_const2
% 5.82/6.17 thf(fact_7643_sumr__diff__mult__const2,axiom,
% 5.82/6.17 ! [F: nat > real,N: nat,R2: real] :
% 5.82/6.17 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 5.82/6.17 = ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R2 )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sumr_diff_mult_const2
% 5.82/6.17 thf(fact_7644_sum_OatLeast1__atMost__eq,axiom,
% 5.82/6.17 ! [G: nat > nat,N: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.17 = ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.atLeast1_atMost_eq
% 5.82/6.17 thf(fact_7645_sum_OatLeast1__atMost__eq,axiom,
% 5.82/6.17 ! [G: nat > real,N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.17 = ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.atLeast1_atMost_eq
% 5.82/6.17 thf(fact_7646_sum_Onat__group,axiom,
% 5.82/6.17 ! [G: nat > nat,K: nat,N: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [M6: nat] : ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M6 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M6 @ K ) @ K ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.nat_group
% 5.82/6.17 thf(fact_7647_sum_Onat__group,axiom,
% 5.82/6.17 ! [G: nat > real,K: nat,N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [M6: nat] : ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M6 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M6 @ K ) @ K ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum.nat_group
% 5.82/6.17 thf(fact_7648_one__diff__power__eq,axiom,
% 5.82/6.17 ! [X2: complex,N: nat] :
% 5.82/6.17 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.82/6.17 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq
% 5.82/6.17 thf(fact_7649_one__diff__power__eq,axiom,
% 5.82/6.17 ! [X2: code_integer,N: nat] :
% 5.82/6.17 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.82/6.17 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X2 ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq
% 5.82/6.17 thf(fact_7650_one__diff__power__eq,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.82/6.17 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq
% 5.82/6.17 thf(fact_7651_one__diff__power__eq,axiom,
% 5.82/6.17 ! [X2: int,N: nat] :
% 5.82/6.17 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.82/6.17 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq
% 5.82/6.17 thf(fact_7652_one__diff__power__eq,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.82/6.17 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq
% 5.82/6.17 thf(fact_7653_power__diff__1__eq,axiom,
% 5.82/6.17 ! [X2: complex,N: nat] :
% 5.82/6.17 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex )
% 5.82/6.17 = ( times_times_complex @ ( minus_minus_complex @ X2 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_1_eq
% 5.82/6.17 thf(fact_7654_power__diff__1__eq,axiom,
% 5.82/6.17 ! [X2: code_integer,N: nat] :
% 5.82/6.17 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X2 @ N ) @ one_one_Code_integer )
% 5.82/6.17 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X2 @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_1_eq
% 5.82/6.17 thf(fact_7655_power__diff__1__eq,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat )
% 5.82/6.17 = ( times_times_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_1_eq
% 5.82/6.17 thf(fact_7656_power__diff__1__eq,axiom,
% 5.82/6.17 ! [X2: int,N: nat] :
% 5.82/6.17 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ one_one_int )
% 5.82/6.17 = ( times_times_int @ ( minus_minus_int @ X2 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_1_eq
% 5.82/6.17 thf(fact_7657_power__diff__1__eq,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real )
% 5.82/6.17 = ( times_times_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_1_eq
% 5.82/6.17 thf(fact_7658_geometric__sum,axiom,
% 5.82/6.17 ! [X2: complex,N: nat] :
% 5.82/6.17 ( ( X2 != one_one_complex )
% 5.82/6.17 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_sum
% 5.82/6.17 thf(fact_7659_geometric__sum,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( X2 != one_one_rat )
% 5.82/6.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_sum
% 5.82/6.17 thf(fact_7660_geometric__sum,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( X2 != one_one_real )
% 5.82/6.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_sum
% 5.82/6.17 thf(fact_7661_lemma__termdiff1,axiom,
% 5.82/6.17 ! [Z: complex,H2: complex,M: nat] :
% 5.82/6.17 ( ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [P4: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ P4 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P4 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff1
% 5.82/6.17 thf(fact_7662_lemma__termdiff1,axiom,
% 5.82/6.17 ! [Z: code_integer,H2: code_integer,M: nat] :
% 5.82/6.17 ( ( groups7501900531339628137nteger
% 5.82/6.17 @ ^ [P4: nat] : ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_8256067586552552935nteger @ Z @ P4 ) ) @ ( power_8256067586552552935nteger @ Z @ M ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( groups7501900531339628137nteger
% 5.82/6.17 @ ^ [P4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Z @ P4 ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_8256067586552552935nteger @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff1
% 5.82/6.17 thf(fact_7663_lemma__termdiff1,axiom,
% 5.82/6.17 ! [Z: rat,H2: rat,M: nat] :
% 5.82/6.17 ( ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [P4: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ P4 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P4 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff1
% 5.82/6.17 thf(fact_7664_lemma__termdiff1,axiom,
% 5.82/6.17 ! [Z: int,H2: int,M: nat] :
% 5.82/6.17 ( ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [P4: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ P4 ) ) @ ( power_power_int @ Z @ M ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ Z @ P4 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff1
% 5.82/6.17 thf(fact_7665_lemma__termdiff1,axiom,
% 5.82/6.17 ! [Z: real,H2: real,M: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [P4: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ P4 ) ) @ ( power_power_real @ Z @ M ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) )
% 5.82/6.17 = ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ Z @ P4 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % lemma_termdiff1
% 5.82/6.17 thf(fact_7666_sum__gp__strict,axiom,
% 5.82/6.17 ! [X2: complex,N: nat] :
% 5.82/6.17 ( ( ( X2 = one_one_complex )
% 5.82/6.17 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.82/6.17 & ( ( X2 != one_one_complex )
% 5.82/6.17 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_gp_strict
% 5.82/6.17 thf(fact_7667_sum__gp__strict,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( ( X2 = one_one_rat )
% 5.82/6.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.82/6.17 & ( ( X2 != one_one_rat )
% 5.82/6.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_gp_strict
% 5.82/6.17 thf(fact_7668_sum__gp__strict,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( ( X2 = one_one_real )
% 5.82/6.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.82/6.17 & ( ( X2 != one_one_real )
% 5.82/6.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_gp_strict
% 5.82/6.17 thf(fact_7669_power__diff__sumr2,axiom,
% 5.82/6.17 ! [X2: complex,N: nat,Y3: complex] :
% 5.82/6.17 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 5.82/6.17 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y3 )
% 5.82/6.17 @ ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_sumr2
% 5.82/6.17 thf(fact_7670_power__diff__sumr2,axiom,
% 5.82/6.17 ! [X2: code_integer,N: nat,Y3: code_integer] :
% 5.82/6.17 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ N ) )
% 5.82/6.17 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X2 @ Y3 )
% 5.82/6.17 @ ( groups7501900531339628137nteger
% 5.82/6.17 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_8256067586552552935nteger @ X2 @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_sumr2
% 5.82/6.17 thf(fact_7671_power__diff__sumr2,axiom,
% 5.82/6.17 ! [X2: rat,N: nat,Y3: rat] :
% 5.82/6.17 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 5.82/6.17 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y3 )
% 5.82/6.17 @ ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_sumr2
% 5.82/6.17 thf(fact_7672_power__diff__sumr2,axiom,
% 5.82/6.17 ! [X2: int,N: nat,Y3: int] :
% 5.82/6.17 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 5.82/6.17 = ( times_times_int @ ( minus_minus_int @ X2 @ Y3 )
% 5.82/6.17 @ ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X2 @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_sumr2
% 5.82/6.17 thf(fact_7673_power__diff__sumr2,axiom,
% 5.82/6.17 ! [X2: real,N: nat,Y3: real] :
% 5.82/6.17 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 5.82/6.17 = ( times_times_real @ ( minus_minus_real @ X2 @ Y3 )
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X2 @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_diff_sumr2
% 5.82/6.17 thf(fact_7674_diff__power__eq__sum,axiom,
% 5.82/6.17 ! [X2: complex,N: nat,Y3: complex] :
% 5.82/6.17 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) @ ( power_power_complex @ Y3 @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y3 )
% 5.82/6.17 @ ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X2 @ P4 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % diff_power_eq_sum
% 5.82/6.17 thf(fact_7675_diff__power__eq__sum,axiom,
% 5.82/6.17 ! [X2: code_integer,N: nat,Y3: code_integer] :
% 5.82/6.17 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X2 @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X2 @ Y3 )
% 5.82/6.17 @ ( groups7501900531339628137nteger
% 5.82/6.17 @ ^ [P4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ P4 ) @ ( power_8256067586552552935nteger @ Y3 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % diff_power_eq_sum
% 5.82/6.17 thf(fact_7676_diff__power__eq__sum,axiom,
% 5.82/6.17 ! [X2: rat,N: nat,Y3: rat] :
% 5.82/6.17 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) @ ( power_power_rat @ Y3 @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y3 )
% 5.82/6.17 @ ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_rat @ ( power_power_rat @ X2 @ P4 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % diff_power_eq_sum
% 5.82/6.17 thf(fact_7677_diff__power__eq__sum,axiom,
% 5.82/6.17 ! [X2: int,N: nat,Y3: int] :
% 5.82/6.17 ( ( minus_minus_int @ ( power_power_int @ X2 @ ( suc @ N ) ) @ ( power_power_int @ Y3 @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_int @ ( minus_minus_int @ X2 @ Y3 )
% 5.82/6.17 @ ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X2 @ P4 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % diff_power_eq_sum
% 5.82/6.17 thf(fact_7678_diff__power__eq__sum,axiom,
% 5.82/6.17 ! [X2: real,N: nat,Y3: real] :
% 5.82/6.17 ( ( minus_minus_real @ ( power_power_real @ X2 @ ( suc @ N ) ) @ ( power_power_real @ Y3 @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_real @ ( minus_minus_real @ X2 @ Y3 )
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X2 @ P4 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ P4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % diff_power_eq_sum
% 5.82/6.17 thf(fact_7679_atLeast1__lessThan__eq__remove0,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.17 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % atLeast1_lessThan_eq_remove0
% 5.82/6.17 thf(fact_7680_real__sum__nat__ivl__bounded2,axiom,
% 5.82/6.17 ! [N: nat,F: nat > rat,K6: rat,K: nat] :
% 5.82/6.17 ( ! [P7: nat] :
% 5.82/6.17 ( ( ord_less_nat @ P7 @ N )
% 5.82/6.17 => ( ord_less_eq_rat @ ( F @ P7 ) @ K6 ) )
% 5.82/6.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ K6 )
% 5.82/6.17 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K6 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % real_sum_nat_ivl_bounded2
% 5.82/6.17 thf(fact_7681_real__sum__nat__ivl__bounded2,axiom,
% 5.82/6.17 ! [N: nat,F: nat > int,K6: int,K: nat] :
% 5.82/6.17 ( ! [P7: nat] :
% 5.82/6.17 ( ( ord_less_nat @ P7 @ N )
% 5.82/6.17 => ( ord_less_eq_int @ ( F @ P7 ) @ K6 ) )
% 5.82/6.17 => ( ( ord_less_eq_int @ zero_zero_int @ K6 )
% 5.82/6.17 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K6 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % real_sum_nat_ivl_bounded2
% 5.82/6.17 thf(fact_7682_real__sum__nat__ivl__bounded2,axiom,
% 5.82/6.17 ! [N: nat,F: nat > nat,K6: nat,K: nat] :
% 5.82/6.17 ( ! [P7: nat] :
% 5.82/6.17 ( ( ord_less_nat @ P7 @ N )
% 5.82/6.17 => ( ord_less_eq_nat @ ( F @ P7 ) @ K6 ) )
% 5.82/6.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ K6 )
% 5.82/6.17 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K6 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % real_sum_nat_ivl_bounded2
% 5.82/6.17 thf(fact_7683_real__sum__nat__ivl__bounded2,axiom,
% 5.82/6.17 ! [N: nat,F: nat > real,K6: real,K: nat] :
% 5.82/6.17 ( ! [P7: nat] :
% 5.82/6.17 ( ( ord_less_nat @ P7 @ N )
% 5.82/6.17 => ( ord_less_eq_real @ ( F @ P7 ) @ K6 ) )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ K6 )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K6 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % real_sum_nat_ivl_bounded2
% 5.82/6.17 thf(fact_7684_one__diff__power__eq_H,axiom,
% 5.82/6.17 ! [X2: complex,N: nat] :
% 5.82/6.17 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.82/6.17 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 )
% 5.82/6.17 @ ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq'
% 5.82/6.17 thf(fact_7685_one__diff__power__eq_H,axiom,
% 5.82/6.17 ! [X2: code_integer,N: nat] :
% 5.82/6.17 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.82/6.17 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X2 )
% 5.82/6.17 @ ( groups7501900531339628137nteger
% 5.82/6.17 @ ^ [I4: nat] : ( power_8256067586552552935nteger @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq'
% 5.82/6.17 thf(fact_7686_one__diff__power__eq_H,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.82/6.17 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 )
% 5.82/6.17 @ ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq'
% 5.82/6.17 thf(fact_7687_one__diff__power__eq_H,axiom,
% 5.82/6.17 ! [X2: int,N: nat] :
% 5.82/6.17 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.82/6.17 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 )
% 5.82/6.17 @ ( groups3539618377306564664at_int
% 5.82/6.17 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq'
% 5.82/6.17 thf(fact_7688_one__diff__power__eq_H,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.82/6.17 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 )
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_diff_power_eq'
% 5.82/6.17 thf(fact_7689_sum__split__even__odd,axiom,
% 5.82/6.17 ! [F: nat > real,G: nat > real,N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.17 = ( plus_plus_real
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_split_even_odd
% 5.82/6.17 thf(fact_7690_Sum__Icc__int,axiom,
% 5.82/6.17 ! [M: int,N: int] :
% 5.82/6.17 ( ( ord_less_eq_int @ M @ N )
% 5.82/6.17 => ( ( groups4538972089207619220nt_int
% 5.82/6.17 @ ^ [X3: int] : X3
% 5.82/6.17 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.82/6.17 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Sum_Icc_int
% 5.82/6.17 thf(fact_7691_sum__bounds__lt__plus1,axiom,
% 5.82/6.17 ! [F: nat > nat,Mm: nat] :
% 5.82/6.17 ( ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.82/6.17 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_bounds_lt_plus1
% 5.82/6.17 thf(fact_7692_sum__bounds__lt__plus1,axiom,
% 5.82/6.17 ! [F: nat > real,Mm: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.82/6.17 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sum_bounds_lt_plus1
% 5.82/6.17 thf(fact_7693_length__corresp,axiom,
% 5.82/6.17 ! [Tree_array2: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBT] :
% 5.82/6.17 ( ( ( ex_ass463751140784270563_VEBTi @ ( snga_assn_VEBT_VEBTi @ Tree_array2 ) )
% 5.82/6.17 = top_top_assn )
% 5.82/6.17 => ( ( heap_Time_return_nat @ ( size_s6755466524823107622T_VEBT @ Tree_is ) )
% 5.82/6.17 = ( array_len_VEBT_VEBTi @ Tree_array2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_corresp
% 5.82/6.17 thf(fact_7694_length__corresp,axiom,
% 5.82/6.17 ! [Tree_array2: array_VEBT_VEBTi,Tree_is: list_real] :
% 5.82/6.17 ( ( ( ex_ass463751140784270563_VEBTi @ ( snga_assn_VEBT_VEBTi @ Tree_array2 ) )
% 5.82/6.17 = top_top_assn )
% 5.82/6.17 => ( ( heap_Time_return_nat @ ( size_size_list_real @ Tree_is ) )
% 5.82/6.17 = ( array_len_VEBT_VEBTi @ Tree_array2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_corresp
% 5.82/6.17 thf(fact_7695_length__corresp,axiom,
% 5.82/6.17 ! [Tree_array2: array_VEBT_VEBTi,Tree_is: list_o] :
% 5.82/6.17 ( ( ( ex_ass463751140784270563_VEBTi @ ( snga_assn_VEBT_VEBTi @ Tree_array2 ) )
% 5.82/6.17 = top_top_assn )
% 5.82/6.17 => ( ( heap_Time_return_nat @ ( size_size_list_o @ Tree_is ) )
% 5.82/6.17 = ( array_len_VEBT_VEBTi @ Tree_array2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_corresp
% 5.82/6.17 thf(fact_7696_length__corresp,axiom,
% 5.82/6.17 ! [Tree_array2: array_VEBT_VEBTi,Tree_is: list_nat] :
% 5.82/6.17 ( ( ( ex_ass463751140784270563_VEBTi @ ( snga_assn_VEBT_VEBTi @ Tree_array2 ) )
% 5.82/6.17 = top_top_assn )
% 5.82/6.17 => ( ( heap_Time_return_nat @ ( size_size_list_nat @ Tree_is ) )
% 5.82/6.17 = ( array_len_VEBT_VEBTi @ Tree_array2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_corresp
% 5.82/6.17 thf(fact_7697_length__corresp,axiom,
% 5.82/6.17 ! [Tree_array2: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi] :
% 5.82/6.17 ( ( ( ex_ass463751140784270563_VEBTi @ ( snga_assn_VEBT_VEBTi @ Tree_array2 ) )
% 5.82/6.17 = top_top_assn )
% 5.82/6.17 => ( ( heap_Time_return_nat @ ( size_s7982070591426661849_VEBTi @ Tree_is ) )
% 5.82/6.17 = ( array_len_VEBT_VEBTi @ Tree_array2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % length_corresp
% 5.82/6.17 thf(fact_7698_sumr__cos__zero__one,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.82/6.17 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % sumr_cos_zero_one
% 5.82/6.17 thf(fact_7699_finite__nat__bounded,axiom,
% 5.82/6.17 ! [S: set_nat] :
% 5.82/6.17 ( ( finite_finite_nat @ S )
% 5.82/6.17 => ? [K2: nat] : ( ord_less_eq_set_nat @ S @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_nat_bounded
% 5.82/6.17 thf(fact_7700_finite__nat__iff__bounded,axiom,
% 5.82/6.17 ( finite_finite_nat
% 5.82/6.17 = ( ^ [S8: set_nat] :
% 5.82/6.17 ? [K3: nat] : ( ord_less_eq_set_nat @ S8 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_nat_iff_bounded
% 5.82/6.17 thf(fact_7701_max__top,axiom,
% 5.82/6.17 ! [X2: extended_enat] :
% 5.82/6.17 ( ( ord_ma741700101516333627d_enat @ top_to3028658606643905974d_enat @ X2 )
% 5.82/6.17 = top_to3028658606643905974d_enat ) ).
% 5.82/6.17
% 5.82/6.17 % max_top
% 5.82/6.17 thf(fact_7702_max__top,axiom,
% 5.82/6.17 ! [X2: set_Product_unit] :
% 5.82/6.17 ( ( ord_ma508538259134630082t_unit @ top_to1996260823553986621t_unit @ X2 )
% 5.82/6.17 = top_to1996260823553986621t_unit ) ).
% 5.82/6.17
% 5.82/6.17 % max_top
% 5.82/6.17 thf(fact_7703_max__top,axiom,
% 5.82/6.17 ! [X2: set_Numeral_num1] :
% 5.82/6.17 ( ( ord_ma2202181864719522458l_num1 @ top_to3689904429138878997l_num1 @ X2 )
% 5.82/6.17 = top_to3689904429138878997l_num1 ) ).
% 5.82/6.17
% 5.82/6.17 % max_top
% 5.82/6.17 thf(fact_7704_max__top,axiom,
% 5.82/6.17 ! [X2: set_real] :
% 5.82/6.17 ( ( ord_max_set_real @ top_top_set_real @ X2 )
% 5.82/6.17 = top_top_set_real ) ).
% 5.82/6.17
% 5.82/6.17 % max_top
% 5.82/6.17 thf(fact_7705_max__top,axiom,
% 5.82/6.17 ! [X2: set_o] :
% 5.82/6.17 ( ( ord_max_set_o @ top_top_set_o @ X2 )
% 5.82/6.17 = top_top_set_o ) ).
% 5.82/6.17
% 5.82/6.17 % max_top
% 5.82/6.17 thf(fact_7706_max__top,axiom,
% 5.82/6.17 ! [X2: set_nat] :
% 5.82/6.17 ( ( ord_max_set_nat @ top_top_set_nat @ X2 )
% 5.82/6.17 = top_top_set_nat ) ).
% 5.82/6.17
% 5.82/6.17 % max_top
% 5.82/6.17 thf(fact_7707_max__top2,axiom,
% 5.82/6.17 ! [X2: extended_enat] :
% 5.82/6.17 ( ( ord_ma741700101516333627d_enat @ X2 @ top_to3028658606643905974d_enat )
% 5.82/6.17 = top_to3028658606643905974d_enat ) ).
% 5.82/6.17
% 5.82/6.17 % max_top2
% 5.82/6.17 thf(fact_7708_max__top2,axiom,
% 5.82/6.17 ! [X2: set_Product_unit] :
% 5.82/6.17 ( ( ord_ma508538259134630082t_unit @ X2 @ top_to1996260823553986621t_unit )
% 5.82/6.17 = top_to1996260823553986621t_unit ) ).
% 5.82/6.17
% 5.82/6.17 % max_top2
% 5.82/6.17 thf(fact_7709_max__top2,axiom,
% 5.82/6.17 ! [X2: set_Numeral_num1] :
% 5.82/6.17 ( ( ord_ma2202181864719522458l_num1 @ X2 @ top_to3689904429138878997l_num1 )
% 5.82/6.17 = top_to3689904429138878997l_num1 ) ).
% 5.82/6.17
% 5.82/6.17 % max_top2
% 5.82/6.17 thf(fact_7710_max__top2,axiom,
% 5.82/6.17 ! [X2: set_real] :
% 5.82/6.17 ( ( ord_max_set_real @ X2 @ top_top_set_real )
% 5.82/6.17 = top_top_set_real ) ).
% 5.82/6.17
% 5.82/6.17 % max_top2
% 5.82/6.17 thf(fact_7711_max__top2,axiom,
% 5.82/6.17 ! [X2: set_o] :
% 5.82/6.17 ( ( ord_max_set_o @ X2 @ top_top_set_o )
% 5.82/6.17 = top_top_set_o ) ).
% 5.82/6.17
% 5.82/6.17 % max_top2
% 5.82/6.17 thf(fact_7712_max__top2,axiom,
% 5.82/6.17 ! [X2: set_nat] :
% 5.82/6.17 ( ( ord_max_set_nat @ X2 @ top_top_set_nat )
% 5.82/6.17 = top_top_set_nat ) ).
% 5.82/6.17
% 5.82/6.17 % max_top2
% 5.82/6.17 thf(fact_7713_merge__true__star,axiom,
% 5.82/6.17 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 5.82/6.17 = top_top_assn ) ).
% 5.82/6.17
% 5.82/6.17 % merge_true_star
% 5.82/6.17 thf(fact_7714_assn__basic__inequalities_I1_J,axiom,
% 5.82/6.17 top_top_assn != one_one_assn ).
% 5.82/6.17
% 5.82/6.17 % assn_basic_inequalities(1)
% 5.82/6.17 thf(fact_7715_cos__coeff__0,axiom,
% 5.82/6.17 ( ( cos_coeff @ zero_zero_nat )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % cos_coeff_0
% 5.82/6.17 thf(fact_7716_top_Oextremum__strict,axiom,
% 5.82/6.17 ! [A2: set_Product_unit] :
% 5.82/6.17 ~ ( ord_le8056459307392131481t_unit @ top_to1996260823553986621t_unit @ A2 ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_strict
% 5.82/6.17 thf(fact_7717_top_Oextremum__strict,axiom,
% 5.82/6.17 ! [A2: set_Numeral_num1] :
% 5.82/6.17 ~ ( ord_le526730876122248049l_num1 @ top_to3689904429138878997l_num1 @ A2 ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_strict
% 5.82/6.17 thf(fact_7718_top_Oextremum__strict,axiom,
% 5.82/6.17 ! [A2: set_real] :
% 5.82/6.17 ~ ( ord_less_set_real @ top_top_set_real @ A2 ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_strict
% 5.82/6.17 thf(fact_7719_top_Oextremum__strict,axiom,
% 5.82/6.17 ! [A2: set_o] :
% 5.82/6.17 ~ ( ord_less_set_o @ top_top_set_o @ A2 ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_strict
% 5.82/6.17 thf(fact_7720_top_Oextremum__strict,axiom,
% 5.82/6.17 ! [A2: set_nat] :
% 5.82/6.17 ~ ( ord_less_set_nat @ top_top_set_nat @ A2 ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_strict
% 5.82/6.17 thf(fact_7721_top_Onot__eq__extremum,axiom,
% 5.82/6.17 ! [A2: set_Product_unit] :
% 5.82/6.17 ( ( A2 != top_to1996260823553986621t_unit )
% 5.82/6.17 = ( ord_le8056459307392131481t_unit @ A2 @ top_to1996260823553986621t_unit ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.not_eq_extremum
% 5.82/6.17 thf(fact_7722_top_Onot__eq__extremum,axiom,
% 5.82/6.17 ! [A2: set_Numeral_num1] :
% 5.82/6.17 ( ( A2 != top_to3689904429138878997l_num1 )
% 5.82/6.17 = ( ord_le526730876122248049l_num1 @ A2 @ top_to3689904429138878997l_num1 ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.not_eq_extremum
% 5.82/6.17 thf(fact_7723_top_Onot__eq__extremum,axiom,
% 5.82/6.17 ! [A2: set_real] :
% 5.82/6.17 ( ( A2 != top_top_set_real )
% 5.82/6.17 = ( ord_less_set_real @ A2 @ top_top_set_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.not_eq_extremum
% 5.82/6.17 thf(fact_7724_top_Onot__eq__extremum,axiom,
% 5.82/6.17 ! [A2: set_o] :
% 5.82/6.17 ( ( A2 != top_top_set_o )
% 5.82/6.17 = ( ord_less_set_o @ A2 @ top_top_set_o ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.not_eq_extremum
% 5.82/6.17 thf(fact_7725_top_Onot__eq__extremum,axiom,
% 5.82/6.17 ! [A2: set_nat] :
% 5.82/6.17 ( ( A2 != top_top_set_nat )
% 5.82/6.17 = ( ord_less_set_nat @ A2 @ top_top_set_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.not_eq_extremum
% 5.82/6.17 thf(fact_7726_merge__true__star__ctx,axiom,
% 5.82/6.17 ! [P: assn] :
% 5.82/6.17 ( ( times_times_assn @ top_top_assn @ ( times_times_assn @ top_top_assn @ P ) )
% 5.82/6.17 = ( times_times_assn @ top_top_assn @ P ) ) ).
% 5.82/6.17
% 5.82/6.17 % merge_true_star_ctx
% 5.82/6.17 thf(fact_7727_top__option__def,axiom,
% 5.82/6.17 ( top_to7662761140297458691t_unit
% 5.82/6.17 = ( some_s8043159101241848530t_unit @ top_to1996260823553986621t_unit ) ) ).
% 5.82/6.17
% 5.82/6.17 % top_option_def
% 5.82/6.17 thf(fact_7728_top__option__def,axiom,
% 5.82/6.17 ( top_to176924430543178203l_num1
% 5.82/6.17 = ( some_s513430669971965098l_num1 @ top_to3689904429138878997l_num1 ) ) ).
% 5.82/6.17
% 5.82/6.17 % top_option_def
% 5.82/6.17 thf(fact_7729_top__option__def,axiom,
% 5.82/6.17 ( top_to1083748111577038690t_real
% 5.82/6.17 = ( some_set_real @ top_top_set_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % top_option_def
% 5.82/6.17 thf(fact_7730_top__option__def,axiom,
% 5.82/6.17 ( top_top_option_set_o
% 5.82/6.17 = ( some_set_o @ top_top_set_o ) ) ).
% 5.82/6.17
% 5.82/6.17 % top_option_def
% 5.82/6.17 thf(fact_7731_top__option__def,axiom,
% 5.82/6.17 ( top_to4826455019444611206et_nat
% 5.82/6.17 = ( some_set_nat @ top_top_set_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % top_option_def
% 5.82/6.17 thf(fact_7732_top__greatest,axiom,
% 5.82/6.17 ! [A2: set_Product_unit] : ( ord_le3507040750410214029t_unit @ A2 @ top_to1996260823553986621t_unit ) ).
% 5.82/6.17
% 5.82/6.17 % top_greatest
% 5.82/6.17 thf(fact_7733_top__greatest,axiom,
% 5.82/6.17 ! [A2: set_Numeral_num1] : ( ord_le5200684355995106405l_num1 @ A2 @ top_to3689904429138878997l_num1 ) ).
% 5.82/6.17
% 5.82/6.17 % top_greatest
% 5.82/6.17 thf(fact_7734_top__greatest,axiom,
% 5.82/6.17 ! [A2: set_real] : ( ord_less_eq_set_real @ A2 @ top_top_set_real ) ).
% 5.82/6.17
% 5.82/6.17 % top_greatest
% 5.82/6.17 thf(fact_7735_top__greatest,axiom,
% 5.82/6.17 ! [A2: set_o] : ( ord_less_eq_set_o @ A2 @ top_top_set_o ) ).
% 5.82/6.17
% 5.82/6.17 % top_greatest
% 5.82/6.17 thf(fact_7736_top__greatest,axiom,
% 5.82/6.17 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 5.82/6.17
% 5.82/6.17 % top_greatest
% 5.82/6.17 thf(fact_7737_top__greatest,axiom,
% 5.82/6.17 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ top_top_set_int ) ).
% 5.82/6.17
% 5.82/6.17 % top_greatest
% 5.82/6.17 thf(fact_7738_top_Oextremum__unique,axiom,
% 5.82/6.17 ! [A2: set_Product_unit] :
% 5.82/6.17 ( ( ord_le3507040750410214029t_unit @ top_to1996260823553986621t_unit @ A2 )
% 5.82/6.17 = ( A2 = top_to1996260823553986621t_unit ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_unique
% 5.82/6.17 thf(fact_7739_top_Oextremum__unique,axiom,
% 5.82/6.17 ! [A2: set_Numeral_num1] :
% 5.82/6.17 ( ( ord_le5200684355995106405l_num1 @ top_to3689904429138878997l_num1 @ A2 )
% 5.82/6.17 = ( A2 = top_to3689904429138878997l_num1 ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_unique
% 5.82/6.17 thf(fact_7740_top_Oextremum__unique,axiom,
% 5.82/6.17 ! [A2: set_real] :
% 5.82/6.17 ( ( ord_less_eq_set_real @ top_top_set_real @ A2 )
% 5.82/6.17 = ( A2 = top_top_set_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_unique
% 5.82/6.17 thf(fact_7741_top_Oextremum__unique,axiom,
% 5.82/6.17 ! [A2: set_o] :
% 5.82/6.17 ( ( ord_less_eq_set_o @ top_top_set_o @ A2 )
% 5.82/6.17 = ( A2 = top_top_set_o ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_unique
% 5.82/6.17 thf(fact_7742_top_Oextremum__unique,axiom,
% 5.82/6.17 ! [A2: set_nat] :
% 5.82/6.17 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A2 )
% 5.82/6.17 = ( A2 = top_top_set_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_unique
% 5.82/6.17 thf(fact_7743_top_Oextremum__unique,axiom,
% 5.82/6.17 ! [A2: set_int] :
% 5.82/6.17 ( ( ord_less_eq_set_int @ top_top_set_int @ A2 )
% 5.82/6.17 = ( A2 = top_top_set_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_unique
% 5.82/6.17 thf(fact_7744_top_Oextremum__uniqueI,axiom,
% 5.82/6.17 ! [A2: set_Product_unit] :
% 5.82/6.17 ( ( ord_le3507040750410214029t_unit @ top_to1996260823553986621t_unit @ A2 )
% 5.82/6.17 => ( A2 = top_to1996260823553986621t_unit ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_uniqueI
% 5.82/6.17 thf(fact_7745_top_Oextremum__uniqueI,axiom,
% 5.82/6.17 ! [A2: set_Numeral_num1] :
% 5.82/6.17 ( ( ord_le5200684355995106405l_num1 @ top_to3689904429138878997l_num1 @ A2 )
% 5.82/6.17 => ( A2 = top_to3689904429138878997l_num1 ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_uniqueI
% 5.82/6.17 thf(fact_7746_top_Oextremum__uniqueI,axiom,
% 5.82/6.17 ! [A2: set_real] :
% 5.82/6.17 ( ( ord_less_eq_set_real @ top_top_set_real @ A2 )
% 5.82/6.17 => ( A2 = top_top_set_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_uniqueI
% 5.82/6.17 thf(fact_7747_top_Oextremum__uniqueI,axiom,
% 5.82/6.17 ! [A2: set_o] :
% 5.82/6.17 ( ( ord_less_eq_set_o @ top_top_set_o @ A2 )
% 5.82/6.17 => ( A2 = top_top_set_o ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_uniqueI
% 5.82/6.17 thf(fact_7748_top_Oextremum__uniqueI,axiom,
% 5.82/6.17 ! [A2: set_nat] :
% 5.82/6.17 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A2 )
% 5.82/6.17 => ( A2 = top_top_set_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_uniqueI
% 5.82/6.17 thf(fact_7749_top_Oextremum__uniqueI,axiom,
% 5.82/6.17 ! [A2: set_int] :
% 5.82/6.17 ( ( ord_less_eq_set_int @ top_top_set_int @ A2 )
% 5.82/6.17 => ( A2 = top_top_set_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % top.extremum_uniqueI
% 5.82/6.17 thf(fact_7750_ent__true,axiom,
% 5.82/6.17 ! [P: assn] : ( entails @ P @ top_top_assn ) ).
% 5.82/6.17
% 5.82/6.17 % ent_true
% 5.82/6.17 thf(fact_7751_ent__true__drop_I2_J,axiom,
% 5.82/6.17 ! [P: assn,Q: assn] :
% 5.82/6.17 ( ( entails @ P @ Q )
% 5.82/6.17 => ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % ent_true_drop(2)
% 5.82/6.17 thf(fact_7752_ent__true__drop_I1_J,axiom,
% 5.82/6.17 ! [P: assn,Q: assn,R: assn] :
% 5.82/6.17 ( ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) )
% 5.82/6.17 => ( entails @ ( times_times_assn @ P @ R ) @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % ent_true_drop(1)
% 5.82/6.17 thf(fact_7753_ent__refl__true,axiom,
% 5.82/6.17 ! [A: assn] : ( entails @ A @ ( times_times_assn @ A @ top_top_assn ) ) ).
% 5.82/6.17
% 5.82/6.17 % ent_refl_true
% 5.82/6.17 thf(fact_7754_ent__star__mono__true,axiom,
% 5.82/6.17 ! [A: assn,A7: assn,B: assn,B8: assn] :
% 5.82/6.17 ( ( entails @ A @ ( times_times_assn @ A7 @ top_top_assn ) )
% 5.82/6.17 => ( ( entails @ B @ ( times_times_assn @ B8 @ top_top_assn ) )
% 5.82/6.17 => ( entails @ ( times_times_assn @ ( times_times_assn @ A @ B ) @ top_top_assn ) @ ( times_times_assn @ ( times_times_assn @ A7 @ B8 ) @ top_top_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % ent_star_mono_true
% 5.82/6.17 thf(fact_7755_mod__star__trueE,axiom,
% 5.82/6.17 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.17 ( ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 )
% 5.82/6.17 => ~ ! [H5: produc3658429121746597890et_nat] :
% 5.82/6.17 ~ ( rep_assn @ P @ H5 ) ) ).
% 5.82/6.17
% 5.82/6.17 % mod_star_trueE
% 5.82/6.17 thf(fact_7756_mod__star__trueI,axiom,
% 5.82/6.17 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 5.82/6.17 ( ( rep_assn @ P @ H2 )
% 5.82/6.17 => ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % mod_star_trueI
% 5.82/6.17 thf(fact_7757_unbounded__k__infinite,axiom,
% 5.82/6.17 ! [K: nat,S: set_nat] :
% 5.82/6.17 ( ! [M5: nat] :
% 5.82/6.17 ( ( ord_less_nat @ K @ M5 )
% 5.82/6.17 => ? [N9: nat] :
% 5.82/6.17 ( ( ord_less_nat @ M5 @ N9 )
% 5.82/6.17 & ( member_nat @ N9 @ S ) ) )
% 5.82/6.17 => ~ ( finite_finite_nat @ S ) ) ).
% 5.82/6.17
% 5.82/6.17 % unbounded_k_infinite
% 5.82/6.17 thf(fact_7758_infinite__nat__iff__unbounded,axiom,
% 5.82/6.17 ! [S: set_nat] :
% 5.82/6.17 ( ( ~ ( finite_finite_nat @ S ) )
% 5.82/6.17 = ( ! [M6: nat] :
% 5.82/6.17 ? [N4: nat] :
% 5.82/6.17 ( ( ord_less_nat @ M6 @ N4 )
% 5.82/6.17 & ( member_nat @ N4 @ S ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % infinite_nat_iff_unbounded
% 5.82/6.17 thf(fact_7759_infinite__nat__iff__unbounded__le,axiom,
% 5.82/6.17 ! [S: set_nat] :
% 5.82/6.17 ( ( ~ ( finite_finite_nat @ S ) )
% 5.82/6.17 = ( ! [M6: nat] :
% 5.82/6.17 ? [N4: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ M6 @ N4 )
% 5.82/6.17 & ( member_nat @ N4 @ S ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % infinite_nat_iff_unbounded_le
% 5.82/6.17 thf(fact_7760_geometric__deriv__sums,axiom,
% 5.82/6.17 ! [Z: real] :
% 5.82/6.17 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) @ ( power_power_real @ Z @ N4 ) )
% 5.82/6.17 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_deriv_sums
% 5.82/6.17 thf(fact_7761_geometric__deriv__sums,axiom,
% 5.82/6.17 ! [Z: complex] :
% 5.82/6.17 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.82/6.17 => ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N4 ) ) @ ( power_power_complex @ Z @ N4 ) )
% 5.82/6.17 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_deriv_sums
% 5.82/6.17 thf(fact_7762_vebt__assn__raw_Opelims,axiom,
% 5.82/6.17 ! [X2: vEBT_VEBT,Xa: vEBT_VEBTi,Y3: assn] :
% 5.82/6.17 ( ( ( vEBT_vebt_assn_raw @ X2 @ Xa )
% 5.82/6.17 = Y3 )
% 5.82/6.17 => ( ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ X2 @ Xa ) )
% 5.82/6.17 => ( ! [A3: $o,B3: $o] :
% 5.82/6.17 ( ( X2
% 5.82/6.17 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.17 => ! [Ai2: $o,Bi2: $o] :
% 5.82/6.17 ( ( Xa
% 5.82/6.17 = ( vEBT_Leafi @ Ai2 @ Bi2 ) )
% 5.82/6.17 => ( ( Y3
% 5.82/6.17 = ( pure_assn
% 5.82/6.17 @ ( ( Ai2 = A3 )
% 5.82/6.17 & ( Bi2 = B3 ) ) ) )
% 5.82/6.17 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A3 @ B3 ) @ ( vEBT_Leafi @ Ai2 @ Bi2 ) ) ) ) ) )
% 5.82/6.17 => ( ! [Mmo: option4927543243414619207at_nat,Deg2: nat,Tree_list: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.17 ( ( X2
% 5.82/6.17 = ( vEBT_Node @ Mmo @ Deg2 @ Tree_list @ Summary2 ) )
% 5.82/6.17 => ! [Mmoi: option4927543243414619207at_nat,Degi: nat,Tree_array: array_VEBT_VEBTi,Summaryi: vEBT_VEBTi] :
% 5.82/6.17 ( ( Xa
% 5.82/6.17 = ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) )
% 5.82/6.17 => ( ( Y3
% 5.82/6.17 = ( times_times_assn
% 5.82/6.17 @ ( times_times_assn
% 5.82/6.17 @ ( pure_assn
% 5.82/6.17 @ ( ( Mmoi = Mmo )
% 5.82/6.17 & ( Degi = Deg2 ) ) )
% 5.82/6.17 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi ) )
% 5.82/6.17 @ ( ex_ass463751140784270563_VEBTi
% 5.82/6.17 @ ^ [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 ) ) ) ) )
% 5.82/6.17 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo @ Deg2 @ Tree_list @ Summary2 ) @ ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) ) ) ) ) )
% 5.82/6.17 => ( ! [V2: option4927543243414619207at_nat,Va3: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 5.82/6.17 ( ( X2
% 5.82/6.17 = ( vEBT_Node @ V2 @ Va3 @ Vb3 @ Vc3 ) )
% 5.82/6.17 => ! [Vd: $o,Ve: $o] :
% 5.82/6.17 ( ( Xa
% 5.82/6.17 = ( vEBT_Leafi @ Vd @ Ve ) )
% 5.82/6.17 => ( ( Y3 = bot_bot_assn )
% 5.82/6.17 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V2 @ Va3 @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd @ Ve ) ) ) ) ) )
% 5.82/6.17 => ~ ! [Vd: $o,Ve: $o] :
% 5.82/6.17 ( ( X2
% 5.82/6.17 = ( vEBT_Leaf @ Vd @ Ve ) )
% 5.82/6.17 => ! [V2: option4927543243414619207at_nat,Va3: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 5.82/6.17 ( ( Xa
% 5.82/6.17 = ( vEBT_Nodei @ V2 @ Va3 @ Vb3 @ Vc3 ) )
% 5.82/6.17 => ( ( Y3 = bot_bot_assn )
% 5.82/6.17 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd @ Ve ) @ ( vEBT_Nodei @ V2 @ Va3 @ Vb3 @ Vc3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % vebt_assn_raw.pelims
% 5.82/6.17 thf(fact_7763_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 5.82/6.17 ! [A2: $o,B2: $o] :
% 5.82/6.17 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A2 @ B2 ) )
% 5.82/6.17 = zero_zero_nat ) ).
% 5.82/6.17
% 5.82/6.17 % VEBT_internal.height.simps(1)
% 5.82/6.17 thf(fact_7764_pochhammer__double,axiom,
% 5.82/6.17 ! [Z: complex,N: nat] :
% 5.82/6.17 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.17 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_double
% 5.82/6.17 thf(fact_7765_pochhammer__double,axiom,
% 5.82/6.17 ! [Z: rat,N: nat] :
% 5.82/6.17 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.17 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_double
% 5.82/6.17 thf(fact_7766_pochhammer__double,axiom,
% 5.82/6.17 ! [Z: real,N: nat] :
% 5.82/6.17 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.17 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_double
% 5.82/6.17 thf(fact_7767_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite1345302120164226195on_int @ top_to6430115241214627170on_int )
% 5.82/6.17 = ( finite_finite_int @ top_top_set_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7768_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite6785661671136154180nteger @ top_to5929521628599800467nteger )
% 5.82/6.17 = ( finite6017078050557962740nteger @ top_to4645266643341252675nteger ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7769_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite2569390945932476949omplex @ top_to6180147692022559204omplex )
% 5.82/6.17 = ( finite3207457112153483333omplex @ top_top_set_complex ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7770_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite1445617369574913404t_unit @ top_to2690860209552263555t_unit )
% 5.82/6.17 = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7771_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite3139260975159805780l_num1 @ top_to4428395536652758875l_num1 )
% 5.82/6.17 = ( finite1111429032697314574l_num1 @ top_to3689904429138878997l_num1 ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7772_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite5731380839103853331n_real @ top_to853713521313446370n_real )
% 5.82/6.17 = ( finite_finite_real @ top_top_set_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7773_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite4093902646404507527tion_o @ top_top_set_option_o )
% 5.82/6.17 = ( finite_finite_o @ top_top_set_o ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7774_finite__option__UNIV,axiom,
% 5.82/6.17 ( ( finite5523153139673422903on_nat @ top_to8920198386146353926on_nat )
% 5.82/6.17 = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_option_UNIV
% 5.82/6.17 thf(fact_7775_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_complex
% 5.82/6.17 @ ^ [S5: complex] : P )
% 5.82/6.17 = top_top_set_complex ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_complex
% 5.82/6.17 @ ^ [S5: complex] : P )
% 5.82/6.17 = bot_bot_set_complex ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7776_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collec213857154873943460nt_int
% 5.82/6.17 @ ^ [S5: product_prod_int_int] : P )
% 5.82/6.17 = top_to4366644338036079209nt_int ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collec213857154873943460nt_int
% 5.82/6.17 @ ^ [S5: product_prod_int_int] : P )
% 5.82/6.17 = bot_bo1796632182523588997nt_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7777_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_int
% 5.82/6.17 @ ^ [S5: int] : P )
% 5.82/6.17 = top_top_set_int ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_int
% 5.82/6.17 @ ^ [S5: int] : P )
% 5.82/6.17 = bot_bot_set_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7778_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_Product_unit
% 5.82/6.17 @ ^ [S5: product_unit] : P )
% 5.82/6.17 = top_to1996260823553986621t_unit ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_Product_unit
% 5.82/6.17 @ ^ [S5: product_unit] : P )
% 5.82/6.17 = bot_bo3957492148770167129t_unit ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7779_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_Numeral_num1
% 5.82/6.17 @ ^ [S5: numeral_num1] : P )
% 5.82/6.17 = top_to3689904429138878997l_num1 ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_Numeral_num1
% 5.82/6.17 @ ^ [S5: numeral_num1] : P )
% 5.82/6.17 = bot_bo5651135754355059505l_num1 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7780_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_real
% 5.82/6.17 @ ^ [S5: real] : P )
% 5.82/6.17 = top_top_set_real ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_real
% 5.82/6.17 @ ^ [S5: real] : P )
% 5.82/6.17 = bot_bot_set_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7781_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_o
% 5.82/6.17 @ ^ [S5: $o] : P )
% 5.82/6.17 = top_top_set_o ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_o
% 5.82/6.17 @ ^ [S5: $o] : P )
% 5.82/6.17 = bot_bot_set_o ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7782_Collect__const,axiom,
% 5.82/6.17 ! [P: $o] :
% 5.82/6.17 ( ( P
% 5.82/6.17 => ( ( collect_nat
% 5.82/6.17 @ ^ [S5: nat] : P )
% 5.82/6.17 = top_top_set_nat ) )
% 5.82/6.17 & ( ~ P
% 5.82/6.17 => ( ( collect_nat
% 5.82/6.17 @ ^ [S5: nat] : P )
% 5.82/6.17 = bot_bot_set_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % Collect_const
% 5.82/6.17 thf(fact_7783_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: product_prod_int_int > $o] :
% 5.82/6.17 ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.82/6.17 => ( ( finite2998713641127702882nt_int
% 5.82/6.17 @ ( collec213857154873943460nt_int
% 5.82/6.17 @ ^ [X3: product_prod_int_int] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite2998713641127702882nt_int @ top_to4366644338036079209nt_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7784_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: int > $o] :
% 5.82/6.17 ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.82/6.17 => ( ( finite_finite_int
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [X3: int] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite_finite_int @ top_top_set_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7785_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: code_integer > $o] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.82/6.17 => ( ( finite6017078050557962740nteger
% 5.82/6.17 @ ( collect_Code_integer
% 5.82/6.17 @ ^ [X3: code_integer] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite6017078050557962740nteger @ top_to4645266643341252675nteger ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7786_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: complex > $o] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.82/6.17 => ( ( finite3207457112153483333omplex
% 5.82/6.17 @ ( collect_complex
% 5.82/6.17 @ ^ [X3: complex] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite3207457112153483333omplex @ top_top_set_complex ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7787_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: product_unit > $o] :
% 5.82/6.17 ( ( finite4290736615968046902t_unit @ ( collect_Product_unit @ P ) )
% 5.82/6.17 => ( ( finite4290736615968046902t_unit
% 5.82/6.17 @ ( collect_Product_unit
% 5.82/6.17 @ ^ [X3: product_unit] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7788_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: numeral_num1 > $o] :
% 5.82/6.17 ( ( finite1111429032697314574l_num1 @ ( collect_Numeral_num1 @ P ) )
% 5.82/6.17 => ( ( finite1111429032697314574l_num1
% 5.82/6.17 @ ( collect_Numeral_num1
% 5.82/6.17 @ ^ [X3: numeral_num1] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite1111429032697314574l_num1 @ top_to3689904429138878997l_num1 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7789_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: real > $o] :
% 5.82/6.17 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.82/6.17 => ( ( finite_finite_real
% 5.82/6.17 @ ( collect_real
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite_finite_real @ top_top_set_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7790_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: $o > $o] :
% 5.82/6.17 ( ( finite_finite_o @ ( collect_o @ P ) )
% 5.82/6.17 => ( ( finite_finite_o
% 5.82/6.17 @ ( collect_o
% 5.82/6.17 @ ^ [X3: $o] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite_finite_o @ top_top_set_o ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7791_finite__Collect__not,axiom,
% 5.82/6.17 ! [P: nat > $o] :
% 5.82/6.17 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.17 => ( ( finite_finite_nat
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [X3: nat] :
% 5.82/6.17 ~ ( P @ X3 ) ) )
% 5.82/6.17 = ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % finite_Collect_not
% 5.82/6.17 thf(fact_7792_Diff__UNIV,axiom,
% 5.82/6.17 ! [A: set_int] :
% 5.82/6.17 ( ( minus_minus_set_int @ A @ top_top_set_int )
% 5.82/6.17 = bot_bot_set_int ) ).
% 5.82/6.17
% 5.82/6.17 % Diff_UNIV
% 5.82/6.17 thf(fact_7793_Diff__UNIV,axiom,
% 5.82/6.17 ! [A: set_Product_unit] :
% 5.82/6.17 ( ( minus_6452836326544984404t_unit @ A @ top_to1996260823553986621t_unit )
% 5.82/6.17 = bot_bo3957492148770167129t_unit ) ).
% 5.82/6.17
% 5.82/6.17 % Diff_UNIV
% 5.82/6.17 thf(fact_7794_Diff__UNIV,axiom,
% 5.82/6.17 ! [A: set_Numeral_num1] :
% 5.82/6.17 ( ( minus_8146479932129876780l_num1 @ A @ top_to3689904429138878997l_num1 )
% 5.82/6.17 = bot_bo5651135754355059505l_num1 ) ).
% 5.82/6.17
% 5.82/6.17 % Diff_UNIV
% 5.82/6.17 thf(fact_7795_Diff__UNIV,axiom,
% 5.82/6.17 ! [A: set_real] :
% 5.82/6.17 ( ( minus_minus_set_real @ A @ top_top_set_real )
% 5.82/6.17 = bot_bot_set_real ) ).
% 5.82/6.17
% 5.82/6.17 % Diff_UNIV
% 5.82/6.17 thf(fact_7796_Diff__UNIV,axiom,
% 5.82/6.17 ! [A: set_o] :
% 5.82/6.17 ( ( minus_minus_set_o @ A @ top_top_set_o )
% 5.82/6.17 = bot_bot_set_o ) ).
% 5.82/6.17
% 5.82/6.17 % Diff_UNIV
% 5.82/6.17 thf(fact_7797_Diff__UNIV,axiom,
% 5.82/6.17 ! [A: set_nat] :
% 5.82/6.17 ( ( minus_minus_set_nat @ A @ top_top_set_nat )
% 5.82/6.17 = bot_bot_set_nat ) ).
% 5.82/6.17
% 5.82/6.17 % Diff_UNIV
% 5.82/6.17 thf(fact_7798_pochhammer__0,axiom,
% 5.82/6.17 ! [A2: real] :
% 5.82/6.17 ( ( comm_s7457072308508201937r_real @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0
% 5.82/6.17 thf(fact_7799_pochhammer__0,axiom,
% 5.82/6.17 ! [A2: rat] :
% 5.82/6.17 ( ( comm_s4028243227959126397er_rat @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_rat ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0
% 5.82/6.17 thf(fact_7800_pochhammer__0,axiom,
% 5.82/6.17 ! [A2: nat] :
% 5.82/6.17 ( ( comm_s4663373288045622133er_nat @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_nat ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0
% 5.82/6.17 thf(fact_7801_pochhammer__0,axiom,
% 5.82/6.17 ! [A2: int] :
% 5.82/6.17 ( ( comm_s4660882817536571857er_int @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0
% 5.82/6.17 thf(fact_7802_powser__sums__zero__iff,axiom,
% 5.82/6.17 ! [A2: nat > complex,X2: complex] :
% 5.82/6.17 ( ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ ( A2 @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 5.82/6.17 @ X2 )
% 5.82/6.17 = ( ( A2 @ zero_zero_nat )
% 5.82/6.17 = X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_zero_iff
% 5.82/6.17 thf(fact_7803_powser__sums__zero__iff,axiom,
% 5.82/6.17 ! [A2: nat > real,X2: real] :
% 5.82/6.17 ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ ( A2 @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 5.82/6.17 @ X2 )
% 5.82/6.17 = ( ( A2 @ zero_zero_nat )
% 5.82/6.17 = X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_zero_iff
% 5.82/6.17 thf(fact_7804_subset__UNIV,axiom,
% 5.82/6.17 ! [A: set_Product_unit] : ( ord_le3507040750410214029t_unit @ A @ top_to1996260823553986621t_unit ) ).
% 5.82/6.17
% 5.82/6.17 % subset_UNIV
% 5.82/6.17 thf(fact_7805_subset__UNIV,axiom,
% 5.82/6.17 ! [A: set_Numeral_num1] : ( ord_le5200684355995106405l_num1 @ A @ top_to3689904429138878997l_num1 ) ).
% 5.82/6.17
% 5.82/6.17 % subset_UNIV
% 5.82/6.17 thf(fact_7806_subset__UNIV,axiom,
% 5.82/6.17 ! [A: set_real] : ( ord_less_eq_set_real @ A @ top_top_set_real ) ).
% 5.82/6.17
% 5.82/6.17 % subset_UNIV
% 5.82/6.17 thf(fact_7807_subset__UNIV,axiom,
% 5.82/6.17 ! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ) ).
% 5.82/6.17
% 5.82/6.17 % subset_UNIV
% 5.82/6.17 thf(fact_7808_subset__UNIV,axiom,
% 5.82/6.17 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 5.82/6.17
% 5.82/6.17 % subset_UNIV
% 5.82/6.17 thf(fact_7809_subset__UNIV,axiom,
% 5.82/6.17 ! [A: set_int] : ( ord_less_eq_set_int @ A @ top_top_set_int ) ).
% 5.82/6.17
% 5.82/6.17 % subset_UNIV
% 5.82/6.17 thf(fact_7810_pochhammer__pos,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.17 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_pos
% 5.82/6.17 thf(fact_7811_pochhammer__pos,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.82/6.17 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_pos
% 5.82/6.17 thf(fact_7812_pochhammer__pos,axiom,
% 5.82/6.17 ! [X2: nat,N: nat] :
% 5.82/6.17 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.17 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_pos
% 5.82/6.17 thf(fact_7813_pochhammer__pos,axiom,
% 5.82/6.17 ! [X2: int,N: nat] :
% 5.82/6.17 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.82/6.17 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_pos
% 5.82/6.17 thf(fact_7814_pochhammer__eq__0__mono,axiom,
% 5.82/6.17 ! [A2: complex,N: nat,M: nat] :
% 5.82/6.17 ( ( ( comm_s2602460028002588243omplex @ A2 @ N )
% 5.82/6.17 = zero_zero_complex )
% 5.82/6.17 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.17 => ( ( comm_s2602460028002588243omplex @ A2 @ M )
% 5.82/6.17 = zero_zero_complex ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_eq_0_mono
% 5.82/6.17 thf(fact_7815_pochhammer__eq__0__mono,axiom,
% 5.82/6.17 ! [A2: real,N: nat,M: nat] :
% 5.82/6.17 ( ( ( comm_s7457072308508201937r_real @ A2 @ N )
% 5.82/6.17 = zero_zero_real )
% 5.82/6.17 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.17 => ( ( comm_s7457072308508201937r_real @ A2 @ M )
% 5.82/6.17 = zero_zero_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_eq_0_mono
% 5.82/6.17 thf(fact_7816_pochhammer__eq__0__mono,axiom,
% 5.82/6.17 ! [A2: rat,N: nat,M: nat] :
% 5.82/6.17 ( ( ( comm_s4028243227959126397er_rat @ A2 @ N )
% 5.82/6.17 = zero_zero_rat )
% 5.82/6.17 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.17 => ( ( comm_s4028243227959126397er_rat @ A2 @ M )
% 5.82/6.17 = zero_zero_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_eq_0_mono
% 5.82/6.17 thf(fact_7817_pochhammer__neq__0__mono,axiom,
% 5.82/6.17 ! [A2: complex,M: nat,N: nat] :
% 5.82/6.17 ( ( ( comm_s2602460028002588243omplex @ A2 @ M )
% 5.82/6.17 != zero_zero_complex )
% 5.82/6.17 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.17 => ( ( comm_s2602460028002588243omplex @ A2 @ N )
% 5.82/6.17 != zero_zero_complex ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_neq_0_mono
% 5.82/6.17 thf(fact_7818_pochhammer__neq__0__mono,axiom,
% 5.82/6.17 ! [A2: real,M: nat,N: nat] :
% 5.82/6.17 ( ( ( comm_s7457072308508201937r_real @ A2 @ M )
% 5.82/6.17 != zero_zero_real )
% 5.82/6.17 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.17 => ( ( comm_s7457072308508201937r_real @ A2 @ N )
% 5.82/6.17 != zero_zero_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_neq_0_mono
% 5.82/6.17 thf(fact_7819_pochhammer__neq__0__mono,axiom,
% 5.82/6.17 ! [A2: rat,M: nat,N: nat] :
% 5.82/6.17 ( ( ( comm_s4028243227959126397er_rat @ A2 @ M )
% 5.82/6.17 != zero_zero_rat )
% 5.82/6.17 => ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.17 => ( ( comm_s4028243227959126397er_rat @ A2 @ N )
% 5.82/6.17 != zero_zero_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_neq_0_mono
% 5.82/6.17 thf(fact_7820_not__UNIV__le__Icc,axiom,
% 5.82/6.17 ! [L: nat,H2: nat] :
% 5.82/6.17 ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % not_UNIV_le_Icc
% 5.82/6.17 thf(fact_7821_not__UNIV__le__Icc,axiom,
% 5.82/6.17 ! [L: int,H2: int] :
% 5.82/6.17 ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % not_UNIV_le_Icc
% 5.82/6.17 thf(fact_7822_not__UNIV__le__Icc,axiom,
% 5.82/6.17 ! [L: real,H2: real] :
% 5.82/6.17 ~ ( ord_less_eq_set_real @ top_top_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % not_UNIV_le_Icc
% 5.82/6.17 thf(fact_7823_pochhammer__nonneg,axiom,
% 5.82/6.17 ! [X2: real,N: nat] :
% 5.82/6.17 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.17 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_nonneg
% 5.82/6.17 thf(fact_7824_pochhammer__nonneg,axiom,
% 5.82/6.17 ! [X2: rat,N: nat] :
% 5.82/6.17 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.82/6.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_nonneg
% 5.82/6.17 thf(fact_7825_pochhammer__nonneg,axiom,
% 5.82/6.17 ! [X2: nat,N: nat] :
% 5.82/6.17 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.82/6.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_nonneg
% 5.82/6.17 thf(fact_7826_pochhammer__nonneg,axiom,
% 5.82/6.17 ! [X2: int,N: nat] :
% 5.82/6.17 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.82/6.17 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_nonneg
% 5.82/6.17 thf(fact_7827_pochhammer__0__left,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( ( N = zero_zero_nat )
% 5.82/6.17 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.82/6.17 = one_one_complex ) )
% 5.82/6.17 & ( ( N != zero_zero_nat )
% 5.82/6.17 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.82/6.17 = zero_zero_complex ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0_left
% 5.82/6.17 thf(fact_7828_pochhammer__0__left,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( ( N = zero_zero_nat )
% 5.82/6.17 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.82/6.17 = one_one_real ) )
% 5.82/6.17 & ( ( N != zero_zero_nat )
% 5.82/6.17 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.82/6.17 = zero_zero_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0_left
% 5.82/6.17 thf(fact_7829_pochhammer__0__left,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( ( N = zero_zero_nat )
% 5.82/6.17 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.82/6.17 = one_one_rat ) )
% 5.82/6.17 & ( ( N != zero_zero_nat )
% 5.82/6.17 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.82/6.17 = zero_zero_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0_left
% 5.82/6.17 thf(fact_7830_pochhammer__0__left,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( ( N = zero_zero_nat )
% 5.82/6.17 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.82/6.17 = one_one_nat ) )
% 5.82/6.17 & ( ( N != zero_zero_nat )
% 5.82/6.17 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.82/6.17 = zero_zero_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0_left
% 5.82/6.17 thf(fact_7831_pochhammer__0__left,axiom,
% 5.82/6.17 ! [N: nat] :
% 5.82/6.17 ( ( ( N = zero_zero_nat )
% 5.82/6.17 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.82/6.17 = one_one_int ) )
% 5.82/6.17 & ( ( N != zero_zero_nat )
% 5.82/6.17 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.82/6.17 = zero_zero_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_0_left
% 5.82/6.17 thf(fact_7832_powser__sums__zero,axiom,
% 5.82/6.17 ! [A2: nat > complex] :
% 5.82/6.17 ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ ( A2 @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 5.82/6.17 @ ( A2 @ zero_zero_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_zero
% 5.82/6.17 thf(fact_7833_powser__sums__zero,axiom,
% 5.82/6.17 ! [A2: nat > real] :
% 5.82/6.17 ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ ( A2 @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 5.82/6.17 @ ( A2 @ zero_zero_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_zero
% 5.82/6.17 thf(fact_7834_pochhammer__rec,axiom,
% 5.82/6.17 ! [A2: real,N: nat] :
% 5.82/6.17 ( ( comm_s7457072308508201937r_real @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_real @ A2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A2 @ one_one_real ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec
% 5.82/6.17 thf(fact_7835_pochhammer__rec,axiom,
% 5.82/6.17 ! [A2: rat,N: nat] :
% 5.82/6.17 ( ( comm_s4028243227959126397er_rat @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_rat @ A2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec
% 5.82/6.17 thf(fact_7836_pochhammer__rec,axiom,
% 5.82/6.17 ! [A2: nat,N: nat] :
% 5.82/6.17 ( ( comm_s4663373288045622133er_nat @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_nat @ A2 @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec
% 5.82/6.17 thf(fact_7837_pochhammer__rec,axiom,
% 5.82/6.17 ! [A2: int,N: nat] :
% 5.82/6.17 ( ( comm_s4660882817536571857er_int @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_int @ A2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A2 @ one_one_int ) @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec
% 5.82/6.17 thf(fact_7838_pochhammer__Suc,axiom,
% 5.82/6.17 ! [A2: rat,N: nat] :
% 5.82/6.17 ( ( comm_s4028243227959126397er_rat @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A2 @ N ) @ ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_Suc
% 5.82/6.17 thf(fact_7839_pochhammer__Suc,axiom,
% 5.82/6.17 ! [A2: real,N: nat] :
% 5.82/6.17 ( ( comm_s7457072308508201937r_real @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A2 @ N ) @ ( plus_plus_real @ A2 @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_Suc
% 5.82/6.17 thf(fact_7840_pochhammer__Suc,axiom,
% 5.82/6.17 ! [A2: int,N: nat] :
% 5.82/6.17 ( ( comm_s4660882817536571857er_int @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A2 @ N ) @ ( plus_plus_int @ A2 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_Suc
% 5.82/6.17 thf(fact_7841_pochhammer__Suc,axiom,
% 5.82/6.17 ! [A2: nat,N: nat] :
% 5.82/6.17 ( ( comm_s4663373288045622133er_nat @ A2 @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A2 @ N ) @ ( plus_plus_nat @ A2 @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_Suc
% 5.82/6.17 thf(fact_7842_pochhammer__rec_H,axiom,
% 5.82/6.17 ! [Z: rat,N: nat] :
% 5.82/6.17 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec'
% 5.82/6.17 thf(fact_7843_pochhammer__rec_H,axiom,
% 5.82/6.17 ! [Z: real,N: nat] :
% 5.82/6.17 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec'
% 5.82/6.17 thf(fact_7844_pochhammer__rec_H,axiom,
% 5.82/6.17 ! [Z: int,N: nat] :
% 5.82/6.17 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec'
% 5.82/6.17 thf(fact_7845_pochhammer__rec_H,axiom,
% 5.82/6.17 ! [Z: nat,N: nat] :
% 5.82/6.17 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.82/6.17 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_rec'
% 5.82/6.17 thf(fact_7846_pochhammer__product_H,axiom,
% 5.82/6.17 ! [Z: rat,N: nat,M: nat] :
% 5.82/6.17 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.82/6.17 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product'
% 5.82/6.17 thf(fact_7847_pochhammer__product_H,axiom,
% 5.82/6.17 ! [Z: real,N: nat,M: nat] :
% 5.82/6.17 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.82/6.17 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product'
% 5.82/6.17 thf(fact_7848_pochhammer__product_H,axiom,
% 5.82/6.17 ! [Z: int,N: nat,M: nat] :
% 5.82/6.17 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.82/6.17 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product'
% 5.82/6.17 thf(fact_7849_pochhammer__product_H,axiom,
% 5.82/6.17 ! [Z: nat,N: nat,M: nat] :
% 5.82/6.17 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.82/6.17 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product'
% 5.82/6.17 thf(fact_7850_pochhammer__product,axiom,
% 5.82/6.17 ! [M: nat,N: nat,Z: rat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.17 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.82/6.17 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product
% 5.82/6.17 thf(fact_7851_pochhammer__product,axiom,
% 5.82/6.17 ! [M: nat,N: nat,Z: real] :
% 5.82/6.17 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.17 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.82/6.17 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product
% 5.82/6.17 thf(fact_7852_pochhammer__product,axiom,
% 5.82/6.17 ! [M: nat,N: nat,Z: int] :
% 5.82/6.17 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.17 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.82/6.17 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product
% 5.82/6.17 thf(fact_7853_pochhammer__product,axiom,
% 5.82/6.17 ! [M: nat,N: nat,Z: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.17 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.82/6.17 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_product
% 5.82/6.17 thf(fact_7854_VEBT__internal_Oheight_Ocases,axiom,
% 5.82/6.17 ! [X2: vEBT_VEBT] :
% 5.82/6.17 ( ! [A3: $o,B3: $o] :
% 5.82/6.17 ( X2
% 5.82/6.17 != ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.17 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.17 ( X2
% 5.82/6.17 != ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % VEBT_internal.height.cases
% 5.82/6.17 thf(fact_7855_sums__if_H,axiom,
% 5.82/6.17 ! [G: nat > real,X2: real] :
% 5.82/6.17 ( ( sums_real @ G @ X2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.17 @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_if'
% 5.82/6.17 thf(fact_7856_sums__if,axiom,
% 5.82/6.17 ! [G: nat > real,X2: real,F: nat > real,Y3: real] :
% 5.82/6.17 ( ( sums_real @ G @ X2 )
% 5.82/6.17 => ( ( sums_real @ F @ Y3 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( F @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.17 @ ( plus_plus_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_if
% 5.82/6.17 thf(fact_7857_geometric__sums,axiom,
% 5.82/6.17 ! [C2: real] :
% 5.82/6.17 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C2 ) @ one_one_real )
% 5.82/6.17 => ( sums_real @ ( power_power_real @ C2 ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_sums
% 5.82/6.17 thf(fact_7858_geometric__sums,axiom,
% 5.82/6.17 ! [C2: complex] :
% 5.82/6.17 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C2 ) @ one_one_real )
% 5.82/6.17 => ( sums_complex @ ( power_power_complex @ C2 ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % geometric_sums
% 5.82/6.17 thf(fact_7859_sums__group,axiom,
% 5.82/6.17 ! [F: nat > nat,S2: nat,K: nat] :
% 5.82/6.17 ( ( sums_nat @ F @ S2 )
% 5.82/6.17 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.17 => ( sums_nat
% 5.82/6.17 @ ^ [N4: nat] : ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ N4 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ N4 @ K ) @ K ) ) )
% 5.82/6.17 @ S2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_group
% 5.82/6.17 thf(fact_7860_sums__group,axiom,
% 5.82/6.17 ! [F: nat > real,S2: real,K: nat] :
% 5.82/6.17 ( ( sums_real @ F @ S2 )
% 5.82/6.17 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ N4 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ N4 @ K ) @ K ) ) )
% 5.82/6.17 @ S2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_group
% 5.82/6.17 thf(fact_7861_power__half__series,axiom,
% 5.82/6.17 ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 5.82/6.17 @ one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % power_half_series
% 5.82/6.17 thf(fact_7862_sums__zero,axiom,
% 5.82/6.17 ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : zero_zero_complex
% 5.82/6.17 @ zero_zero_complex ) ).
% 5.82/6.17
% 5.82/6.17 % sums_zero
% 5.82/6.17 thf(fact_7863_sums__zero,axiom,
% 5.82/6.17 ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : zero_zero_real
% 5.82/6.17 @ zero_zero_real ) ).
% 5.82/6.17
% 5.82/6.17 % sums_zero
% 5.82/6.17 thf(fact_7864_sums__zero,axiom,
% 5.82/6.17 ( sums_nat
% 5.82/6.17 @ ^ [N4: nat] : zero_zero_nat
% 5.82/6.17 @ zero_zero_nat ) ).
% 5.82/6.17
% 5.82/6.17 % sums_zero
% 5.82/6.17 thf(fact_7865_sums__zero,axiom,
% 5.82/6.17 ( sums_int
% 5.82/6.17 @ ^ [N4: nat] : zero_zero_int
% 5.82/6.17 @ zero_zero_int ) ).
% 5.82/6.17
% 5.82/6.17 % sums_zero
% 5.82/6.17 thf(fact_7866_sums__If__finite__set_H,axiom,
% 5.82/6.17 ! [G: nat > real,S: real,A: set_nat,S7: real,F: nat > real] :
% 5.82/6.17 ( ( sums_real @ G @ S )
% 5.82/6.17 => ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( S7
% 5.82/6.17 = ( plus_plus_real @ S
% 5.82/6.17 @ ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.17 @ A ) ) )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( if_real @ ( member_nat @ N4 @ A ) @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.17 @ S7 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite_set'
% 5.82/6.17 thf(fact_7867_UNIV__def,axiom,
% 5.82/6.17 ( top_top_set_int
% 5.82/6.17 = ( collect_int
% 5.82/6.17 @ ^ [X3: int] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7868_UNIV__def,axiom,
% 5.82/6.17 ( top_top_set_complex
% 5.82/6.17 = ( collect_complex
% 5.82/6.17 @ ^ [X3: complex] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7869_UNIV__def,axiom,
% 5.82/6.17 ( top_to4366644338036079209nt_int
% 5.82/6.17 = ( collec213857154873943460nt_int
% 5.82/6.17 @ ^ [X3: product_prod_int_int] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7870_UNIV__def,axiom,
% 5.82/6.17 ( top_to1996260823553986621t_unit
% 5.82/6.17 = ( collect_Product_unit
% 5.82/6.17 @ ^ [X3: product_unit] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7871_UNIV__def,axiom,
% 5.82/6.17 ( top_to3689904429138878997l_num1
% 5.82/6.17 = ( collect_Numeral_num1
% 5.82/6.17 @ ^ [X3: numeral_num1] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7872_UNIV__def,axiom,
% 5.82/6.17 ( top_top_set_real
% 5.82/6.17 = ( collect_real
% 5.82/6.17 @ ^ [X3: real] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7873_UNIV__def,axiom,
% 5.82/6.17 ( top_top_set_o
% 5.82/6.17 = ( collect_o
% 5.82/6.17 @ ^ [X3: $o] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7874_UNIV__def,axiom,
% 5.82/6.17 ( top_top_set_nat
% 5.82/6.17 = ( collect_nat
% 5.82/6.17 @ ^ [X3: nat] : $true ) ) ).
% 5.82/6.17
% 5.82/6.17 % UNIV_def
% 5.82/6.17 thf(fact_7875_sums__le,axiom,
% 5.82/6.17 ! [F: nat > real,G: nat > real,S2: real,T: real] :
% 5.82/6.17 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.82/6.17 => ( ( sums_real @ F @ S2 )
% 5.82/6.17 => ( ( sums_real @ G @ T )
% 5.82/6.17 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_le
% 5.82/6.17 thf(fact_7876_sums__le,axiom,
% 5.82/6.17 ! [F: nat > nat,G: nat > nat,S2: nat,T: nat] :
% 5.82/6.17 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.82/6.17 => ( ( sums_nat @ F @ S2 )
% 5.82/6.17 => ( ( sums_nat @ G @ T )
% 5.82/6.17 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_le
% 5.82/6.17 thf(fact_7877_sums__le,axiom,
% 5.82/6.17 ! [F: nat > int,G: nat > int,S2: int,T: int] :
% 5.82/6.17 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.82/6.17 => ( ( sums_int @ F @ S2 )
% 5.82/6.17 => ( ( sums_int @ G @ T )
% 5.82/6.17 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_le
% 5.82/6.17 thf(fact_7878_sums__single,axiom,
% 5.82/6.17 ! [I: nat,F: nat > complex] :
% 5.82/6.17 ( sums_complex
% 5.82/6.17 @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.82/6.17 @ ( F @ I ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_single
% 5.82/6.17 thf(fact_7879_sums__single,axiom,
% 5.82/6.17 ! [I: nat,F: nat > real] :
% 5.82/6.17 ( sums_real
% 5.82/6.17 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real )
% 5.82/6.17 @ ( F @ I ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_single
% 5.82/6.17 thf(fact_7880_sums__single,axiom,
% 5.82/6.17 ! [I: nat,F: nat > nat] :
% 5.82/6.17 ( sums_nat
% 5.82/6.17 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.82/6.17 @ ( F @ I ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_single
% 5.82/6.17 thf(fact_7881_sums__single,axiom,
% 5.82/6.17 ! [I: nat,F: nat > int] :
% 5.82/6.17 ( sums_int
% 5.82/6.17 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int )
% 5.82/6.17 @ ( F @ I ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_single
% 5.82/6.17 thf(fact_7882_sums__add,axiom,
% 5.82/6.17 ! [F: nat > real,A2: real,G: nat > real,B2: real] :
% 5.82/6.17 ( ( sums_real @ F @ A2 )
% 5.82/6.17 => ( ( sums_real @ G @ B2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( plus_plus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.17 @ ( plus_plus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_add
% 5.82/6.17 thf(fact_7883_sums__add,axiom,
% 5.82/6.17 ! [F: nat > nat,A2: nat,G: nat > nat,B2: nat] :
% 5.82/6.17 ( ( sums_nat @ F @ A2 )
% 5.82/6.17 => ( ( sums_nat @ G @ B2 )
% 5.82/6.17 => ( sums_nat
% 5.82/6.17 @ ^ [N4: nat] : ( plus_plus_nat @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.17 @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_add
% 5.82/6.17 thf(fact_7884_sums__add,axiom,
% 5.82/6.17 ! [F: nat > int,A2: int,G: nat > int,B2: int] :
% 5.82/6.17 ( ( sums_int @ F @ A2 )
% 5.82/6.17 => ( ( sums_int @ G @ B2 )
% 5.82/6.17 => ( sums_int
% 5.82/6.17 @ ^ [N4: nat] : ( plus_plus_int @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.17 @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_add
% 5.82/6.17 thf(fact_7885_sums__mult,axiom,
% 5.82/6.17 ! [F: nat > real,A2: real,C2: real] :
% 5.82/6.17 ( ( sums_real @ F @ A2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F @ N4 ) )
% 5.82/6.17 @ ( times_times_real @ C2 @ A2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult
% 5.82/6.17 thf(fact_7886_sums__mult2,axiom,
% 5.82/6.17 ! [F: nat > real,A2: real,C2: real] :
% 5.82/6.17 ( ( sums_real @ F @ A2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ C2 )
% 5.82/6.17 @ ( times_times_real @ A2 @ C2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult2
% 5.82/6.17 thf(fact_7887_sums__diff,axiom,
% 5.82/6.17 ! [F: nat > real,A2: real,G: nat > real,B2: real] :
% 5.82/6.17 ( ( sums_real @ F @ A2 )
% 5.82/6.17 => ( ( sums_real @ G @ B2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.17 @ ( minus_minus_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_diff
% 5.82/6.17 thf(fact_7888_sums__divide,axiom,
% 5.82/6.17 ! [F: nat > complex,A2: complex,C2: complex] :
% 5.82/6.17 ( ( sums_complex @ F @ A2 )
% 5.82/6.17 => ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ C2 )
% 5.82/6.17 @ ( divide1717551699836669952omplex @ A2 @ C2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_divide
% 5.82/6.17 thf(fact_7889_sums__divide,axiom,
% 5.82/6.17 ! [F: nat > real,A2: real,C2: real] :
% 5.82/6.17 ( ( sums_real @ F @ A2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C2 )
% 5.82/6.17 @ ( divide_divide_real @ A2 @ C2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_divide
% 5.82/6.17 thf(fact_7890_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > nat > real,X2: vEBT_VEBT > real] :
% 5.82/6.17 ( ! [I2: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.17 => ( sums_real @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups2240296850493347238T_real
% 5.82/6.17 @ ^ [I4: vEBT_VEBT] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups2240296850493347238T_real @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7891_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_real,F: real > nat > real,X2: real > real] :
% 5.82/6.17 ( ! [I2: real] :
% 5.82/6.17 ( ( member_real @ I2 @ I6 )
% 5.82/6.17 => ( sums_real @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups8097168146408367636l_real
% 5.82/6.17 @ ^ [I4: real] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups8097168146408367636l_real @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7892_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_int,F: int > nat > real,X2: int > real] :
% 5.82/6.17 ( ! [I2: int] :
% 5.82/6.17 ( ( member_int @ I2 @ I6 )
% 5.82/6.17 => ( sums_real @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups8778361861064173332t_real
% 5.82/6.17 @ ^ [I4: int] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups8778361861064173332t_real @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7893_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_nat,F: nat > nat > nat,X2: nat > nat] :
% 5.82/6.17 ( ! [I2: nat] :
% 5.82/6.17 ( ( member_nat @ I2 @ I6 )
% 5.82/6.17 => ( sums_nat @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_nat
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups3542108847815614940at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups3542108847815614940at_nat @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7894_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_complex,F: complex > nat > complex,X2: complex > complex] :
% 5.82/6.17 ( ! [I2: complex] :
% 5.82/6.17 ( ( member_complex @ I2 @ I6 )
% 5.82/6.17 => ( sums_complex @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups7754918857620584856omplex
% 5.82/6.17 @ ^ [I4: complex] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups7754918857620584856omplex @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7895_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_nat,F: nat > nat > real,X2: nat > real] :
% 5.82/6.17 ( ! [I2: nat] :
% 5.82/6.17 ( ( member_nat @ I2 @ I6 )
% 5.82/6.17 => ( sums_real @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [I4: nat] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups6591440286371151544t_real @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7896_sums__sum,axiom,
% 5.82/6.17 ! [I6: set_int,F: int > nat > int,X2: int > int] :
% 5.82/6.17 ( ! [I2: int] :
% 5.82/6.17 ( ( member_int @ I2 @ I6 )
% 5.82/6.17 => ( sums_int @ ( F @ I2 ) @ ( X2 @ I2 ) ) )
% 5.82/6.17 => ( sums_int
% 5.82/6.17 @ ^ [N4: nat] :
% 5.82/6.17 ( groups4538972089207619220nt_int
% 5.82/6.17 @ ^ [I4: int] : ( F @ I4 @ N4 )
% 5.82/6.17 @ I6 )
% 5.82/6.17 @ ( groups4538972089207619220nt_int @ X2 @ I6 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_sum
% 5.82/6.17 thf(fact_7897_sums__mult__iff,axiom,
% 5.82/6.17 ! [C2: complex,F: nat > complex,D2: complex] :
% 5.82/6.17 ( ( C2 != zero_zero_complex )
% 5.82/6.17 => ( ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F @ N4 ) )
% 5.82/6.17 @ ( times_times_complex @ C2 @ D2 ) )
% 5.82/6.17 = ( sums_complex @ F @ D2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult_iff
% 5.82/6.17 thf(fact_7898_sums__mult__iff,axiom,
% 5.82/6.17 ! [C2: real,F: nat > real,D2: real] :
% 5.82/6.17 ( ( C2 != zero_zero_real )
% 5.82/6.17 => ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F @ N4 ) )
% 5.82/6.17 @ ( times_times_real @ C2 @ D2 ) )
% 5.82/6.17 = ( sums_real @ F @ D2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult_iff
% 5.82/6.17 thf(fact_7899_sums__mult2__iff,axiom,
% 5.82/6.17 ! [C2: complex,F: nat > complex,D2: complex] :
% 5.82/6.17 ( ( C2 != zero_zero_complex )
% 5.82/6.17 => ( ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ C2 )
% 5.82/6.17 @ ( times_times_complex @ D2 @ C2 ) )
% 5.82/6.17 = ( sums_complex @ F @ D2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult2_iff
% 5.82/6.17 thf(fact_7900_sums__mult2__iff,axiom,
% 5.82/6.17 ! [C2: real,F: nat > real,D2: real] :
% 5.82/6.17 ( ( C2 != zero_zero_real )
% 5.82/6.17 => ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ C2 )
% 5.82/6.17 @ ( times_times_real @ D2 @ C2 ) )
% 5.82/6.17 = ( sums_real @ F @ D2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult2_iff
% 5.82/6.17 thf(fact_7901_sums__mult__D,axiom,
% 5.82/6.17 ! [C2: complex,F: nat > complex,A2: complex] :
% 5.82/6.17 ( ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F @ N4 ) )
% 5.82/6.17 @ A2 )
% 5.82/6.17 => ( ( C2 != zero_zero_complex )
% 5.82/6.17 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A2 @ C2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult_D
% 5.82/6.17 thf(fact_7902_sums__mult__D,axiom,
% 5.82/6.17 ! [C2: real,F: nat > real,A2: real] :
% 5.82/6.17 ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F @ N4 ) )
% 5.82/6.17 @ A2 )
% 5.82/6.17 => ( ( C2 != zero_zero_real )
% 5.82/6.17 => ( sums_real @ F @ ( divide_divide_real @ A2 @ C2 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_mult_D
% 5.82/6.17 thf(fact_7903_sums__Suc__imp,axiom,
% 5.82/6.17 ! [F: nat > complex,S2: complex] :
% 5.82/6.17 ( ( ( F @ zero_zero_nat )
% 5.82/6.17 = zero_zero_complex )
% 5.82/6.17 => ( ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.82/6.17 @ S2 )
% 5.82/6.17 => ( sums_complex @ F @ S2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_Suc_imp
% 5.82/6.17 thf(fact_7904_sums__Suc__imp,axiom,
% 5.82/6.17 ! [F: nat > real,S2: real] :
% 5.82/6.17 ( ( ( F @ zero_zero_nat )
% 5.82/6.17 = zero_zero_real )
% 5.82/6.17 => ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.82/6.17 @ S2 )
% 5.82/6.17 => ( sums_real @ F @ S2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_Suc_imp
% 5.82/6.17 thf(fact_7905_sums__Suc__iff,axiom,
% 5.82/6.17 ! [F: nat > real,S2: real] :
% 5.82/6.17 ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.82/6.17 @ S2 )
% 5.82/6.17 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_Suc_iff
% 5.82/6.17 thf(fact_7906_sums__Suc,axiom,
% 5.82/6.17 ! [F: nat > real,L: real] :
% 5.82/6.17 ( ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.82/6.17 @ L )
% 5.82/6.17 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_Suc
% 5.82/6.17 thf(fact_7907_sums__Suc,axiom,
% 5.82/6.17 ! [F: nat > nat,L: nat] :
% 5.82/6.17 ( ( sums_nat
% 5.82/6.17 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.82/6.17 @ L )
% 5.82/6.17 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_Suc
% 5.82/6.17 thf(fact_7908_sums__Suc,axiom,
% 5.82/6.17 ! [F: nat > int,L: int] :
% 5.82/6.17 ( ( sums_int
% 5.82/6.17 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.82/6.17 @ L )
% 5.82/6.17 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_Suc
% 5.82/6.17 thf(fact_7909_sums__zero__iff__shift,axiom,
% 5.82/6.17 ! [N: nat,F: nat > complex,S2: complex] :
% 5.82/6.17 ( ! [I2: nat] :
% 5.82/6.17 ( ( ord_less_nat @ I2 @ N )
% 5.82/6.17 => ( ( F @ I2 )
% 5.82/6.17 = zero_zero_complex ) )
% 5.82/6.17 => ( ( sums_complex
% 5.82/6.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.82/6.17 @ S2 )
% 5.82/6.17 = ( sums_complex @ F @ S2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_zero_iff_shift
% 5.82/6.17 thf(fact_7910_sums__zero__iff__shift,axiom,
% 5.82/6.17 ! [N: nat,F: nat > real,S2: real] :
% 5.82/6.17 ( ! [I2: nat] :
% 5.82/6.17 ( ( ord_less_nat @ I2 @ N )
% 5.82/6.17 => ( ( F @ I2 )
% 5.82/6.17 = zero_zero_real ) )
% 5.82/6.17 => ( ( sums_real
% 5.82/6.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.82/6.17 @ S2 )
% 5.82/6.17 = ( sums_real @ F @ S2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_zero_iff_shift
% 5.82/6.17 thf(fact_7911_sums__finite,axiom,
% 5.82/6.17 ! [N7: set_nat,F: nat > complex] :
% 5.82/6.17 ( ( finite_finite_nat @ N7 )
% 5.82/6.17 => ( ! [N3: nat] :
% 5.82/6.17 ( ~ ( member_nat @ N3 @ N7 )
% 5.82/6.17 => ( ( F @ N3 )
% 5.82/6.17 = zero_zero_complex ) )
% 5.82/6.17 => ( sums_complex @ F @ ( groups2073611262835488442omplex @ F @ N7 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_finite
% 5.82/6.17 thf(fact_7912_sums__finite,axiom,
% 5.82/6.17 ! [N7: set_nat,F: nat > int] :
% 5.82/6.17 ( ( finite_finite_nat @ N7 )
% 5.82/6.17 => ( ! [N3: nat] :
% 5.82/6.17 ( ~ ( member_nat @ N3 @ N7 )
% 5.82/6.17 => ( ( F @ N3 )
% 5.82/6.17 = zero_zero_int ) )
% 5.82/6.17 => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N7 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_finite
% 5.82/6.17 thf(fact_7913_sums__finite,axiom,
% 5.82/6.17 ! [N7: set_nat,F: nat > nat] :
% 5.82/6.17 ( ( finite_finite_nat @ N7 )
% 5.82/6.17 => ( ! [N3: nat] :
% 5.82/6.17 ( ~ ( member_nat @ N3 @ N7 )
% 5.82/6.17 => ( ( F @ N3 )
% 5.82/6.17 = zero_zero_nat ) )
% 5.82/6.17 => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N7 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_finite
% 5.82/6.17 thf(fact_7914_sums__finite,axiom,
% 5.82/6.17 ! [N7: set_nat,F: nat > real] :
% 5.82/6.17 ( ( finite_finite_nat @ N7 )
% 5.82/6.17 => ( ! [N3: nat] :
% 5.82/6.17 ( ~ ( member_nat @ N3 @ N7 )
% 5.82/6.17 => ( ( F @ N3 )
% 5.82/6.17 = zero_zero_real ) )
% 5.82/6.17 => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N7 ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_finite
% 5.82/6.17 thf(fact_7915_sums__If__finite,axiom,
% 5.82/6.17 ! [P: nat > $o,F: nat > complex] :
% 5.82/6.17 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.17 => ( sums_complex
% 5.82/6.17 @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.82/6.17 @ ( groups2073611262835488442omplex @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite
% 5.82/6.17 thf(fact_7916_sums__If__finite,axiom,
% 5.82/6.17 ! [P: nat > $o,F: nat > int] :
% 5.82/6.17 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.17 => ( sums_int
% 5.82/6.17 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.82/6.17 @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite
% 5.82/6.17 thf(fact_7917_sums__If__finite,axiom,
% 5.82/6.17 ! [P: nat > $o,F: nat > nat] :
% 5.82/6.17 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.17 => ( sums_nat
% 5.82/6.17 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.82/6.17 @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite
% 5.82/6.17 thf(fact_7918_sums__If__finite,axiom,
% 5.82/6.17 ! [P: nat > $o,F: nat > real] :
% 5.82/6.17 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.82/6.17 @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite
% 5.82/6.17 thf(fact_7919_sums__If__finite__set,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > complex] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( sums_complex
% 5.82/6.17 @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.82/6.17 @ ( groups2073611262835488442omplex @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite_set
% 5.82/6.17 thf(fact_7920_sums__If__finite__set,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > int] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( sums_int
% 5.82/6.17 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A ) @ ( F @ R5 ) @ zero_zero_int )
% 5.82/6.17 @ ( groups3539618377306564664at_int @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite_set
% 5.82/6.17 thf(fact_7921_sums__If__finite__set,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( sums_nat
% 5.82/6.17 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.82/6.17 @ ( groups3542108847815614940at_nat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite_set
% 5.82/6.17 thf(fact_7922_sums__If__finite__set,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > real] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A ) @ ( F @ R5 ) @ zero_zero_real )
% 5.82/6.17 @ ( groups6591440286371151544t_real @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_If_finite_set
% 5.82/6.17 thf(fact_7923_powser__sums__if,axiom,
% 5.82/6.17 ! [M: nat,Z: complex] :
% 5.82/6.17 ( sums_complex
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_complex @ ( if_complex @ ( N4 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N4 ) )
% 5.82/6.17 @ ( power_power_complex @ Z @ M ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_if
% 5.82/6.17 thf(fact_7924_powser__sums__if,axiom,
% 5.82/6.17 ! [M: nat,Z: real] :
% 5.82/6.17 ( sums_real
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_real @ ( if_real @ ( N4 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N4 ) )
% 5.82/6.17 @ ( power_power_real @ Z @ M ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_if
% 5.82/6.17 thf(fact_7925_powser__sums__if,axiom,
% 5.82/6.17 ! [M: nat,Z: int] :
% 5.82/6.17 ( sums_int
% 5.82/6.17 @ ^ [N4: nat] : ( times_times_int @ ( if_int @ ( N4 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N4 ) )
% 5.82/6.17 @ ( power_power_int @ Z @ M ) ) ).
% 5.82/6.17
% 5.82/6.17 % powser_sums_if
% 5.82/6.17 thf(fact_7926_sums__iff__shift,axiom,
% 5.82/6.17 ! [F: nat > real,N: nat,S2: real] :
% 5.82/6.17 ( ( sums_real
% 5.82/6.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.82/6.17 @ S2 )
% 5.82/6.17 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_iff_shift
% 5.82/6.17 thf(fact_7927_sums__split__initial__segment,axiom,
% 5.82/6.17 ! [F: nat > real,S2: real,N: nat] :
% 5.82/6.17 ( ( sums_real @ F @ S2 )
% 5.82/6.17 => ( sums_real
% 5.82/6.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.82/6.17 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_split_initial_segment
% 5.82/6.17 thf(fact_7928_sums__iff__shift_H,axiom,
% 5.82/6.17 ! [F: nat > real,N: nat,S2: real] :
% 5.82/6.17 ( ( sums_real
% 5.82/6.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.82/6.17 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.82/6.17 = ( sums_real @ F @ S2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % sums_iff_shift'
% 5.82/6.17 thf(fact_7929_pochhammer__times__pochhammer__half,axiom,
% 5.82/6.17 ! [Z: complex,N: nat] :
% 5.82/6.17 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups6464643781859351333omplex
% 5.82/6.17 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_times_pochhammer_half
% 5.82/6.17 thf(fact_7930_pochhammer__times__pochhammer__half,axiom,
% 5.82/6.17 ! [Z: rat,N: nat] :
% 5.82/6.17 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups73079841787564623at_rat
% 5.82/6.17 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_times_pochhammer_half
% 5.82/6.17 thf(fact_7931_pochhammer__times__pochhammer__half,axiom,
% 5.82/6.17 ! [Z: real,N: nat] :
% 5.82/6.17 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_times_pochhammer_half
% 5.82/6.17 thf(fact_7932_pochhammer__code,axiom,
% 5.82/6.17 ( comm_s4028243227959126397er_rat
% 5.82/6.17 = ( ^ [A5: rat,N4: nat] :
% 5.82/6.17 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 5.82/6.17 @ ( set_fo1949268297981939178at_rat
% 5.82/6.17 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.82/6.17 @ zero_zero_nat
% 5.82/6.17 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.82/6.17 @ one_one_rat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_code
% 5.82/6.17 thf(fact_7933_pochhammer__code,axiom,
% 5.82/6.17 ( comm_s7457072308508201937r_real
% 5.82/6.17 = ( ^ [A5: real,N4: nat] :
% 5.82/6.17 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 5.82/6.17 @ ( set_fo3111899725591712190t_real
% 5.82/6.17 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.82/6.17 @ zero_zero_nat
% 5.82/6.17 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.82/6.17 @ one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_code
% 5.82/6.17 thf(fact_7934_pochhammer__code,axiom,
% 5.82/6.17 ( comm_s4660882817536571857er_int
% 5.82/6.17 = ( ^ [A5: int,N4: nat] :
% 5.82/6.17 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 5.82/6.17 @ ( set_fo2581907887559384638at_int
% 5.82/6.17 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.82/6.17 @ zero_zero_nat
% 5.82/6.17 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.82/6.17 @ one_one_int ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_code
% 5.82/6.17 thf(fact_7935_pochhammer__code,axiom,
% 5.82/6.17 ( comm_s4663373288045622133er_nat
% 5.82/6.17 = ( ^ [A5: nat,N4: nat] :
% 5.82/6.17 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 5.82/6.17 @ ( set_fo2584398358068434914at_nat
% 5.82/6.17 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.82/6.17 @ zero_zero_nat
% 5.82/6.17 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.82/6.17 @ one_one_nat ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % pochhammer_code
% 5.82/6.17 thf(fact_7936_of__nat__code,axiom,
% 5.82/6.17 ( semiri8010041392384452111omplex
% 5.82/6.17 = ( ^ [N4: nat] :
% 5.82/6.17 ( semiri2816024913162550771omplex
% 5.82/6.17 @ ^ [I4: complex] : ( plus_plus_complex @ I4 @ one_one_complex )
% 5.82/6.17 @ N4
% 5.82/6.17 @ zero_zero_complex ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_code
% 5.82/6.17 thf(fact_7937_of__nat__code,axiom,
% 5.82/6.17 ( semiri681578069525770553at_rat
% 5.82/6.17 = ( ^ [N4: nat] :
% 5.82/6.17 ( semiri7787848453975740701ux_rat
% 5.82/6.17 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.82/6.17 @ N4
% 5.82/6.17 @ zero_zero_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_code
% 5.82/6.17 thf(fact_7938_of__nat__code,axiom,
% 5.82/6.17 ( semiri5074537144036343181t_real
% 5.82/6.17 = ( ^ [N4: nat] :
% 5.82/6.17 ( semiri7260567687927622513x_real
% 5.82/6.17 @ ^ [I4: real] : ( plus_plus_real @ I4 @ one_one_real )
% 5.82/6.17 @ N4
% 5.82/6.17 @ zero_zero_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_code
% 5.82/6.17 thf(fact_7939_of__nat__code,axiom,
% 5.82/6.17 ( semiri1314217659103216013at_int
% 5.82/6.17 = ( ^ [N4: nat] :
% 5.82/6.17 ( semiri8420488043553186161ux_int
% 5.82/6.17 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.82/6.17 @ N4
% 5.82/6.17 @ zero_zero_int ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_code
% 5.82/6.17 thf(fact_7940_of__nat__code,axiom,
% 5.82/6.17 ( semiri1316708129612266289at_nat
% 5.82/6.17 = ( ^ [N4: nat] :
% 5.82/6.17 ( semiri8422978514062236437ux_nat
% 5.82/6.17 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.82/6.17 @ N4
% 5.82/6.17 @ zero_zero_nat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_code
% 5.82/6.17 thf(fact_7941_floor__log__nat__eq__powr__iff,axiom,
% 5.82/6.17 ! [B2: nat,K: nat,N: nat] :
% 5.82/6.17 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.17 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.17 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.82/6.17 = ( semiri1314217659103216013at_int @ N ) )
% 5.82/6.17 = ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.82/6.17 & ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_log_nat_eq_powr_iff
% 5.82/6.17 thf(fact_7942_gchoose__row__sum__weighted,axiom,
% 5.82/6.17 ! [R2: complex,M: nat] :
% 5.82/6.17 ( ( groups2073611262835488442omplex
% 5.82/6.17 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.82/6.17 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % gchoose_row_sum_weighted
% 5.82/6.17 thf(fact_7943_gchoose__row__sum__weighted,axiom,
% 5.82/6.17 ! [R2: rat,M: nat] :
% 5.82/6.17 ( ( groups2906978787729119204at_rat
% 5.82/6.17 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.82/6.17 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % gchoose_row_sum_weighted
% 5.82/6.17 thf(fact_7944_gchoose__row__sum__weighted,axiom,
% 5.82/6.17 ! [R2: real,M: nat] :
% 5.82/6.17 ( ( groups6591440286371151544t_real
% 5.82/6.17 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.82/6.17 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % gchoose_row_sum_weighted
% 5.82/6.17 thf(fact_7945_prod_Oneutral__const,axiom,
% 5.82/6.17 ! [A: set_nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [Uu3: nat] : one_one_int
% 5.82/6.17 @ A )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % prod.neutral_const
% 5.82/6.17 thf(fact_7946_prod_Oneutral__const,axiom,
% 5.82/6.17 ! [A: set_int] :
% 5.82/6.17 ( ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [Uu3: int] : one_one_int
% 5.82/6.17 @ A )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % prod.neutral_const
% 5.82/6.17 thf(fact_7947_prod_Oneutral__const,axiom,
% 5.82/6.17 ! [A: set_nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [Uu3: nat] : one_one_nat
% 5.82/6.17 @ A )
% 5.82/6.17 = one_one_nat ) ).
% 5.82/6.17
% 5.82/6.17 % prod.neutral_const
% 5.82/6.17 thf(fact_7948_of__nat__prod,axiom,
% 5.82/6.17 ! [F: int > nat,A: set_int] :
% 5.82/6.17 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A ) )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_prod
% 5.82/6.17 thf(fact_7949_of__nat__prod,axiom,
% 5.82/6.17 ! [F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A ) )
% 5.82/6.17 = ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [X3: nat] : ( semiri5074537144036343181t_real @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_prod
% 5.82/6.17 thf(fact_7950_of__nat__prod,axiom,
% 5.82/6.17 ! [F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_prod
% 5.82/6.17 thf(fact_7951_of__nat__prod,axiom,
% 5.82/6.17 ! [F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A ) )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [X3: nat] : ( semiri1316708129612266289at_nat @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_nat_prod
% 5.82/6.17 thf(fact_7952_of__int__prod,axiom,
% 5.82/6.17 ! [F: nat > int,A: set_nat] :
% 5.82/6.17 ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A ) )
% 5.82/6.17 = ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [X3: nat] : ( ring_1_of_int_real @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_prod
% 5.82/6.17 thf(fact_7953_of__int__prod,axiom,
% 5.82/6.17 ! [F: nat > int,A: set_nat] :
% 5.82/6.17 ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A ) )
% 5.82/6.17 = ( groups73079841787564623at_rat
% 5.82/6.17 @ ^ [X3: nat] : ( ring_1_of_int_rat @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_prod
% 5.82/6.17 thf(fact_7954_of__int__prod,axiom,
% 5.82/6.17 ! [F: nat > int,A: set_nat] :
% 5.82/6.17 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [X3: nat] : ( ring_1_of_int_int @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_prod
% 5.82/6.17 thf(fact_7955_of__int__prod,axiom,
% 5.82/6.17 ! [F: int > int,A: set_int] :
% 5.82/6.17 ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A ) )
% 5.82/6.17 = ( groups2316167850115554303t_real
% 5.82/6.17 @ ^ [X3: int] : ( ring_1_of_int_real @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_prod
% 5.82/6.17 thf(fact_7956_of__int__prod,axiom,
% 5.82/6.17 ! [F: int > int,A: set_int] :
% 5.82/6.17 ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A ) )
% 5.82/6.17 = ( groups1072433553688619179nt_rat
% 5.82/6.17 @ ^ [X3: int] : ( ring_1_of_int_rat @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_prod
% 5.82/6.17 thf(fact_7957_of__int__prod,axiom,
% 5.82/6.17 ! [F: int > int,A: set_int] :
% 5.82/6.17 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A ) )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [X3: int] : ( ring_1_of_int_int @ ( F @ X3 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_prod
% 5.82/6.17 thf(fact_7958_prod_Oempty,axiom,
% 5.82/6.17 ! [G: nat > assn] :
% 5.82/6.17 ( ( groups6906906614972039071t_assn @ G @ bot_bot_set_nat )
% 5.82/6.17 = one_one_assn ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7959_prod_Oempty,axiom,
% 5.82/6.17 ! [G: nat > real] :
% 5.82/6.17 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7960_prod_Oempty,axiom,
% 5.82/6.17 ! [G: nat > rat] :
% 5.82/6.17 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.82/6.17 = one_one_rat ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7961_prod_Oempty,axiom,
% 5.82/6.17 ! [G: int > assn] :
% 5.82/6.17 ( ( groups7882442080178216443t_assn @ G @ bot_bot_set_int )
% 5.82/6.17 = one_one_assn ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7962_prod_Oempty,axiom,
% 5.82/6.17 ! [G: int > real] :
% 5.82/6.17 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7963_prod_Oempty,axiom,
% 5.82/6.17 ! [G: int > rat] :
% 5.82/6.17 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.82/6.17 = one_one_rat ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7964_prod_Oempty,axiom,
% 5.82/6.17 ! [G: int > nat] :
% 5.82/6.17 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.82/6.17 = one_one_nat ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7965_prod_Oempty,axiom,
% 5.82/6.17 ! [G: nat > int] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ G @ bot_bot_set_nat )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7966_prod_Oempty,axiom,
% 5.82/6.17 ! [G: int > int] :
% 5.82/6.17 ( ( groups1705073143266064639nt_int @ G @ bot_bot_set_int )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7967_prod_Oempty,axiom,
% 5.82/6.17 ! [G: nat > nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ G @ bot_bot_set_nat )
% 5.82/6.17 = one_one_nat ) ).
% 5.82/6.17
% 5.82/6.17 % prod.empty
% 5.82/6.17 thf(fact_7968_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > assn] :
% 5.82/6.17 ( ~ ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn @ G @ A )
% 5.82/6.17 = one_one_assn ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7969_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_int,G: int > assn] :
% 5.82/6.17 ( ~ ( finite_finite_int @ A )
% 5.82/6.17 => ( ( groups7882442080178216443t_assn @ G @ A )
% 5.82/6.17 = one_one_assn ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7970_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_Code_integer,G: code_integer > assn] :
% 5.82/6.17 ( ~ ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( groups1304777262505850412r_assn @ G @ A )
% 5.82/6.17 = one_one_assn ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7971_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_complex,G: complex > assn] :
% 5.82/6.17 ( ~ ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( groups4150731942483176573x_assn @ G @ A )
% 5.82/6.17 = one_one_assn ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7972_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > real] :
% 5.82/6.17 ( ~ ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G @ A )
% 5.82/6.17 = one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7973_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_int,G: int > real] :
% 5.82/6.17 ( ~ ( finite_finite_int @ A )
% 5.82/6.17 => ( ( groups2316167850115554303t_real @ G @ A )
% 5.82/6.17 = one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7974_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_Code_integer,G: code_integer > real] :
% 5.82/6.17 ( ~ ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( groups9004974159866482096r_real @ G @ A )
% 5.82/6.17 = one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7975_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_complex,G: complex > real] :
% 5.82/6.17 ( ~ ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( groups766887009212190081x_real @ G @ A )
% 5.82/6.17 = one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7976_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > rat] :
% 5.82/6.17 ( ~ ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( groups73079841787564623at_rat @ G @ A )
% 5.82/6.17 = one_one_rat ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7977_prod_Oinfinite,axiom,
% 5.82/6.17 ! [A: set_int,G: int > rat] :
% 5.82/6.17 ( ~ ( finite_finite_int @ A )
% 5.82/6.17 => ( ( groups1072433553688619179nt_rat @ G @ A )
% 5.82/6.17 = one_one_rat ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.infinite
% 5.82/6.17 thf(fact_7978_floor__numeral,axiom,
% 5.82/6.17 ! [V: num] :
% 5.82/6.17 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.82/6.17 = ( numeral_numeral_int @ V ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_numeral
% 5.82/6.17 thf(fact_7979_floor__numeral,axiom,
% 5.82/6.17 ! [V: num] :
% 5.82/6.17 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.82/6.17 = ( numeral_numeral_int @ V ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_numeral
% 5.82/6.17 thf(fact_7980_gbinomial__0_I2_J,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.82/6.17 = zero_zero_complex ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(2)
% 5.82/6.17 thf(fact_7981_gbinomial__0_I2_J,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.82/6.17 = zero_zero_real ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(2)
% 5.82/6.17 thf(fact_7982_gbinomial__0_I2_J,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.82/6.17 = zero_zero_rat ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(2)
% 5.82/6.17 thf(fact_7983_gbinomial__0_I2_J,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.82/6.17 = zero_zero_nat ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(2)
% 5.82/6.17 thf(fact_7984_gbinomial__0_I2_J,axiom,
% 5.82/6.17 ! [K: nat] :
% 5.82/6.17 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.82/6.17 = zero_zero_int ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(2)
% 5.82/6.17 thf(fact_7985_gbinomial__0_I1_J,axiom,
% 5.82/6.17 ! [A2: real] :
% 5.82/6.17 ( ( gbinomial_real @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_real ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(1)
% 5.82/6.17 thf(fact_7986_gbinomial__0_I1_J,axiom,
% 5.82/6.17 ! [A2: rat] :
% 5.82/6.17 ( ( gbinomial_rat @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_rat ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(1)
% 5.82/6.17 thf(fact_7987_gbinomial__0_I1_J,axiom,
% 5.82/6.17 ! [A2: nat] :
% 5.82/6.17 ( ( gbinomial_nat @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_nat ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(1)
% 5.82/6.17 thf(fact_7988_gbinomial__0_I1_J,axiom,
% 5.82/6.17 ! [A2: int] :
% 5.82/6.17 ( ( gbinomial_int @ A2 @ zero_zero_nat )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % gbinomial_0(1)
% 5.82/6.17 thf(fact_7989_floor__one,axiom,
% 5.82/6.17 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % floor_one
% 5.82/6.17 thf(fact_7990_floor__one,axiom,
% 5.82/6.17 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.82/6.17 = one_one_int ) ).
% 5.82/6.17
% 5.82/6.17 % floor_one
% 5.82/6.17 thf(fact_7991_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > assn] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.17 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups569574905686396791T_assn
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups569574905686396791T_assn
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7992_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_real,A2: real,B2: real > assn] :
% 5.82/6.17 ( ( finite_finite_real @ S )
% 5.82/6.17 => ( ( ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1155561341820557179l_assn
% 5.82/6.17 @ ^ [K3: real] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1155561341820557179l_assn
% 5.82/6.17 @ ^ [K3: real] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7993_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_nat,A2: nat,B2: nat > assn] :
% 5.82/6.17 ( ( finite_finite_nat @ S )
% 5.82/6.17 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn
% 5.82/6.17 @ ^ [K3: nat] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn
% 5.82/6.17 @ ^ [K3: nat] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7994_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_int,A2: int,B2: int > assn] :
% 5.82/6.17 ( ( finite_finite_int @ S )
% 5.82/6.17 => ( ( ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups7882442080178216443t_assn
% 5.82/6.17 @ ^ [K3: int] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups7882442080178216443t_assn
% 5.82/6.17 @ ^ [K3: int] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7995_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > assn] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.17 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.17 => ( ( groups1304777262505850412r_assn
% 5.82/6.17 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.17 => ( ( groups1304777262505850412r_assn
% 5.82/6.17 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7996_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_complex,A2: complex,B2: complex > assn] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.17 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.17 => ( ( groups4150731942483176573x_assn
% 5.82/6.17 @ ^ [K3: complex] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.17 => ( ( groups4150731942483176573x_assn
% 5.82/6.17 @ ^ [K3: complex] : ( if_assn @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7997_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > real] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.17 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups2703838992350267259T_real
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups2703838992350267259T_real
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7998_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_real,A2: real,B2: real > real] :
% 5.82/6.17 ( ( finite_finite_real @ S )
% 5.82/6.17 => ( ( ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1681761925125756287l_real
% 5.82/6.17 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1681761925125756287l_real
% 5.82/6.17 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_7999_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_nat,A2: nat,B2: nat > real] :
% 5.82/6.17 ( ( finite_finite_nat @ S )
% 5.82/6.17 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [K3: nat] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [K3: nat] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_8000_prod_Odelta,axiom,
% 5.82/6.17 ! [S: set_int,A2: int,B2: int > real] :
% 5.82/6.17 ( ( finite_finite_int @ S )
% 5.82/6.17 => ( ( ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups2316167850115554303t_real
% 5.82/6.17 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups2316167850115554303t_real
% 5.82/6.17 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta
% 5.82/6.17 thf(fact_8001_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > assn] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.17 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups569574905686396791T_assn
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups569574905686396791T_assn
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8002_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_real,A2: real,B2: real > assn] :
% 5.82/6.17 ( ( finite_finite_real @ S )
% 5.82/6.17 => ( ( ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1155561341820557179l_assn
% 5.82/6.17 @ ^ [K3: real] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1155561341820557179l_assn
% 5.82/6.17 @ ^ [K3: real] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8003_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_nat,A2: nat,B2: nat > assn] :
% 5.82/6.17 ( ( finite_finite_nat @ S )
% 5.82/6.17 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn
% 5.82/6.17 @ ^ [K3: nat] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn
% 5.82/6.17 @ ^ [K3: nat] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8004_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_int,A2: int,B2: int > assn] :
% 5.82/6.17 ( ( finite_finite_int @ S )
% 5.82/6.17 => ( ( ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups7882442080178216443t_assn
% 5.82/6.17 @ ^ [K3: int] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups7882442080178216443t_assn
% 5.82/6.17 @ ^ [K3: int] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8005_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > assn] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.17 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.17 => ( ( groups1304777262505850412r_assn
% 5.82/6.17 @ ^ [K3: code_integer] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.17 => ( ( groups1304777262505850412r_assn
% 5.82/6.17 @ ^ [K3: code_integer] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8006_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_complex,A2: complex,B2: complex > assn] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.17 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.17 => ( ( groups4150731942483176573x_assn
% 5.82/6.17 @ ^ [K3: complex] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.17 => ( ( groups4150731942483176573x_assn
% 5.82/6.17 @ ^ [K3: complex] : ( if_assn @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_assn )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_assn ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8007_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > real] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.17 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups2703838992350267259T_real
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.17 => ( ( groups2703838992350267259T_real
% 5.82/6.17 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8008_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_real,A2: real,B2: real > real] :
% 5.82/6.17 ( ( finite_finite_real @ S )
% 5.82/6.17 => ( ( ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1681761925125756287l_real
% 5.82/6.17 @ ^ [K3: real] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.17 => ( ( groups1681761925125756287l_real
% 5.82/6.17 @ ^ [K3: real] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8009_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_nat,A2: nat,B2: nat > real] :
% 5.82/6.17 ( ( finite_finite_nat @ S )
% 5.82/6.17 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [K3: nat] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.17 => ( ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [K3: nat] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8010_prod_Odelta_H,axiom,
% 5.82/6.17 ! [S: set_int,A2: int,B2: int > real] :
% 5.82/6.17 ( ( finite_finite_int @ S )
% 5.82/6.17 => ( ( ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups2316167850115554303t_real
% 5.82/6.17 @ ^ [K3: int] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = ( B2 @ A2 ) ) )
% 5.82/6.17 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.17 => ( ( groups2316167850115554303t_real
% 5.82/6.17 @ ^ [K3: int] : ( if_real @ ( A2 = K3 ) @ ( B2 @ K3 ) @ one_one_real )
% 5.82/6.17 @ S )
% 5.82/6.17 = one_one_real ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.delta'
% 5.82/6.17 thf(fact_8011_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.17 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.17 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8012_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_real,X2: real,G: real > real] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ~ ( member_real @ X2 @ A )
% 5.82/6.17 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.17 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8013_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_nat,X2: nat,G: nat > real] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ~ ( member_nat @ X2 @ A )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.17 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8014_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_int,X2: int,G: int > real] :
% 5.82/6.17 ( ( finite_finite_int @ A )
% 5.82/6.17 => ( ~ ( member_int @ X2 @ A )
% 5.82/6.17 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.17 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8015_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_Code_integer,X2: code_integer,G: code_integer > real] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ~ ( member_Code_integer @ X2 @ A )
% 5.82/6.17 => ( ( groups9004974159866482096r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.17 = ( times_times_real @ ( G @ X2 ) @ ( groups9004974159866482096r_real @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8016_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_complex,X2: complex,G: complex > real] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ~ ( member_complex @ X2 @ A )
% 5.82/6.17 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.17 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8017_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.17 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.17 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8018_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_real,X2: real,G: real > rat] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ~ ( member_real @ X2 @ A )
% 5.82/6.17 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.17 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8019_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_nat,X2: nat,G: nat > rat] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ~ ( member_nat @ X2 @ A )
% 5.82/6.17 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.17 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8020_prod_Oinsert,axiom,
% 5.82/6.17 ! [A: set_int,X2: int,G: int > rat] :
% 5.82/6.17 ( ( finite_finite_int @ A )
% 5.82/6.17 => ( ~ ( member_int @ X2 @ A )
% 5.82/6.17 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.17 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.insert
% 5.82/6.17 thf(fact_8021_prod_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > real,N: nat] :
% 5.82/6.17 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.lessThan_Suc
% 5.82/6.17 thf(fact_8022_prod_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > rat,N: nat] :
% 5.82/6.17 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.lessThan_Suc
% 5.82/6.17 thf(fact_8023_prod_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > int,N: nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.lessThan_Suc
% 5.82/6.17 thf(fact_8024_prod_OlessThan__Suc,axiom,
% 5.82/6.17 ! [G: nat > nat,N: nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.lessThan_Suc
% 5.82/6.17 thf(fact_8025_floor__diff__of__int,axiom,
% 5.82/6.17 ! [X2: real,Z: int] :
% 5.82/6.17 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.82/6.17 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_diff_of_int
% 5.82/6.17 thf(fact_8026_floor__diff__of__int,axiom,
% 5.82/6.17 ! [X2: rat,Z: int] :
% 5.82/6.17 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.82/6.17 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_diff_of_int
% 5.82/6.17 thf(fact_8027_zero__le__floor,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % zero_le_floor
% 5.82/6.17 thf(fact_8028_zero__le__floor,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % zero_le_floor
% 5.82/6.17 thf(fact_8029_numeral__le__floor,axiom,
% 5.82/6.17 ! [V: num,X2: real] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % numeral_le_floor
% 5.82/6.17 thf(fact_8030_numeral__le__floor,axiom,
% 5.82/6.17 ! [V: num,X2: rat] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % numeral_le_floor
% 5.82/6.17 thf(fact_8031_floor__less__zero,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.82/6.17 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_zero
% 5.82/6.17 thf(fact_8032_floor__less__zero,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.82/6.17 = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_zero
% 5.82/6.17 thf(fact_8033_floor__less__numeral,axiom,
% 5.82/6.17 ! [X2: real,V: num] :
% 5.82/6.17 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.17 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_numeral
% 5.82/6.17 thf(fact_8034_floor__less__numeral,axiom,
% 5.82/6.17 ! [X2: rat,V: num] :
% 5.82/6.17 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.17 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_numeral
% 5.82/6.17 thf(fact_8035_zero__less__floor,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % zero_less_floor
% 5.82/6.17 thf(fact_8036_zero__less__floor,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % zero_less_floor
% 5.82/6.17 thf(fact_8037_floor__le__zero,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.82/6.17 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_zero
% 5.82/6.17 thf(fact_8038_floor__le__zero,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.82/6.17 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_zero
% 5.82/6.17 thf(fact_8039_one__le__floor,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_le_floor
% 5.82/6.17 thf(fact_8040_one__le__floor,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_le_floor
% 5.82/6.17 thf(fact_8041_floor__less__one,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.82/6.17 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_one
% 5.82/6.17 thf(fact_8042_floor__less__one,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.82/6.17 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_one
% 5.82/6.17 thf(fact_8043_floor__diff__numeral,axiom,
% 5.82/6.17 ! [X2: real,V: num] :
% 5.82/6.17 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.82/6.17 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_diff_numeral
% 5.82/6.17 thf(fact_8044_floor__diff__numeral,axiom,
% 5.82/6.17 ! [X2: rat,V: num] :
% 5.82/6.17 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.82/6.17 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_diff_numeral
% 5.82/6.17 thf(fact_8045_floor__numeral__power,axiom,
% 5.82/6.17 ! [X2: num,N: nat] :
% 5.82/6.17 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.82/6.17 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_numeral_power
% 5.82/6.17 thf(fact_8046_floor__numeral__power,axiom,
% 5.82/6.17 ! [X2: num,N: nat] :
% 5.82/6.17 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.82/6.17 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_numeral_power
% 5.82/6.17 thf(fact_8047_floor__diff__one,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.82/6.17 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_diff_one
% 5.82/6.17 thf(fact_8048_floor__diff__one,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.82/6.17 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_diff_one
% 5.82/6.17 thf(fact_8049_prod_Oop__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > assn] :
% 5.82/6.17 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_assn ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.op_ivl_Suc
% 5.82/6.17 thf(fact_8050_prod_Oop__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > real] :
% 5.82/6.17 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_real ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.op_ivl_Suc
% 5.82/6.17 thf(fact_8051_prod_Oop__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > rat] :
% 5.82/6.17 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_rat ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.op_ivl_Suc
% 5.82/6.17 thf(fact_8052_prod_Oop__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > int] :
% 5.82/6.17 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_int ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.op_ivl_Suc
% 5.82/6.17 thf(fact_8053_prod_Oop__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > nat] :
% 5.82/6.17 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_nat ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.17 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.op_ivl_Suc
% 5.82/6.17 thf(fact_8054_prod_Ocl__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > assn] :
% 5.82/6.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_assn ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.cl_ivl_Suc
% 5.82/6.17 thf(fact_8055_prod_Ocl__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > real] :
% 5.82/6.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_real ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.cl_ivl_Suc
% 5.82/6.17 thf(fact_8056_prod_Ocl__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > rat] :
% 5.82/6.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_rat ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.cl_ivl_Suc
% 5.82/6.17 thf(fact_8057_prod_Ocl__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > int] :
% 5.82/6.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_int ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.cl_ivl_Suc
% 5.82/6.17 thf(fact_8058_prod_Ocl__ivl__Suc,axiom,
% 5.82/6.17 ! [N: nat,M: nat,G: nat > nat] :
% 5.82/6.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = one_one_nat ) )
% 5.82/6.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.82/6.17 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.17 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.cl_ivl_Suc
% 5.82/6.17 thf(fact_8059_numeral__less__floor,axiom,
% 5.82/6.17 ! [V: num,X2: real] :
% 5.82/6.17 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % numeral_less_floor
% 5.82/6.17 thf(fact_8060_numeral__less__floor,axiom,
% 5.82/6.17 ! [V: num,X2: rat] :
% 5.82/6.17 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % numeral_less_floor
% 5.82/6.17 thf(fact_8061_floor__le__numeral,axiom,
% 5.82/6.17 ! [X2: real,V: num] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.17 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_numeral
% 5.82/6.17 thf(fact_8062_floor__le__numeral,axiom,
% 5.82/6.17 ! [X2: rat,V: num] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.82/6.17 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_numeral
% 5.82/6.17 thf(fact_8063_one__less__floor,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_less_floor
% 5.82/6.17 thf(fact_8064_one__less__floor,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.17 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % one_less_floor
% 5.82/6.17 thf(fact_8065_floor__le__one,axiom,
% 5.82/6.17 ! [X2: real] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.82/6.17 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_one
% 5.82/6.17 thf(fact_8066_floor__le__one,axiom,
% 5.82/6.17 ! [X2: rat] :
% 5.82/6.17 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.82/6.17 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_one
% 5.82/6.17 thf(fact_8067_floor__one__divide__eq__div__numeral,axiom,
% 5.82/6.17 ! [B2: num] :
% 5.82/6.17 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B2 ) ) )
% 5.82/6.17 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B2 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_one_divide_eq_div_numeral
% 5.82/6.17 thf(fact_8068_prod_Oneutral,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > int] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ( G @ X4 )
% 5.82/6.17 = one_one_int ) )
% 5.82/6.17 => ( ( groups705719431365010083at_int @ G @ A )
% 5.82/6.17 = one_one_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.neutral
% 5.82/6.17 thf(fact_8069_prod_Oneutral,axiom,
% 5.82/6.17 ! [A: set_int,G: int > int] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ( G @ X4 )
% 5.82/6.17 = one_one_int ) )
% 5.82/6.17 => ( ( groups1705073143266064639nt_int @ G @ A )
% 5.82/6.17 = one_one_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.neutral
% 5.82/6.17 thf(fact_8070_prod_Oneutral,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > nat] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ( G @ X4 )
% 5.82/6.17 = one_one_nat ) )
% 5.82/6.17 => ( ( groups708209901874060359at_nat @ G @ A )
% 5.82/6.17 = one_one_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.neutral
% 5.82/6.17 thf(fact_8071_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: nat > assn,A: set_nat] :
% 5.82/6.17 ( ( ( groups6906906614972039071t_assn @ G @ A )
% 5.82/6.17 != one_one_assn )
% 5.82/6.17 => ~ ! [A3: nat] :
% 5.82/6.17 ( ( member_nat @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_assn ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8072_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: vEBT_VEBT > assn,A: set_VEBT_VEBT] :
% 5.82/6.17 ( ( ( groups569574905686396791T_assn @ G @ A )
% 5.82/6.17 != one_one_assn )
% 5.82/6.17 => ~ ! [A3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_assn ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8073_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: real > assn,A: set_real] :
% 5.82/6.17 ( ( ( groups1155561341820557179l_assn @ G @ A )
% 5.82/6.17 != one_one_assn )
% 5.82/6.17 => ~ ! [A3: real] :
% 5.82/6.17 ( ( member_real @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_assn ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8074_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: int > assn,A: set_int] :
% 5.82/6.17 ( ( ( groups7882442080178216443t_assn @ G @ A )
% 5.82/6.17 != one_one_assn )
% 5.82/6.17 => ~ ! [A3: int] :
% 5.82/6.17 ( ( member_int @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_assn ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8075_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: nat > real,A: set_nat] :
% 5.82/6.17 ( ( ( groups129246275422532515t_real @ G @ A )
% 5.82/6.17 != one_one_real )
% 5.82/6.17 => ~ ! [A3: nat] :
% 5.82/6.17 ( ( member_nat @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8076_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: vEBT_VEBT > real,A: set_VEBT_VEBT] :
% 5.82/6.17 ( ( ( groups2703838992350267259T_real @ G @ A )
% 5.82/6.17 != one_one_real )
% 5.82/6.17 => ~ ! [A3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8077_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: real > real,A: set_real] :
% 5.82/6.17 ( ( ( groups1681761925125756287l_real @ G @ A )
% 5.82/6.17 != one_one_real )
% 5.82/6.17 => ~ ! [A3: real] :
% 5.82/6.17 ( ( member_real @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8078_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: int > real,A: set_int] :
% 5.82/6.17 ( ( ( groups2316167850115554303t_real @ G @ A )
% 5.82/6.17 != one_one_real )
% 5.82/6.17 => ~ ! [A3: int] :
% 5.82/6.17 ( ( member_int @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_real ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8079_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: nat > rat,A: set_nat] :
% 5.82/6.17 ( ( ( groups73079841787564623at_rat @ G @ A )
% 5.82/6.17 != one_one_rat )
% 5.82/6.17 => ~ ! [A3: nat] :
% 5.82/6.17 ( ( member_nat @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8080_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.82/6.17 ! [G: vEBT_VEBT > rat,A: set_VEBT_VEBT] :
% 5.82/6.17 ( ( ( groups5726676334696518183BT_rat @ G @ A )
% 5.82/6.17 != one_one_rat )
% 5.82/6.17 => ~ ! [A3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.17 => ( ( G @ A3 )
% 5.82/6.17 = one_one_rat ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.not_neutral_contains_not_neutral
% 5.82/6.17 thf(fact_8081_prod_Oswap,axiom,
% 5.82/6.17 ! [G: nat > nat > int,B: set_nat,A: set_nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( G @ I4 ) @ B )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [J3: nat] :
% 5.82/6.17 ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ B ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap
% 5.82/6.17 thf(fact_8082_prod_Oswap,axiom,
% 5.82/6.17 ! [G: nat > int > int,B: set_int,A: set_nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( groups1705073143266064639nt_int @ ( G @ I4 ) @ B )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [J3: int] :
% 5.82/6.17 ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ B ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap
% 5.82/6.17 thf(fact_8083_prod_Oswap,axiom,
% 5.82/6.17 ! [G: int > nat > int,B: set_nat,A: set_int] :
% 5.82/6.17 ( ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [I4: int] : ( groups705719431365010083at_int @ ( G @ I4 ) @ B )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [J3: nat] :
% 5.82/6.17 ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [I4: int] : ( G @ I4 @ J3 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ B ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap
% 5.82/6.17 thf(fact_8084_prod_Oswap,axiom,
% 5.82/6.17 ! [G: int > int > int,B: set_int,A: set_int] :
% 5.82/6.17 ( ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [I4: int] : ( groups1705073143266064639nt_int @ ( G @ I4 ) @ B )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [J3: int] :
% 5.82/6.17 ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [I4: int] : ( G @ I4 @ J3 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ B ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap
% 5.82/6.17 thf(fact_8085_prod_Oswap,axiom,
% 5.82/6.17 ! [G: nat > nat > nat,B: set_nat,A: set_nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( G @ I4 ) @ B )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [J3: nat] :
% 5.82/6.17 ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ B ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap
% 5.82/6.17 thf(fact_8086_prod_Odistrib,axiom,
% 5.82/6.17 ! [G: nat > int,H2: nat > int,A: set_nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [X3: nat] : ( times_times_int @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A ) @ ( groups705719431365010083at_int @ H2 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.distrib
% 5.82/6.17 thf(fact_8087_prod_Odistrib,axiom,
% 5.82/6.17 ! [G: int > int,H2: int > int,A: set_int] :
% 5.82/6.17 ( ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [X3: int] : ( times_times_int @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A ) @ ( groups1705073143266064639nt_int @ H2 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.distrib
% 5.82/6.17 thf(fact_8088_prod_Odistrib,axiom,
% 5.82/6.17 ! [G: nat > nat,H2: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [X3: nat] : ( times_times_nat @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A ) @ ( groups708209901874060359at_nat @ H2 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.distrib
% 5.82/6.17 thf(fact_8089_prod__power__distrib,axiom,
% 5.82/6.17 ! [F: nat > int,A: set_nat,N: nat] :
% 5.82/6.17 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A ) @ N )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [X3: nat] : ( power_power_int @ ( F @ X3 ) @ N )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_power_distrib
% 5.82/6.17 thf(fact_8090_prod__power__distrib,axiom,
% 5.82/6.17 ! [F: int > int,A: set_int,N: nat] :
% 5.82/6.17 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A ) @ N )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [X3: int] : ( power_power_int @ ( F @ X3 ) @ N )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_power_distrib
% 5.82/6.17 thf(fact_8091_prod__power__distrib,axiom,
% 5.82/6.17 ! [F: nat > nat,A: set_nat,N: nat] :
% 5.82/6.17 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A ) @ N )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [X3: nat] : ( power_power_nat @ ( F @ X3 ) @ N )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_power_distrib
% 5.82/6.17 thf(fact_8092_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,B: set_nat,G: vEBT_VEBT > nat > int,R: vEBT_VEBT > nat > $o] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( groups6359315924273963643BT_int
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( groups705719431365010083at_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( groups6359315924273963643BT_int
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_VEBT_VEBT
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8093_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_real,B: set_nat,G: real > nat > int,R: real > nat > $o] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( groups4694064378042380927al_int
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( groups705719431365010083at_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( groups4694064378042380927al_int
% 5.82/6.17 @ ^ [X3: real] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_real
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( ( member_real @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8094_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_Code_integer,B: set_nat,G: code_integer > nat > int,R: code_integer > nat > $o] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( groups3188404863801439024er_int
% 5.82/6.17 @ ^ [X3: code_integer] :
% 5.82/6.17 ( groups705719431365010083at_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( groups3188404863801439024er_int
% 5.82/6.17 @ ^ [X3: code_integer] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_Code_integer
% 5.82/6.17 @ ^ [X3: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8095_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_complex,B: set_nat,G: complex > nat > int,R: complex > nat > $o] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( groups858564598930262913ex_int
% 5.82/6.17 @ ^ [X3: complex] :
% 5.82/6.17 ( groups705719431365010083at_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( groups858564598930262913ex_int
% 5.82/6.17 @ ^ [X3: complex] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_complex
% 5.82/6.17 @ ^ [X3: complex] :
% 5.82/6.17 ( ( member_complex @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8096_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,B: set_int,G: vEBT_VEBT > int > int,R: vEBT_VEBT > int > $o] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ( finite_finite_int @ B )
% 5.82/6.17 => ( ( groups6359315924273963643BT_int
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( groups1705073143266064639nt_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( ( member_int @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( groups6359315924273963643BT_int
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_VEBT_VEBT
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8097_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_real,B: set_int,G: real > int > int,R: real > int > $o] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ( finite_finite_int @ B )
% 5.82/6.17 => ( ( groups4694064378042380927al_int
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( groups1705073143266064639nt_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( ( member_int @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( groups4694064378042380927al_int
% 5.82/6.17 @ ^ [X3: real] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_real
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( ( member_real @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8098_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_Code_integer,B: set_int,G: code_integer > int > int,R: code_integer > int > $o] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( finite_finite_int @ B )
% 5.82/6.17 => ( ( groups3188404863801439024er_int
% 5.82/6.17 @ ^ [X3: code_integer] :
% 5.82/6.17 ( groups1705073143266064639nt_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( ( member_int @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( groups3188404863801439024er_int
% 5.82/6.17 @ ^ [X3: code_integer] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_Code_integer
% 5.82/6.17 @ ^ [X3: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8099_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_complex,B: set_int,G: complex > int > int,R: complex > int > $o] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( finite_finite_int @ B )
% 5.82/6.17 => ( ( groups858564598930262913ex_int
% 5.82/6.17 @ ^ [X3: complex] :
% 5.82/6.17 ( groups1705073143266064639nt_int @ ( G @ X3 )
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( ( member_int @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [Y: int] :
% 5.82/6.17 ( groups858564598930262913ex_int
% 5.82/6.17 @ ^ [X3: complex] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_complex
% 5.82/6.17 @ ^ [X3: complex] :
% 5.82/6.17 ( ( member_complex @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8100_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,B: set_nat,G: vEBT_VEBT > nat > nat,R: vEBT_VEBT > nat > $o] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( groups6361806394783013919BT_nat
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( groups708209901874060359at_nat @ ( G @ X3 )
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( groups6361806394783013919BT_nat
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_VEBT_VEBT
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8101_prod_Oswap__restrict,axiom,
% 5.82/6.17 ! [A: set_real,B: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ( finite_finite_nat @ B )
% 5.82/6.17 => ( ( groups4696554848551431203al_nat
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( groups708209901874060359at_nat @ ( G @ X3 )
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( ( member_nat @ Y @ B )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ A )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [Y: nat] :
% 5.82/6.17 ( groups4696554848551431203al_nat
% 5.82/6.17 @ ^ [X3: real] : ( G @ X3 @ Y )
% 5.82/6.17 @ ( collect_real
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( ( member_real @ X3 @ A )
% 5.82/6.17 & ( R @ X3 @ Y ) ) ) )
% 5.82/6.17 @ B ) ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.swap_restrict
% 5.82/6.17 thf(fact_8102_mod__prod__eq,axiom,
% 5.82/6.17 ! [F: nat > int,A2: int,A: set_nat] :
% 5.82/6.17 ( ( modulo_modulo_int
% 5.82/6.17 @ ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( modulo_modulo_int @ ( F @ I4 ) @ A2 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ A2 )
% 5.82/6.17 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A ) @ A2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % mod_prod_eq
% 5.82/6.17 thf(fact_8103_mod__prod__eq,axiom,
% 5.82/6.17 ! [F: int > int,A2: int,A: set_int] :
% 5.82/6.17 ( ( modulo_modulo_int
% 5.82/6.17 @ ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A2 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ A2 )
% 5.82/6.17 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A ) @ A2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % mod_prod_eq
% 5.82/6.17 thf(fact_8104_mod__prod__eq,axiom,
% 5.82/6.17 ! [F: nat > nat,A2: nat,A: set_nat] :
% 5.82/6.17 ( ( modulo_modulo_nat
% 5.82/6.17 @ ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A2 )
% 5.82/6.17 @ A )
% 5.82/6.17 @ A2 )
% 5.82/6.17 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A ) @ A2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % mod_prod_eq
% 5.82/6.17 thf(fact_8105_prod__nonneg,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > int] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_nonneg
% 5.82/6.17 thf(fact_8106_prod__nonneg,axiom,
% 5.82/6.17 ! [A: set_int,F: int > int] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_nonneg
% 5.82/6.17 thf(fact_8107_prod__nonneg,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_nonneg
% 5.82/6.17 thf(fact_8108_prod__mono,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > real,G: nat > real] :
% 5.82/6.17 ( ! [I2: nat] :
% 5.82/6.17 ( ( member_nat @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A ) @ ( groups129246275422532515t_real @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8109_prod__mono,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.17 ( ! [I2: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A ) @ ( groups2703838992350267259T_real @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8110_prod__mono,axiom,
% 5.82/6.17 ! [A: set_real,F: real > real,G: real > real] :
% 5.82/6.17 ( ! [I2: real] :
% 5.82/6.17 ( ( member_real @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A ) @ ( groups1681761925125756287l_real @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8111_prod__mono,axiom,
% 5.82/6.17 ! [A: set_int,F: int > real,G: int > real] :
% 5.82/6.17 ( ! [I2: int] :
% 5.82/6.17 ( ( member_int @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A ) @ ( groups2316167850115554303t_real @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8112_prod__mono,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > rat,G: nat > rat] :
% 5.82/6.17 ( ! [I2: nat] :
% 5.82/6.17 ( ( member_nat @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A ) @ ( groups73079841787564623at_rat @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8113_prod__mono,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 5.82/6.17 ( ! [I2: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A ) @ ( groups5726676334696518183BT_rat @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8114_prod__mono,axiom,
% 5.82/6.17 ! [A: set_real,F: real > rat,G: real > rat] :
% 5.82/6.17 ( ! [I2: real] :
% 5.82/6.17 ( ( member_real @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A ) @ ( groups4061424788464935467al_rat @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8115_prod__mono,axiom,
% 5.82/6.17 ! [A: set_int,F: int > rat,G: int > rat] :
% 5.82/6.17 ( ! [I2: int] :
% 5.82/6.17 ( ( member_int @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A ) @ ( groups1072433553688619179nt_rat @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8116_prod__mono,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.17 ( ! [I2: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_nat @ ( groups6361806394783013919BT_nat @ F @ A ) @ ( groups6361806394783013919BT_nat @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8117_prod__mono,axiom,
% 5.82/6.17 ! [A: set_real,F: real > nat,G: real > nat] :
% 5.82/6.17 ( ! [I2: real] :
% 5.82/6.17 ( ( member_real @ I2 @ A )
% 5.82/6.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.82/6.17 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.17 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A ) @ ( groups4696554848551431203al_nat @ G @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_mono
% 5.82/6.17 thf(fact_8118_prod__pos,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > int] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_pos
% 5.82/6.17 thf(fact_8119_prod__pos,axiom,
% 5.82/6.17 ! [A: set_int,F: int > int] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_pos
% 5.82/6.17 thf(fact_8120_prod__pos,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > nat] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_pos
% 5.82/6.17 thf(fact_8121_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > real] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8122_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.17 ( ! [X4: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8123_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_real,F: real > real] :
% 5.82/6.17 ( ! [X4: real] :
% 5.82/6.17 ( ( member_real @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8124_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_int,F: int > real] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8125_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > rat] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8126_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.17 ( ! [X4: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8127_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_real,F: real > rat] :
% 5.82/6.17 ( ! [X4: real] :
% 5.82/6.17 ( ( member_real @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8128_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_int,F: int > rat] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8129_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.17 ( ! [X4: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_nat @ one_one_nat @ ( groups6361806394783013919BT_nat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8130_prod__ge__1,axiom,
% 5.82/6.17 ! [A: set_real,F: real > nat] :
% 5.82/6.17 ( ! [X4: real] :
% 5.82/6.17 ( ( member_real @ X4 @ A )
% 5.82/6.17 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.82/6.17 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_ge_1
% 5.82/6.17 thf(fact_8131_of__int__floor__le,axiom,
% 5.82/6.17 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_floor_le
% 5.82/6.17 thf(fact_8132_of__int__floor__le,axiom,
% 5.82/6.17 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 5.82/6.17
% 5.82/6.17 % of_int_floor_le
% 5.82/6.17 thf(fact_8133_floor__mono,axiom,
% 5.82/6.17 ! [X2: real,Y3: real] :
% 5.82/6.17 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.17 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_mono
% 5.82/6.17 thf(fact_8134_floor__mono,axiom,
% 5.82/6.17 ! [X2: rat,Y3: rat] :
% 5.82/6.17 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.82/6.17 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_mono
% 5.82/6.17 thf(fact_8135_floor__less__cancel,axiom,
% 5.82/6.17 ! [X2: real,Y3: real] :
% 5.82/6.17 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y3 ) )
% 5.82/6.17 => ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_cancel
% 5.82/6.17 thf(fact_8136_floor__less__cancel,axiom,
% 5.82/6.17 ! [X2: rat,Y3: rat] :
% 5.82/6.17 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y3 ) )
% 5.82/6.17 => ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_less_cancel
% 5.82/6.17 thf(fact_8137_prod__atLeastAtMost__code,axiom,
% 5.82/6.17 ! [F: nat > assn,A2: nat,B2: nat] :
% 5.82/6.17 ( ( groups6906906614972039071t_assn @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.17 = ( set_fo1959793692361082170t_assn
% 5.82/6.17 @ ^ [A5: nat] : ( times_times_assn @ ( F @ A5 ) )
% 5.82/6.17 @ A2
% 5.82/6.17 @ B2
% 5.82/6.17 @ one_one_assn ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_atLeastAtMost_code
% 5.82/6.17 thf(fact_8138_prod__atLeastAtMost__code,axiom,
% 5.82/6.17 ! [F: nat > real,A2: nat,B2: nat] :
% 5.82/6.17 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.17 = ( set_fo3111899725591712190t_real
% 5.82/6.17 @ ^ [A5: nat] : ( times_times_real @ ( F @ A5 ) )
% 5.82/6.17 @ A2
% 5.82/6.17 @ B2
% 5.82/6.17 @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_atLeastAtMost_code
% 5.82/6.17 thf(fact_8139_prod__atLeastAtMost__code,axiom,
% 5.82/6.17 ! [F: nat > rat,A2: nat,B2: nat] :
% 5.82/6.17 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.17 = ( set_fo1949268297981939178at_rat
% 5.82/6.17 @ ^ [A5: nat] : ( times_times_rat @ ( F @ A5 ) )
% 5.82/6.17 @ A2
% 5.82/6.17 @ B2
% 5.82/6.17 @ one_one_rat ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_atLeastAtMost_code
% 5.82/6.17 thf(fact_8140_prod__atLeastAtMost__code,axiom,
% 5.82/6.17 ! [F: nat > int,A2: nat,B2: nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.17 = ( set_fo2581907887559384638at_int
% 5.82/6.17 @ ^ [A5: nat] : ( times_times_int @ ( F @ A5 ) )
% 5.82/6.17 @ A2
% 5.82/6.17 @ B2
% 5.82/6.17 @ one_one_int ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_atLeastAtMost_code
% 5.82/6.17 thf(fact_8141_prod__atLeastAtMost__code,axiom,
% 5.82/6.17 ! [F: nat > nat,A2: nat,B2: nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.17 = ( set_fo2584398358068434914at_nat
% 5.82/6.17 @ ^ [A5: nat] : ( times_times_nat @ ( F @ A5 ) )
% 5.82/6.17 @ A2
% 5.82/6.17 @ B2
% 5.82/6.17 @ one_one_nat ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_atLeastAtMost_code
% 5.82/6.17 thf(fact_8142_floor__le__ceiling,axiom,
% 5.82/6.17 ! [X2: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_ceiling
% 5.82/6.17 thf(fact_8143_floor__le__ceiling,axiom,
% 5.82/6.17 ! [X2: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_ceiling
% 5.82/6.17 thf(fact_8144_floor__le__round,axiom,
% 5.82/6.17 ! [X2: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim8280529875227126926d_real @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_round
% 5.82/6.17 thf(fact_8145_floor__le__round,axiom,
% 5.82/6.17 ! [X2: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ X2 ) ) ).
% 5.82/6.17
% 5.82/6.17 % floor_le_round
% 5.82/6.17 thf(fact_8146_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > assn,P: vEBT_VEBT > $o] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ( groups569574905686396791T_assn @ G
% 5.82/6.17 @ ( collect_VEBT_VEBT
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups569574905686396791T_assn
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8147_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_real,G: real > assn,P: real > $o] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ( groups1155561341820557179l_assn @ G
% 5.82/6.17 @ ( collect_real
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( ( member_real @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups1155561341820557179l_assn
% 5.82/6.17 @ ^ [X3: real] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8148_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > assn,P: nat > $o] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( groups6906906614972039071t_assn @ G
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [X3: nat] :
% 5.82/6.17 ( ( member_nat @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups6906906614972039071t_assn
% 5.82/6.17 @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8149_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_int,G: int > assn,P: int > $o] :
% 5.82/6.17 ( ( finite_finite_int @ A )
% 5.82/6.17 => ( ( groups7882442080178216443t_assn @ G
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [X3: int] :
% 5.82/6.17 ( ( member_int @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups7882442080178216443t_assn
% 5.82/6.17 @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8150_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_Code_integer,G: code_integer > assn,P: code_integer > $o] :
% 5.82/6.17 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.17 => ( ( groups1304777262505850412r_assn @ G
% 5.82/6.17 @ ( collect_Code_integer
% 5.82/6.17 @ ^ [X3: code_integer] :
% 5.82/6.17 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups1304777262505850412r_assn
% 5.82/6.17 @ ^ [X3: code_integer] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8151_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_complex,G: complex > assn,P: complex > $o] :
% 5.82/6.17 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.17 => ( ( groups4150731942483176573x_assn @ G
% 5.82/6.17 @ ( collect_complex
% 5.82/6.17 @ ^ [X3: complex] :
% 5.82/6.17 ( ( member_complex @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups4150731942483176573x_assn
% 5.82/6.17 @ ^ [X3: complex] : ( if_assn @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_assn )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8152_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 5.82/6.17 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.17 => ( ( groups2703838992350267259T_real @ G
% 5.82/6.17 @ ( collect_VEBT_VEBT
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups2703838992350267259T_real
% 5.82/6.17 @ ^ [X3: vEBT_VEBT] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_real )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8153_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_real,G: real > real,P: real > $o] :
% 5.82/6.17 ( ( finite_finite_real @ A )
% 5.82/6.17 => ( ( groups1681761925125756287l_real @ G
% 5.82/6.17 @ ( collect_real
% 5.82/6.17 @ ^ [X3: real] :
% 5.82/6.17 ( ( member_real @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups1681761925125756287l_real
% 5.82/6.17 @ ^ [X3: real] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_real )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8154_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_nat,G: nat > real,P: nat > $o] :
% 5.82/6.17 ( ( finite_finite_nat @ A )
% 5.82/6.17 => ( ( groups129246275422532515t_real @ G
% 5.82/6.17 @ ( collect_nat
% 5.82/6.17 @ ^ [X3: nat] :
% 5.82/6.17 ( ( member_nat @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [X3: nat] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_real )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8155_prod_Ointer__filter,axiom,
% 5.82/6.17 ! [A: set_int,G: int > real,P: int > $o] :
% 5.82/6.17 ( ( finite_finite_int @ A )
% 5.82/6.17 => ( ( groups2316167850115554303t_real @ G
% 5.82/6.17 @ ( collect_int
% 5.82/6.17 @ ^ [X3: int] :
% 5.82/6.17 ( ( member_int @ X3 @ A )
% 5.82/6.17 & ( P @ X3 ) ) ) )
% 5.82/6.17 = ( groups2316167850115554303t_real
% 5.82/6.17 @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ one_one_real )
% 5.82/6.17 @ A ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.inter_filter
% 5.82/6.17 thf(fact_8156_prod_Oshift__bounds__Suc__ivl,axiom,
% 5.82/6.17 ! [G: nat > int,M: nat,N: nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_Suc_ivl
% 5.82/6.17 thf(fact_8157_prod_Oshift__bounds__Suc__ivl,axiom,
% 5.82/6.17 ! [G: nat > nat,M: nat,N: nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_Suc_ivl
% 5.82/6.17 thf(fact_8158_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.82/6.17 ! [G: nat > int,M: nat,N: nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_cl_Suc_ivl
% 5.82/6.17 thf(fact_8159_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.82/6.17 ! [G: nat > nat,M: nat,N: nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_cl_Suc_ivl
% 5.82/6.17 thf(fact_8160_power__sum,axiom,
% 5.82/6.17 ! [C2: real,F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( power_power_real @ C2 @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.17 = ( groups129246275422532515t_real
% 5.82/6.17 @ ^ [A5: nat] : ( power_power_real @ C2 @ ( F @ A5 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_sum
% 5.82/6.17 thf(fact_8161_power__sum,axiom,
% 5.82/6.17 ! [C2: complex,F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( power_power_complex @ C2 @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.17 = ( groups6464643781859351333omplex
% 5.82/6.17 @ ^ [A5: nat] : ( power_power_complex @ C2 @ ( F @ A5 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_sum
% 5.82/6.17 thf(fact_8162_power__sum,axiom,
% 5.82/6.17 ! [C2: code_integer,F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( power_8256067586552552935nteger @ C2 @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.17 = ( groups3455450783089532116nteger
% 5.82/6.17 @ ^ [A5: nat] : ( power_8256067586552552935nteger @ C2 @ ( F @ A5 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_sum
% 5.82/6.17 thf(fact_8163_power__sum,axiom,
% 5.82/6.17 ! [C2: int,F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( power_power_int @ C2 @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [A5: nat] : ( power_power_int @ C2 @ ( F @ A5 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_sum
% 5.82/6.17 thf(fact_8164_power__sum,axiom,
% 5.82/6.17 ! [C2: int,F: int > nat,A: set_int] :
% 5.82/6.17 ( ( power_power_int @ C2 @ ( groups4541462559716669496nt_nat @ F @ A ) )
% 5.82/6.17 = ( groups1705073143266064639nt_int
% 5.82/6.17 @ ^ [A5: int] : ( power_power_int @ C2 @ ( F @ A5 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_sum
% 5.82/6.17 thf(fact_8165_power__sum,axiom,
% 5.82/6.17 ! [C2: nat,F: nat > nat,A: set_nat] :
% 5.82/6.17 ( ( power_power_nat @ C2 @ ( groups3542108847815614940at_nat @ F @ A ) )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [A5: nat] : ( power_power_nat @ C2 @ ( F @ A5 ) )
% 5.82/6.17 @ A ) ) ).
% 5.82/6.17
% 5.82/6.17 % power_sum
% 5.82/6.17 thf(fact_8166_prod_Oshift__bounds__nat__ivl,axiom,
% 5.82/6.17 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_nat_ivl
% 5.82/6.17 thf(fact_8167_prod_Oshift__bounds__nat__ivl,axiom,
% 5.82/6.17 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.17 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_nat_ivl
% 5.82/6.17 thf(fact_8168_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.82/6.17 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.82/6.17 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.17 = ( groups705719431365010083at_int
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_cl_nat_ivl
% 5.82/6.17 thf(fact_8169_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.82/6.17 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.82/6.17 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.82/6.17 = ( groups708209901874060359at_nat
% 5.82/6.17 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.17 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod.shift_bounds_cl_nat_ivl
% 5.82/6.17 thf(fact_8170_prod__le__1,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > real] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A ) @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_le_1
% 5.82/6.17 thf(fact_8171_prod__le__1,axiom,
% 5.82/6.17 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.17 ( ! [X4: vEBT_VEBT] :
% 5.82/6.17 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A ) @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_le_1
% 5.82/6.17 thf(fact_8172_prod__le__1,axiom,
% 5.82/6.17 ! [A: set_real,F: real > real] :
% 5.82/6.17 ( ! [X4: real] :
% 5.82/6.17 ( ( member_real @ X4 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A ) @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_le_1
% 5.82/6.17 thf(fact_8173_prod__le__1,axiom,
% 5.82/6.17 ! [A: set_int,F: int > real] :
% 5.82/6.17 ( ! [X4: int] :
% 5.82/6.17 ( ( member_int @ X4 @ A )
% 5.82/6.17 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.82/6.17 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.82/6.17 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A ) @ one_one_real ) ) ).
% 5.82/6.17
% 5.82/6.17 % prod_le_1
% 5.82/6.17 thf(fact_8174_prod__le__1,axiom,
% 5.82/6.17 ! [A: set_nat,F: nat > rat] :
% 5.82/6.17 ( ! [X4: nat] :
% 5.82/6.17 ( ( member_nat @ X4 @ A )
% 5.82/6.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.82/6.17 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.82/6.17 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A ) @ one_one_rat ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_le_1
% 5.82/6.18 thf(fact_8175_prod__le__1,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.18 ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.82/6.18 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A ) @ one_one_rat ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_le_1
% 5.82/6.18 thf(fact_8176_prod__le__1,axiom,
% 5.82/6.18 ! [A: set_real,F: real > rat] :
% 5.82/6.18 ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.82/6.18 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A ) @ one_one_rat ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_le_1
% 5.82/6.18 thf(fact_8177_prod__le__1,axiom,
% 5.82/6.18 ! [A: set_int,F: int > rat] :
% 5.82/6.18 ( ! [X4: int] :
% 5.82/6.18 ( ( member_int @ X4 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.82/6.18 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A ) @ one_one_rat ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_le_1
% 5.82/6.18 thf(fact_8178_prod__le__1,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.82/6.18 ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ A )
% 5.82/6.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.82/6.18 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.82/6.18 => ( ord_less_eq_nat @ ( groups6361806394783013919BT_nat @ F @ A ) @ one_one_nat ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_le_1
% 5.82/6.18 thf(fact_8179_prod__le__1,axiom,
% 5.82/6.18 ! [A: set_real,F: real > nat] :
% 5.82/6.18 ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ A )
% 5.82/6.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.82/6.18 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.82/6.18 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A ) @ one_one_nat ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_le_1
% 5.82/6.18 thf(fact_8180_prod_Orelated,axiom,
% 5.82/6.18 ! [R: assn > assn > $o,S: set_nat,H2: nat > assn,G: nat > assn] :
% 5.82/6.18 ( ( R @ one_one_assn @ one_one_assn )
% 5.82/6.18 => ( ! [X15: assn,Y1: assn,X23: assn,Y22: assn] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_assn @ X15 @ Y1 ) @ ( times_times_assn @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite_finite_nat @ S )
% 5.82/6.18 => ( ! [X4: nat] :
% 5.82/6.18 ( ( member_nat @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups6906906614972039071t_assn @ H2 @ S ) @ ( groups6906906614972039071t_assn @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8181_prod_Orelated,axiom,
% 5.82/6.18 ! [R: assn > assn > $o,S: set_int,H2: int > assn,G: int > assn] :
% 5.82/6.18 ( ( R @ one_one_assn @ one_one_assn )
% 5.82/6.18 => ( ! [X15: assn,Y1: assn,X23: assn,Y22: assn] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_assn @ X15 @ Y1 ) @ ( times_times_assn @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite_finite_int @ S )
% 5.82/6.18 => ( ! [X4: int] :
% 5.82/6.18 ( ( member_int @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups7882442080178216443t_assn @ H2 @ S ) @ ( groups7882442080178216443t_assn @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8182_prod_Orelated,axiom,
% 5.82/6.18 ! [R: assn > assn > $o,S: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 5.82/6.18 ( ( R @ one_one_assn @ one_one_assn )
% 5.82/6.18 => ( ! [X15: assn,Y1: assn,X23: assn,Y22: assn] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_assn @ X15 @ Y1 ) @ ( times_times_assn @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ S )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups1304777262505850412r_assn @ H2 @ S ) @ ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8183_prod_Orelated,axiom,
% 5.82/6.18 ! [R: assn > assn > $o,S: set_complex,H2: complex > assn,G: complex > assn] :
% 5.82/6.18 ( ( R @ one_one_assn @ one_one_assn )
% 5.82/6.18 => ( ! [X15: assn,Y1: assn,X23: assn,Y22: assn] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_assn @ X15 @ Y1 ) @ ( times_times_assn @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ S )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups4150731942483176573x_assn @ H2 @ S ) @ ( groups4150731942483176573x_assn @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8184_prod_Orelated,axiom,
% 5.82/6.18 ! [R: real > real > $o,S: set_nat,H2: nat > real,G: nat > real] :
% 5.82/6.18 ( ( R @ one_one_real @ one_one_real )
% 5.82/6.18 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_real @ X15 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite_finite_nat @ S )
% 5.82/6.18 => ( ! [X4: nat] :
% 5.82/6.18 ( ( member_nat @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups129246275422532515t_real @ H2 @ S ) @ ( groups129246275422532515t_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8185_prod_Orelated,axiom,
% 5.82/6.18 ! [R: real > real > $o,S: set_int,H2: int > real,G: int > real] :
% 5.82/6.18 ( ( R @ one_one_real @ one_one_real )
% 5.82/6.18 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_real @ X15 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite_finite_int @ S )
% 5.82/6.18 => ( ! [X4: int] :
% 5.82/6.18 ( ( member_int @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups2316167850115554303t_real @ H2 @ S ) @ ( groups2316167850115554303t_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8186_prod_Orelated,axiom,
% 5.82/6.18 ! [R: real > real > $o,S: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 5.82/6.18 ( ( R @ one_one_real @ one_one_real )
% 5.82/6.18 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_real @ X15 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ S )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups9004974159866482096r_real @ H2 @ S ) @ ( groups9004974159866482096r_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8187_prod_Orelated,axiom,
% 5.82/6.18 ! [R: real > real > $o,S: set_complex,H2: complex > real,G: complex > real] :
% 5.82/6.18 ( ( R @ one_one_real @ one_one_real )
% 5.82/6.18 => ( ! [X15: real,Y1: real,X23: real,Y22: real] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_real @ X15 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ S )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups766887009212190081x_real @ H2 @ S ) @ ( groups766887009212190081x_real @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8188_prod_Orelated,axiom,
% 5.82/6.18 ! [R: rat > rat > $o,S: set_nat,H2: nat > rat,G: nat > rat] :
% 5.82/6.18 ( ( R @ one_one_rat @ one_one_rat )
% 5.82/6.18 => ( ! [X15: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_rat @ X15 @ Y1 ) @ ( times_times_rat @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite_finite_nat @ S )
% 5.82/6.18 => ( ! [X4: nat] :
% 5.82/6.18 ( ( member_nat @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups73079841787564623at_rat @ H2 @ S ) @ ( groups73079841787564623at_rat @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8189_prod_Orelated,axiom,
% 5.82/6.18 ! [R: rat > rat > $o,S: set_int,H2: int > rat,G: int > rat] :
% 5.82/6.18 ( ( R @ one_one_rat @ one_one_rat )
% 5.82/6.18 => ( ! [X15: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.82/6.18 ( ( ( R @ X15 @ X23 )
% 5.82/6.18 & ( R @ Y1 @ Y22 ) )
% 5.82/6.18 => ( R @ ( times_times_rat @ X15 @ Y1 ) @ ( times_times_rat @ X23 @ Y22 ) ) )
% 5.82/6.18 => ( ( finite_finite_int @ S )
% 5.82/6.18 => ( ! [X4: int] :
% 5.82/6.18 ( ( member_int @ X4 @ S )
% 5.82/6.18 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.82/6.18 => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S ) @ ( groups1072433553688619179nt_rat @ G @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.related
% 5.82/6.18 thf(fact_8190_prod_Oivl__cong,axiom,
% 5.82/6.18 ! [A2: nat,C2: nat,B2: nat,D2: nat,G: nat > int,H2: nat > int] :
% 5.82/6.18 ( ( A2 = C2 )
% 5.82/6.18 => ( ( B2 = D2 )
% 5.82/6.18 => ( ! [X4: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ C2 @ X4 )
% 5.82/6.18 => ( ( ord_less_nat @ X4 @ D2 )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) ) )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( groups705719431365010083at_int @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ivl_cong
% 5.82/6.18 thf(fact_8191_prod_Oivl__cong,axiom,
% 5.82/6.18 ! [A2: nat,C2: nat,B2: nat,D2: nat,G: nat > nat,H2: nat > nat] :
% 5.82/6.18 ( ( A2 = C2 )
% 5.82/6.18 => ( ( B2 = D2 )
% 5.82/6.18 => ( ! [X4: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ C2 @ X4 )
% 5.82/6.18 => ( ( ord_less_nat @ X4 @ D2 )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) ) )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( groups708209901874060359at_nat @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ivl_cong
% 5.82/6.18 thf(fact_8192_prod_Oivl__cong,axiom,
% 5.82/6.18 ! [A2: int,C2: int,B2: int,D2: int,G: int > int,H2: int > int] :
% 5.82/6.18 ( ( A2 = C2 )
% 5.82/6.18 => ( ( B2 = D2 )
% 5.82/6.18 => ( ! [X4: int] :
% 5.82/6.18 ( ( ord_less_eq_int @ C2 @ X4 )
% 5.82/6.18 => ( ( ord_less_int @ X4 @ D2 )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) ) )
% 5.82/6.18 => ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ A2 @ B2 ) )
% 5.82/6.18 = ( groups1705073143266064639nt_int @ H2 @ ( set_or4662586982721622107an_int @ C2 @ D2 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ivl_cong
% 5.82/6.18 thf(fact_8193_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.18 = ( groups2703838992350267259T_real @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8194_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_real,X2: real,G: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ( ( member_real @ X2 @ A )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.18 = ( groups1681761925125756287l_real @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_real @ X2 @ A )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8195_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_nat,X2: nat,G: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( ( member_nat @ X2 @ A )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.18 = ( groups129246275422532515t_real @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_nat @ X2 @ A )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8196_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_int,X2: int,G: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( ( member_int @ X2 @ A )
% 5.82/6.18 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.18 = ( groups2316167850115554303t_real @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_int @ X2 @ A )
% 5.82/6.18 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8197_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_Code_integer,X2: code_integer,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( ( member_Code_integer @ X2 @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.18 = ( groups9004974159866482096r_real @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_Code_integer @ X2 @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups9004974159866482096r_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8198_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_complex,X2: complex,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( ( member_complex @ X2 @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.18 = ( groups766887009212190081x_real @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_complex @ X2 @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8199_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8200_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_real,X2: real,G: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ( ( member_real @ X2 @ A )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_real @ X2 @ A )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8201_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_nat,X2: nat,G: nat > rat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( ( member_nat @ X2 @ A )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.18 = ( groups73079841787564623at_rat @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_nat @ X2 @ A )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8202_prod_Oinsert__if,axiom,
% 5.82/6.18 ! [A: set_int,X2: int,G: int > rat] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( ( member_int @ X2 @ A )
% 5.82/6.18 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.18 = ( groups1072433553688619179nt_rat @ G @ A ) ) )
% 5.82/6.18 & ( ~ ( member_int @ X2 @ A )
% 5.82/6.18 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_if
% 5.82/6.18 thf(fact_8203_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_VEBT_VEBT,T6: set_VEBT_VEBT,S: 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] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.18 => ( ( finite5795047828879050333T_VEBT @ T6 )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ S )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8204_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_VEBT_VEBT,T6: set_real,S: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T5: set_real,G: vEBT_VEBT > assn,H2: real > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.18 => ( ( finite_finite_real @ T6 )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ S )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8205_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_real,T6: set_VEBT_VEBT,S: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T5: set_VEBT_VEBT,G: real > assn,H2: vEBT_VEBT > assn] :
% 5.82/6.18 ( ( finite_finite_real @ S7 )
% 5.82/6.18 => ( ( finite5795047828879050333T_VEBT @ T6 )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T5 @ T6 ) )
% 5.82/6.18 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ S )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8206_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_real,T6: set_real,S: set_real,I: real > real,J: real > real,T5: set_real,G: real > assn,H2: real > assn] :
% 5.82/6.18 ( ( finite_finite_real @ S7 )
% 5.82/6.18 => ( ( finite_finite_real @ T6 )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T6 ) )
% 5.82/6.18 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ S )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8207_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_VEBT_VEBT,T6: set_int,S: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T5: set_int,G: vEBT_VEBT > assn,H2: int > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.18 => ( ( finite_finite_int @ T6 )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: int] :
% 5.82/6.18 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: int] :
% 5.82/6.18 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: int] :
% 5.82/6.18 ( ( member_int @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ S )
% 5.82/6.18 = ( groups7882442080178216443t_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8208_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_real,T6: set_int,S: set_real,I: int > real,J: real > int,T5: set_int,G: real > assn,H2: int > assn] :
% 5.82/6.18 ( ( finite_finite_real @ S7 )
% 5.82/6.18 => ( ( finite_finite_int @ T6 )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: int] :
% 5.82/6.18 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: int] :
% 5.82/6.18 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T6 ) )
% 5.82/6.18 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: int] :
% 5.82/6.18 ( ( member_int @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ S )
% 5.82/6.18 = ( groups7882442080178216443t_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8209_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_VEBT_VEBT,T6: set_Code_integer,S: 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] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ T6 )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ S )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8210_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_real,T6: set_Code_integer,S: set_real,I: code_integer > real,J: real > code_integer,T5: set_Code_integer,G: real > assn,H2: code_integer > assn] :
% 5.82/6.18 ( ( finite_finite_real @ S7 )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ T6 )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T5 @ T6 ) )
% 5.82/6.18 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ S )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8211_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_VEBT_VEBT,T6: set_complex,S: set_VEBT_VEBT,I: complex > vEBT_VEBT,J: vEBT_VEBT > complex,T5: set_complex,G: vEBT_VEBT > assn,H2: complex > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S7 )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ T6 )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) )
% 5.82/6.18 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T6 ) )
% 5.82/6.18 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ S )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8212_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.82/6.18 ! [S7: set_real,T6: set_complex,S: set_real,I: complex > real,J: real > complex,T5: set_complex,G: real > assn,H2: complex > assn] :
% 5.82/6.18 ( ( finite_finite_real @ S7 )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ T6 )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( ( I @ ( J @ A3 ) )
% 5.82/6.18 = A3 ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S7 ) )
% 5.82/6.18 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T6 ) ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T6 ) )
% 5.82/6.18 => ( ( J @ ( I @ B3 ) )
% 5.82/6.18 = B3 ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T6 ) )
% 5.82/6.18 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S @ S7 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S7 )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ T6 )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ S )
% 5.82/6.18 => ( ( H2 @ ( J @ A3 ) )
% 5.82/6.18 = ( G @ A3 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ S )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.reindex_bij_witness_not_neutral
% 5.82/6.18 thf(fact_8213_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups6361806394783013919BT_nat @ F @ A ) @ ( groups6361806394783013919BT_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8214_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_real,A: set_real,F: real > nat,G: real > nat] :
% 5.82/6.18 ( ( finite_finite_real @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A ) @ ( groups4696554848551431203al_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8215_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A ) @ ( groups3190895334310489300er_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8216_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,F: complex > nat,G: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A ) @ ( groups861055069439313189ex_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8217_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups6359315924273963643BT_int @ F @ A ) @ ( groups6359315924273963643BT_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8218_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_real,A: set_real,F: real > int,G: real > int] :
% 5.82/6.18 ( ( finite_finite_real @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A ) @ ( groups4694064378042380927al_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8219_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A ) @ ( groups3188404863801439024er_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8220_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,F: complex > int,G: complex > int] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A ) @ ( groups858564598930262913ex_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8221_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_int,A: set_int,F: int > nat,G: int > nat] :
% 5.82/6.18 ( ( finite_finite_int @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.18 => ( ! [A3: int] :
% 5.82/6.18 ( ( member_int @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A ) @ ( groups1707563613775114915nt_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8222_prod__dvd__prod__subset2,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,F: nat > int,G: nat > int] :
% 5.82/6.18 ( ( finite_finite_nat @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.18 => ( ! [A3: nat] :
% 5.82/6.18 ( ( member_nat @ A3 @ A )
% 5.82/6.18 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A ) @ ( groups705719431365010083at_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset2
% 5.82/6.18 thf(fact_8223_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A ) @ ( groups3190895334310489300er_nat @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8224_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,F: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A ) @ ( groups861055069439313189ex_nat @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8225_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > int] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A ) @ ( groups3188404863801439024er_int @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8226_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,F: complex > int] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A ) @ ( groups858564598930262913ex_int @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8227_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_int,A: set_int,F: int > nat] :
% 5.82/6.18 ( ( finite_finite_int @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A ) @ ( groups1707563613775114915nt_nat @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8228_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,F: nat > int] :
% 5.82/6.18 ( ( finite_finite_nat @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A ) @ ( groups705719431365010083at_int @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8229_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_int,A: set_int,F: int > int] :
% 5.82/6.18 ( ( finite_finite_int @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_int @ A @ B )
% 5.82/6.18 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A ) @ ( groups1705073143266064639nt_int @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8230_prod__dvd__prod__subset,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,F: nat > nat] :
% 5.82/6.18 ( ( finite_finite_nat @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.18 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A ) @ ( groups708209901874060359at_nat @ F @ B ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_dvd_prod_subset
% 5.82/6.18 thf(fact_8231_le__floor__iff,axiom,
% 5.82/6.18 ! [Z: int,X2: real] :
% 5.82/6.18 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.18 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_floor_iff
% 5.82/6.18 thf(fact_8232_le__floor__iff,axiom,
% 5.82/6.18 ! [Z: int,X2: rat] :
% 5.82/6.18 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.18 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_floor_iff
% 5.82/6.18 thf(fact_8233_floor__less__iff,axiom,
% 5.82/6.18 ! [X2: real,Z: int] :
% 5.82/6.18 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.82/6.18 = ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_less_iff
% 5.82/6.18 thf(fact_8234_floor__less__iff,axiom,
% 5.82/6.18 ! [X2: rat,Z: int] :
% 5.82/6.18 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.82/6.18 = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_less_iff
% 5.82/6.18 thf(fact_8235_int__add__floor,axiom,
% 5.82/6.18 ! [Z: int,X2: real] :
% 5.82/6.18 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.18 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % int_add_floor
% 5.82/6.18 thf(fact_8236_int__add__floor,axiom,
% 5.82/6.18 ! [Z: int,X2: rat] :
% 5.82/6.18 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.18 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % int_add_floor
% 5.82/6.18 thf(fact_8237_floor__add__int,axiom,
% 5.82/6.18 ! [X2: real,Z: int] :
% 5.82/6.18 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.82/6.18 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_add_int
% 5.82/6.18 thf(fact_8238_floor__add__int,axiom,
% 5.82/6.18 ! [X2: rat,Z: int] :
% 5.82/6.18 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.82/6.18 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_add_int
% 5.82/6.18 thf(fact_8239_le__floor__add,axiom,
% 5.82/6.18 ! [X2: real,Y3: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_floor_add
% 5.82/6.18 thf(fact_8240_le__floor__add,axiom,
% 5.82/6.18 ! [X2: rat,Y3: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y3 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_floor_add
% 5.82/6.18 thf(fact_8241_floor__power,axiom,
% 5.82/6.18 ! [X2: real,N: nat] :
% 5.82/6.18 ( ( X2
% 5.82/6.18 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X2 @ N ) )
% 5.82/6.18 = ( power_power_int @ ( archim6058952711729229775r_real @ X2 ) @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_power
% 5.82/6.18 thf(fact_8242_floor__power,axiom,
% 5.82/6.18 ! [X2: rat,N: nat] :
% 5.82/6.18 ( ( X2
% 5.82/6.18 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) )
% 5.82/6.18 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X2 @ N ) )
% 5.82/6.18 = ( power_power_int @ ( archim3151403230148437115or_rat @ X2 ) @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_power
% 5.82/6.18 thf(fact_8243_floor__divide__of__int__eq,axiom,
% 5.82/6.18 ! [K: int,L: int] :
% 5.82/6.18 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.82/6.18 = ( divide_divide_int @ K @ L ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_of_int_eq
% 5.82/6.18 thf(fact_8244_floor__divide__of__int__eq,axiom,
% 5.82/6.18 ! [K: int,L: int] :
% 5.82/6.18 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.82/6.18 = ( divide_divide_int @ K @ L ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_of_int_eq
% 5.82/6.18 thf(fact_8245_prod_OatLeastLessThan__concat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,P6: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.18 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_concat
% 5.82/6.18 thf(fact_8246_prod_OatLeastLessThan__concat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,P6: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.18 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_concat
% 5.82/6.18 thf(fact_8247_prod_OatLeastLessThan__concat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,P6: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.18 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_concat
% 5.82/6.18 thf(fact_8248_prod_OatLeastLessThan__concat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,P6: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( ord_less_eq_nat @ N @ P6 )
% 5.82/6.18 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_concat
% 5.82/6.18 thf(fact_8249_gbinomial__altdef__of__nat,axiom,
% 5.82/6.18 ( gbinomial_complex
% 5.82/6.18 = ( ^ [A5: complex,K3: nat] :
% 5.82/6.18 ( groups6464643781859351333omplex
% 5.82/6.18 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ I4 ) ) @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_altdef_of_nat
% 5.82/6.18 thf(fact_8250_gbinomial__altdef__of__nat,axiom,
% 5.82/6.18 ( gbinomial_rat
% 5.82/6.18 = ( ^ [A5: rat,K3: nat] :
% 5.82/6.18 ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( divide_divide_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_altdef_of_nat
% 5.82/6.18 thf(fact_8251_gbinomial__altdef__of__nat,axiom,
% 5.82/6.18 ( gbinomial_real
% 5.82/6.18 = ( ^ [A5: real,K3: nat] :
% 5.82/6.18 ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( divide_divide_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ I4 ) ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_altdef_of_nat
% 5.82/6.18 thf(fact_8252_gbinomial__Suc__Suc,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( gbinomial_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( suc @ K ) )
% 5.82/6.18 = ( plus_plus_real @ ( gbinomial_real @ A2 @ K ) @ ( gbinomial_real @ A2 @ ( suc @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_Suc_Suc
% 5.82/6.18 thf(fact_8253_gbinomial__Suc__Suc,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( gbinomial_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( suc @ K ) )
% 5.82/6.18 = ( plus_plus_rat @ ( gbinomial_rat @ A2 @ K ) @ ( gbinomial_rat @ A2 @ ( suc @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_Suc_Suc
% 5.82/6.18 thf(fact_8254_gbinomial__of__nat__symmetric,axiom,
% 5.82/6.18 ! [K: nat,N: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.18 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.82/6.18 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_of_nat_symmetric
% 5.82/6.18 thf(fact_8255_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_int,G: int > assn] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( groups7882442080178216443t_assn @ G
% 5.82/6.18 @ ( minus_minus_set_int @ A
% 5.82/6.18 @ ( collect_int
% 5.82/6.18 @ ^ [X3: int] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_assn ) ) ) )
% 5.82/6.18 = ( groups7882442080178216443t_assn @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8256_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_Code_integer,G: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups1304777262505850412r_assn @ G
% 5.82/6.18 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.18 @ ( collect_Code_integer
% 5.82/6.18 @ ^ [X3: code_integer] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_assn ) ) ) )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8257_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_complex,G: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups4150731942483176573x_assn @ G
% 5.82/6.18 @ ( minus_811609699411566653omplex @ A
% 5.82/6.18 @ ( collect_complex
% 5.82/6.18 @ ^ [X3: complex] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_assn ) ) ) )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8258_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_int,G: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( groups2316167850115554303t_real @ G
% 5.82/6.18 @ ( minus_minus_set_int @ A
% 5.82/6.18 @ ( collect_int
% 5.82/6.18 @ ^ [X3: int] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_real ) ) ) )
% 5.82/6.18 = ( groups2316167850115554303t_real @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8259_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_Code_integer,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G
% 5.82/6.18 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.18 @ ( collect_Code_integer
% 5.82/6.18 @ ^ [X3: code_integer] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_real ) ) ) )
% 5.82/6.18 = ( groups9004974159866482096r_real @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8260_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_complex,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G
% 5.82/6.18 @ ( minus_811609699411566653omplex @ A
% 5.82/6.18 @ ( collect_complex
% 5.82/6.18 @ ^ [X3: complex] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_real ) ) ) )
% 5.82/6.18 = ( groups766887009212190081x_real @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8261_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_int,G: int > rat] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( groups1072433553688619179nt_rat @ G
% 5.82/6.18 @ ( minus_minus_set_int @ A
% 5.82/6.18 @ ( collect_int
% 5.82/6.18 @ ^ [X3: int] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_rat ) ) ) )
% 5.82/6.18 = ( groups1072433553688619179nt_rat @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8262_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_Code_integer,G: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat @ G
% 5.82/6.18 @ ( minus_2355218937544613996nteger @ A
% 5.82/6.18 @ ( collect_Code_integer
% 5.82/6.18 @ ^ [X3: code_integer] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_rat ) ) ) )
% 5.82/6.18 = ( groups2555765274223993564er_rat @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8263_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_complex,G: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat @ G
% 5.82/6.18 @ ( minus_811609699411566653omplex @ A
% 5.82/6.18 @ ( collect_complex
% 5.82/6.18 @ ^ [X3: complex] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_rat ) ) ) )
% 5.82/6.18 = ( groups225925009352817453ex_rat @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8264_prod_Osetdiff__irrelevant,axiom,
% 5.82/6.18 ! [A: set_int,G: int > nat] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( groups1707563613775114915nt_nat @ G
% 5.82/6.18 @ ( minus_minus_set_int @ A
% 5.82/6.18 @ ( collect_int
% 5.82/6.18 @ ^ [X3: int] :
% 5.82/6.18 ( ( G @ X3 )
% 5.82/6.18 = one_one_nat ) ) ) )
% 5.82/6.18 = ( groups1707563613775114915nt_nat @ G @ A ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.setdiff_irrelevant
% 5.82/6.18 thf(fact_8265_prod_Onat__diff__reindex,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.18 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_diff_reindex
% 5.82/6.18 thf(fact_8266_prod_Onat__diff__reindex,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.18 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_diff_reindex
% 5.82/6.18 thf(fact_8267_prod_OatLeastAtMost__rev,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat,M: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastAtMost_rev
% 5.82/6.18 thf(fact_8268_prod_OatLeastAtMost__rev,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat,M: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastAtMost_rev
% 5.82/6.18 thf(fact_8269_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.18 => ( ( member_VEBT_VEBT @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8270_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_real,I: real,F: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ I6 )
% 5.82/6.18 => ( ( member_real @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8271_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_nat,I: nat,F: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ I6 )
% 5.82/6.18 => ( ( member_nat @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8272_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_int,I: int,F: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ I6 )
% 5.82/6.18 => ( ( member_int @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8273_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_Code_integer,I: code_integer,F: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.18 => ( ( member_Code_integer @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups9004974159866482096r_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8274_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_complex,I: complex,F: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.18 => ( ( member_complex @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: complex] :
% 5.82/6.18 ( ( member_complex @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8275_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.18 => ( ( member_VEBT_VEBT @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8276_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_real,I: real,F: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ I6 )
% 5.82/6.18 => ( ( member_real @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8277_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_nat,I: nat,F: nat > rat] :
% 5.82/6.18 ( ( finite_finite_nat @ I6 )
% 5.82/6.18 => ( ( member_nat @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8278_less__1__prod2,axiom,
% 5.82/6.18 ! [I6: set_int,I: int,F: int > rat] :
% 5.82/6.18 ( ( finite_finite_int @ I6 )
% 5.82/6.18 => ( ( member_int @ I @ I6 )
% 5.82/6.18 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.82/6.18 => ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod2
% 5.82/6.18 thf(fact_8279_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8280_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_real,F: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bot_set_real )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8281_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_Code_integer,F: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bo3990330152332043303nteger )
% 5.82/6.18 => ( ! [I2: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups9004974159866482096r_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8282_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_complex,F: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bot_set_complex )
% 5.82/6.18 => ( ! [I2: complex] :
% 5.82/6.18 ( ( member_complex @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8283_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_nat,F: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bot_set_nat )
% 5.82/6.18 => ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8284_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_int,F: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bot_set_int )
% 5.82/6.18 => ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8285_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8286_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_real,F: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bot_set_real )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8287_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_Code_integer,F: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bo3990330152332043303nteger )
% 5.82/6.18 => ( ! [I2: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8288_less__1__prod,axiom,
% 5.82/6.18 ! [I6: set_complex,F: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ I6 )
% 5.82/6.18 => ( ( I6 != bot_bot_set_complex )
% 5.82/6.18 => ( ! [I2: complex] :
% 5.82/6.18 ( ( member_complex @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 5.82/6.18 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_1_prod
% 5.82/6.18 thf(fact_8289_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ T5 )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8290_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_real,S: set_real,G: real > assn,H2: real > assn] :
% 5.82/6.18 ( ( finite_finite_real @ T5 )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ T5 )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8291_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8292_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > assn,H2: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups4150731942483176573x_assn @ G @ T5 )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8293_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ T5 )
% 5.82/6.18 = ( groups2703838992350267259T_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8294_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_real,S: set_real,G: real > real,H2: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ T5 )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ G @ T5 )
% 5.82/6.18 = ( groups1681761925125756287l_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8295_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ T5 )
% 5.82/6.18 = ( groups9004974159866482096r_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8296_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > real,H2: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ T5 )
% 5.82/6.18 = ( groups766887009212190081x_real @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8297_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ T5 )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8298_prod_Omono__neutral__cong__right,axiom,
% 5.82/6.18 ! [T5: set_real,S: set_real,G: real > rat,H2: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ T5 )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat @ G @ T5 )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_right
% 5.82/6.18 thf(fact_8299_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,H2: vEBT_VEBT > assn,G: vEBT_VEBT > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ S )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8300_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_real,S: set_real,H2: real > assn,G: real > assn] :
% 5.82/6.18 ( ( finite_finite_real @ T5 )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ S )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8301_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups1304777262505850412r_assn @ G @ S )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8302_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,H2: complex > assn,G: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups4150731942483176573x_assn @ G @ S )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8303_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ S )
% 5.82/6.18 = ( groups2703838992350267259T_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8304_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_real,S: set_real,H2: real > real,G: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ T5 )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ G @ S )
% 5.82/6.18 = ( groups1681761925125756287l_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8305_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ S )
% 5.82/6.18 = ( groups9004974159866482096r_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8306_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,H2: complex > real,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ S )
% 5.82/6.18 = ( groups766887009212190081x_real @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8307_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_VEBT_VEBT,S: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ T5 )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ S @ T5 )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ S )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8308_prod_Omono__neutral__cong__left,axiom,
% 5.82/6.18 ! [T5: set_real,S: set_real,H2: real > rat,G: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ T5 )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ S @ T5 )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ ( minus_minus_set_real @ T5 @ S ) )
% 5.82/6.18 => ( ( H2 @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [X4: real] :
% 5.82/6.18 ( ( member_real @ X4 @ S )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = ( H2 @ X4 ) ) )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat @ G @ S )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ H2 @ T5 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_cong_left
% 5.82/6.18 thf(fact_8309_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8310_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( groups4150731942483176573x_assn @ G @ T5 )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8311_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ T5 )
% 5.82/6.18 = ( groups9004974159866482096r_real @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8312_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ T5 )
% 5.82/6.18 = ( groups766887009212190081x_real @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8313_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat @ G @ T5 )
% 5.82/6.18 = ( groups2555765274223993564er_rat @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8314_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat @ G @ T5 )
% 5.82/6.18 = ( groups225925009352817453ex_rat @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8315_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_nat ) )
% 5.82/6.18 => ( ( groups3190895334310489300er_nat @ G @ T5 )
% 5.82/6.18 = ( groups3190895334310489300er_nat @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8316_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_nat ) )
% 5.82/6.18 => ( ( groups861055069439313189ex_nat @ G @ T5 )
% 5.82/6.18 = ( groups861055069439313189ex_nat @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8317_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_int ) )
% 5.82/6.18 => ( ( groups3188404863801439024er_int @ G @ T5 )
% 5.82/6.18 = ( groups3188404863801439024er_int @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8318_prod_Omono__neutral__right,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > int] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_int ) )
% 5.82/6.18 => ( ( groups858564598930262913ex_int @ G @ T5 )
% 5.82/6.18 = ( groups858564598930262913ex_int @ G @ S ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_right
% 5.82/6.18 thf(fact_8319_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( groups1304777262505850412r_assn @ G @ S )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8320_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( groups4150731942483176573x_assn @ G @ S )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8321_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ S )
% 5.82/6.18 = ( groups9004974159866482096r_real @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8322_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ S )
% 5.82/6.18 = ( groups766887009212190081x_real @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8323_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat @ G @ S )
% 5.82/6.18 = ( groups2555765274223993564er_rat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8324_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat @ G @ S )
% 5.82/6.18 = ( groups225925009352817453ex_rat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8325_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_nat ) )
% 5.82/6.18 => ( ( groups3190895334310489300er_nat @ G @ S )
% 5.82/6.18 = ( groups3190895334310489300er_nat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8326_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_nat ) )
% 5.82/6.18 => ( ( groups861055069439313189ex_nat @ G @ S )
% 5.82/6.18 = ( groups861055069439313189ex_nat @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8327_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ T5 )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ S @ T5 )
% 5.82/6.18 => ( ! [X4: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X4 @ ( minus_2355218937544613996nteger @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_int ) )
% 5.82/6.18 => ( ( groups3188404863801439024er_int @ G @ S )
% 5.82/6.18 = ( groups3188404863801439024er_int @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8328_prod_Omono__neutral__left,axiom,
% 5.82/6.18 ! [T5: set_complex,S: set_complex,G: complex > int] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ T5 )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ S @ T5 )
% 5.82/6.18 => ( ! [X4: complex] :
% 5.82/6.18 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T5 @ S ) )
% 5.82/6.18 => ( ( G @ X4 )
% 5.82/6.18 = one_one_int ) )
% 5.82/6.18 => ( ( groups858564598930262913ex_int @ G @ S )
% 5.82/6.18 = ( groups858564598930262913ex_int @ G @ T5 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.mono_neutral_left
% 5.82/6.18 thf(fact_8329_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups569574905686396791T_assn @ G @ C )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ C ) )
% 5.82/6.18 => ( ( groups569574905686396791T_assn @ G @ A )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8330_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_real,A: set_real,B: set_real,G: real > assn,H2: real > assn] :
% 5.82/6.18 ( ( finite_finite_real @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups1155561341820557179l_assn @ G @ C )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ C ) )
% 5.82/6.18 => ( ( groups1155561341820557179l_assn @ G @ A )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8331_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups1304777262505850412r_assn @ G @ C )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ C ) )
% 5.82/6.18 => ( ( groups1304777262505850412r_assn @ G @ A )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8332_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_complex,A: set_complex,B: set_complex,G: complex > assn,H2: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ B @ C )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups4150731942483176573x_assn @ G @ C )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ C ) )
% 5.82/6.18 => ( ( groups4150731942483176573x_assn @ G @ A )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8333_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups2703838992350267259T_real @ G @ C )
% 5.82/6.18 = ( groups2703838992350267259T_real @ H2 @ C ) )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ A )
% 5.82/6.18 = ( groups2703838992350267259T_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8334_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_real,A: set_real,B: set_real,G: real > real,H2: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups1681761925125756287l_real @ G @ C )
% 5.82/6.18 = ( groups1681761925125756287l_real @ H2 @ C ) )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ G @ A )
% 5.82/6.18 = ( groups1681761925125756287l_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8335_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups9004974159866482096r_real @ G @ C )
% 5.82/6.18 = ( groups9004974159866482096r_real @ H2 @ C ) )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ A )
% 5.82/6.18 = ( groups9004974159866482096r_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8336_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_complex,A: set_complex,B: set_complex,G: complex > real,H2: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ B @ C )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups766887009212190081x_real @ G @ C )
% 5.82/6.18 = ( groups766887009212190081x_real @ H2 @ C ) )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ A )
% 5.82/6.18 = ( groups766887009212190081x_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8337_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( ( groups5726676334696518183BT_rat @ G @ C )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ H2 @ C ) )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ A )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8338_prod_Osame__carrierI,axiom,
% 5.82/6.18 ! [C: set_real,A: set_real,B: set_real,G: real > rat,H2: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( ( groups4061424788464935467al_rat @ G @ C )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ H2 @ C ) )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat @ G @ A )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrierI
% 5.82/6.18 thf(fact_8339_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups569574905686396791T_assn @ G @ A )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ B ) )
% 5.82/6.18 = ( ( groups569574905686396791T_assn @ G @ C )
% 5.82/6.18 = ( groups569574905686396791T_assn @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8340_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_real,A: set_real,B: set_real,G: real > assn,H2: real > assn] :
% 5.82/6.18 ( ( finite_finite_real @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups1155561341820557179l_assn @ G @ A )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ B ) )
% 5.82/6.18 = ( ( groups1155561341820557179l_assn @ G @ C )
% 5.82/6.18 = ( groups1155561341820557179l_assn @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8341_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups1304777262505850412r_assn @ G @ A )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ B ) )
% 5.82/6.18 = ( ( groups1304777262505850412r_assn @ G @ C )
% 5.82/6.18 = ( groups1304777262505850412r_assn @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8342_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_complex,A: set_complex,B: set_complex,G: complex > assn,H2: complex > assn] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ B @ C )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 => ( ( ( groups4150731942483176573x_assn @ G @ A )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ B ) )
% 5.82/6.18 = ( ( groups4150731942483176573x_assn @ G @ C )
% 5.82/6.18 = ( groups4150731942483176573x_assn @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8343_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups2703838992350267259T_real @ G @ A )
% 5.82/6.18 = ( groups2703838992350267259T_real @ H2 @ B ) )
% 5.82/6.18 = ( ( groups2703838992350267259T_real @ G @ C )
% 5.82/6.18 = ( groups2703838992350267259T_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8344_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_real,A: set_real,B: set_real,G: real > real,H2: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups1681761925125756287l_real @ G @ A )
% 5.82/6.18 = ( groups1681761925125756287l_real @ H2 @ B ) )
% 5.82/6.18 = ( ( groups1681761925125756287l_real @ G @ C )
% 5.82/6.18 = ( groups1681761925125756287l_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8345_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_Code_integer,A: set_Code_integer,B: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ C )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ B @ C )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups9004974159866482096r_real @ G @ A )
% 5.82/6.18 = ( groups9004974159866482096r_real @ H2 @ B ) )
% 5.82/6.18 = ( ( groups9004974159866482096r_real @ G @ C )
% 5.82/6.18 = ( groups9004974159866482096r_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8346_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_complex,A: set_complex,B: set_complex,G: complex > real,H2: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ C )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ B @ C )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 => ( ( ( groups766887009212190081x_real @ G @ A )
% 5.82/6.18 = ( groups766887009212190081x_real @ H2 @ B ) )
% 5.82/6.18 = ( ( groups766887009212190081x_real @ G @ C )
% 5.82/6.18 = ( groups766887009212190081x_real @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8347_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_VEBT_VEBT,A: set_VEBT_VEBT,B: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ C )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ B @ C )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( ( groups5726676334696518183BT_rat @ G @ A )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ H2 @ B ) )
% 5.82/6.18 = ( ( groups5726676334696518183BT_rat @ G @ C )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8348_prod_Osame__carrier,axiom,
% 5.82/6.18 ! [C: set_real,A: set_real,B: set_real,G: real > rat,H2: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ C )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ B @ C )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ ( minus_minus_set_real @ C @ A ) )
% 5.82/6.18 => ( ( G @ A3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ C @ B ) )
% 5.82/6.18 => ( ( H2 @ B3 )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 => ( ( ( groups4061424788464935467al_rat @ G @ A )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ H2 @ B ) )
% 5.82/6.18 = ( ( groups4061424788464935467al_rat @ G @ C )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ H2 @ C ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.same_carrier
% 5.82/6.18 thf(fact_8349_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > real] :
% 5.82/6.18 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( groups9004974159866482096r_real @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups9004974159866482096r_real @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8350_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,G: complex > real] :
% 5.82/6.18 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups766887009212190081x_real @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8351_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.18 => ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A @ B ) ) @ ( groups129246275422532515t_real @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8352_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > rat] :
% 5.82/6.18 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups2555765274223993564er_rat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8353_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,G: complex > rat] :
% 5.82/6.18 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups225925009352817453ex_rat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8354_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_set_nat @ B @ A )
% 5.82/6.18 => ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ B ) ) @ ( groups73079841787564623at_rat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8355_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > nat] :
% 5.82/6.18 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups3190895334310489300er_nat @ G @ A )
% 5.82/6.18 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups3190895334310489300er_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8356_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,G: complex > nat] :
% 5.82/6.18 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups861055069439313189ex_nat @ G @ A )
% 5.82/6.18 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups861055069439313189ex_nat @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8357_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,G: code_integer > int] :
% 5.82/6.18 ( ( ord_le7084787975880047091nteger @ B @ A )
% 5.82/6.18 => ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups3188404863801439024er_int @ G @ A )
% 5.82/6.18 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A @ B ) ) @ ( groups3188404863801439024er_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8358_prod_Osubset__diff,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,G: complex > int] :
% 5.82/6.18 ( ( ord_le211207098394363844omplex @ B @ A )
% 5.82/6.18 => ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups858564598930262913ex_int @ G @ A )
% 5.82/6.18 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A @ B ) ) @ ( groups858564598930262913ex_int @ G @ B ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.subset_diff
% 5.82/6.18 thf(fact_8359_of__nat__floor,axiom,
% 5.82/6.18 ! [R2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.82/6.18 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % of_nat_floor
% 5.82/6.18 thf(fact_8360_of__nat__floor,axiom,
% 5.82/6.18 ! [R2: rat] :
% 5.82/6.18 ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.82/6.18 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % of_nat_floor
% 5.82/6.18 thf(fact_8361_one__add__floor,axiom,
% 5.82/6.18 ! [X2: real] :
% 5.82/6.18 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.82/6.18 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % one_add_floor
% 5.82/6.18 thf(fact_8362_one__add__floor,axiom,
% 5.82/6.18 ! [X2: rat] :
% 5.82/6.18 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.82/6.18 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % one_add_floor
% 5.82/6.18 thf(fact_8363_floor__divide__of__nat__eq,axiom,
% 5.82/6.18 ! [M: nat,N: nat] :
% 5.82/6.18 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.82/6.18 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_of_nat_eq
% 5.82/6.18 thf(fact_8364_floor__divide__of__nat__eq,axiom,
% 5.82/6.18 ! [M: nat,N: nat] :
% 5.82/6.18 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.82/6.18 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_of_nat_eq
% 5.82/6.18 thf(fact_8365_le__mult__nat__floor,axiom,
% 5.82/6.18 ! [A2: real,B2: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A2 ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B2 ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A2 @ B2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_mult_nat_floor
% 5.82/6.18 thf(fact_8366_le__mult__nat__floor,axiom,
% 5.82/6.18 ! [A2: rat,B2: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A2 ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B2 ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_mult_nat_floor
% 5.82/6.18 thf(fact_8367_prod_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_lessThan_Suc
% 5.82/6.18 thf(fact_8368_prod_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_lessThan_Suc
% 5.82/6.18 thf(fact_8369_prod_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_lessThan_Suc
% 5.82/6.18 thf(fact_8370_prod_OatLeast0__lessThan__Suc,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_lessThan_Suc
% 5.82/6.18 thf(fact_8371_prod_OatLeast__Suc__lessThan,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_nat @ M @ N )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_lessThan
% 5.82/6.18 thf(fact_8372_prod_OatLeast__Suc__lessThan,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_nat @ M @ N )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_lessThan
% 5.82/6.18 thf(fact_8373_prod_OatLeast__Suc__lessThan,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_nat @ M @ N )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_lessThan
% 5.82/6.18 thf(fact_8374_prod_OatLeast__Suc__lessThan,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_nat @ M @ N )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_lessThan
% 5.82/6.18 thf(fact_8375_prod_OatLeast0__atMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_atMost_Suc
% 5.82/6.18 thf(fact_8376_prod_OatLeast0__atMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_atMost_Suc
% 5.82/6.18 thf(fact_8377_prod_OatLeast0__atMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_atMost_Suc
% 5.82/6.18 thf(fact_8378_prod_OatLeast0__atMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast0_atMost_Suc
% 5.82/6.18 thf(fact_8379_prod_OatLeastLessThan__Suc,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_Suc
% 5.82/6.18 thf(fact_8380_prod_OatLeastLessThan__Suc,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_Suc
% 5.82/6.18 thf(fact_8381_prod_OatLeastLessThan__Suc,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.18 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_Suc
% 5.82/6.18 thf(fact_8382_prod_OatLeastLessThan__Suc,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A2 @ ( suc @ B2 ) ) )
% 5.82/6.18 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A2 @ B2 ) ) @ ( G @ B2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_Suc
% 5.82/6.18 thf(fact_8383_prod_OatLeast__Suc__atMost,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_atMost
% 5.82/6.18 thf(fact_8384_prod_OatLeast__Suc__atMost,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_atMost
% 5.82/6.18 thf(fact_8385_prod_OatLeast__Suc__atMost,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_atMost
% 5.82/6.18 thf(fact_8386_prod_OatLeast__Suc__atMost,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast_Suc_atMost
% 5.82/6.18 thf(fact_8387_prod_Onat__ivl__Suc_H,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_ivl_Suc'
% 5.82/6.18 thf(fact_8388_prod_Onat__ivl__Suc_H,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_ivl_Suc'
% 5.82/6.18 thf(fact_8389_prod_Onat__ivl__Suc_H,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_ivl_Suc'
% 5.82/6.18 thf(fact_8390_prod_Onat__ivl__Suc_H,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_ivl_Suc'
% 5.82/6.18 thf(fact_8391_nat__floor__neg,axiom,
% 5.82/6.18 ! [X2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.18 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.18 = zero_zero_nat ) ) ).
% 5.82/6.18
% 5.82/6.18 % nat_floor_neg
% 5.82/6.18 thf(fact_8392_prod_Olast__plus,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_real @ ( G @ N ) @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.last_plus
% 5.82/6.18 thf(fact_8393_prod_Olast__plus,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ N ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.last_plus
% 5.82/6.18 thf(fact_8394_prod_Olast__plus,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_int @ ( G @ N ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.last_plus
% 5.82/6.18 thf(fact_8395_prod_Olast__plus,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ N ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.last_plus
% 5.82/6.18 thf(fact_8396_floor__eq3,axiom,
% 5.82/6.18 ! [N: nat,X2: real] :
% 5.82/6.18 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.82/6.18 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.82/6.18 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.18 = N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_eq3
% 5.82/6.18 thf(fact_8397_ceiling__altdef,axiom,
% 5.82/6.18 ( archim7802044766580827645g_real
% 5.82/6.18 = ( ^ [X3: real] :
% 5.82/6.18 ( if_int
% 5.82/6.18 @ ( X3
% 5.82/6.18 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) )
% 5.82/6.18 @ ( archim6058952711729229775r_real @ X3 )
% 5.82/6.18 @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % ceiling_altdef
% 5.82/6.18 thf(fact_8398_ceiling__altdef,axiom,
% 5.82/6.18 ( archim2889992004027027881ng_rat
% 5.82/6.18 = ( ^ [X3: rat] :
% 5.82/6.18 ( if_int
% 5.82/6.18 @ ( X3
% 5.82/6.18 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 5.82/6.18 @ ( archim3151403230148437115or_rat @ X3 )
% 5.82/6.18 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % ceiling_altdef
% 5.82/6.18 thf(fact_8399_le__nat__floor,axiom,
% 5.82/6.18 ! [X2: nat,A2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A2 )
% 5.82/6.18 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_nat_floor
% 5.82/6.18 thf(fact_8400_gbinomial__addition__formula,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( gbinomial_real @ A2 @ ( suc @ K ) )
% 5.82/6.18 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_addition_formula
% 5.82/6.18 thf(fact_8401_gbinomial__addition__formula,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( gbinomial_rat @ A2 @ ( suc @ K ) )
% 5.82/6.18 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_addition_formula
% 5.82/6.18 thf(fact_8402_ceiling__diff__floor__le__1,axiom,
% 5.82/6.18 ! [X2: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) @ one_one_int ) ).
% 5.82/6.18
% 5.82/6.18 % ceiling_diff_floor_le_1
% 5.82/6.18 thf(fact_8403_ceiling__diff__floor__le__1,axiom,
% 5.82/6.18 ! [X2: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) @ one_one_int ) ).
% 5.82/6.18
% 5.82/6.18 % ceiling_diff_floor_le_1
% 5.82/6.18 thf(fact_8404_gbinomial__mult__1,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( times_times_rat @ A2 @ ( gbinomial_rat @ A2 @ K ) )
% 5.82/6.18 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A2 @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A2 @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_mult_1
% 5.82/6.18 thf(fact_8405_gbinomial__mult__1,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( times_times_real @ A2 @ ( gbinomial_real @ A2 @ K ) )
% 5.82/6.18 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A2 @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A2 @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_mult_1
% 5.82/6.18 thf(fact_8406_gbinomial__mult__1_H,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( times_times_rat @ ( gbinomial_rat @ A2 @ K ) @ A2 )
% 5.82/6.18 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A2 @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A2 @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_mult_1'
% 5.82/6.18 thf(fact_8407_gbinomial__mult__1_H,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( times_times_real @ ( gbinomial_real @ A2 @ K ) @ A2 )
% 5.82/6.18 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A2 @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A2 @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_mult_1'
% 5.82/6.18 thf(fact_8408_gbinomial__absorb__comp,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( times_times_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A2 @ K ) )
% 5.82/6.18 = ( times_times_rat @ A2 @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorb_comp
% 5.82/6.18 thf(fact_8409_gbinomial__absorb__comp,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( times_times_real @ ( minus_minus_real @ A2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A2 @ K ) )
% 5.82/6.18 = ( times_times_real @ A2 @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorb_comp
% 5.82/6.18 thf(fact_8410_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.82/6.18 ! [K: nat,A2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A2 )
% 5.82/6.18 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A2 @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_ge_n_over_k_pow_k
% 5.82/6.18 thf(fact_8411_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.82/6.18 ! [K: nat,A2: rat] :
% 5.82/6.18 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A2 )
% 5.82/6.18 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A2 @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_ge_n_over_k_pow_k
% 5.82/6.18 thf(fact_8412_real__of__int__floor__add__one__gt,axiom,
% 5.82/6.18 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.82/6.18
% 5.82/6.18 % real_of_int_floor_add_one_gt
% 5.82/6.18 thf(fact_8413_floor__eq,axiom,
% 5.82/6.18 ! [N: int,X2: real] :
% 5.82/6.18 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.82/6.18 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ X2 )
% 5.82/6.18 = N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_eq
% 5.82/6.18 thf(fact_8414_real__of__int__floor__add__one__ge,axiom,
% 5.82/6.18 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.82/6.18
% 5.82/6.18 % real_of_int_floor_add_one_ge
% 5.82/6.18 thf(fact_8415_real__of__int__floor__gt__diff__one,axiom,
% 5.82/6.18 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % real_of_int_floor_gt_diff_one
% 5.82/6.18 thf(fact_8416_real__of__int__floor__ge__diff__one,axiom,
% 5.82/6.18 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % real_of_int_floor_ge_diff_one
% 5.82/6.18 thf(fact_8417_prod_OlessThan__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.lessThan_Suc_shift
% 5.82/6.18 thf(fact_8418_prod_OlessThan__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.lessThan_Suc_shift
% 5.82/6.18 thf(fact_8419_prod_OlessThan__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.lessThan_Suc_shift
% 5.82/6.18 thf(fact_8420_prod_OlessThan__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.lessThan_Suc_shift
% 5.82/6.18 thf(fact_8421_prod_OSuc__reindex__ivl,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( G @ M )
% 5.82/6.18 @ ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.Suc_reindex_ivl
% 5.82/6.18 thf(fact_8422_prod_OSuc__reindex__ivl,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ M )
% 5.82/6.18 @ ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.Suc_reindex_ivl
% 5.82/6.18 thf(fact_8423_prod_OSuc__reindex__ivl,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > int] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( G @ M )
% 5.82/6.18 @ ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.Suc_reindex_ivl
% 5.82/6.18 thf(fact_8424_prod_OSuc__reindex__ivl,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.18 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ M )
% 5.82/6.18 @ ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.Suc_reindex_ivl
% 5.82/6.18 thf(fact_8425_prod_OatLeastLessThan__rev,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat,M: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_rev
% 5.82/6.18 thf(fact_8426_prod_OatLeastLessThan__rev,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat,M: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_rev
% 5.82/6.18 thf(fact_8427_prod_Onested__swap,axiom,
% 5.82/6.18 ! [A2: nat > nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A2 @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [J3: nat] :
% 5.82/6.18 ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nested_swap
% 5.82/6.18 thf(fact_8428_prod_Onested__swap,axiom,
% 5.82/6.18 ! [A2: nat > nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A2 @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [J3: nat] :
% 5.82/6.18 ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nested_swap
% 5.82/6.18 thf(fact_8429_prod_OatLeast1__atMost__eq,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast1_atMost_eq
% 5.82/6.18 thf(fact_8430_prod_OatLeast1__atMost__eq,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeast1_atMost_eq
% 5.82/6.18 thf(fact_8431_prod_Onat__group,axiom,
% 5.82/6.18 ! [G: nat > int,K: nat,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [M6: nat] : ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M6 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M6 @ K ) @ K ) ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.18 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_group
% 5.82/6.18 thf(fact_8432_prod_Onat__group,axiom,
% 5.82/6.18 ! [G: nat > nat,K: nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [M6: nat] : ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M6 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M6 @ K ) @ K ) ) )
% 5.82/6.18 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.18 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.nat_group
% 5.82/6.18 thf(fact_8433_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bo8194388402131092736T_VEBT )
% 5.82/6.18 => ( ord_less_real @ ( groups2703838992350267259T_real @ F @ A ) @ ( groups2703838992350267259T_real @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8434_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_real,F: real > real,G: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bot_set_real )
% 5.82/6.18 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A ) @ ( groups1681761925125756287l_real @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8435_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ! [I2: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bo3990330152332043303nteger )
% 5.82/6.18 => ( ord_less_real @ ( groups9004974159866482096r_real @ F @ A ) @ ( groups9004974159866482096r_real @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8436_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > real,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ! [I2: complex] :
% 5.82/6.18 ( ( member_complex @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bot_set_complex )
% 5.82/6.18 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A ) @ ( groups766887009212190081x_real @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8437_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_nat,F: nat > real,G: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bot_set_nat )
% 5.82/6.18 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A ) @ ( groups129246275422532515t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8438_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_int,F: int > real,G: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bot_set_int )
% 5.82/6.18 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A ) @ ( groups2316167850115554303t_real @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8439_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bo8194388402131092736T_VEBT )
% 5.82/6.18 => ( ord_less_rat @ ( groups5726676334696518183BT_rat @ F @ A ) @ ( groups5726676334696518183BT_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8440_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_real,F: real > rat,G: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bot_set_real )
% 5.82/6.18 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A ) @ ( groups4061424788464935467al_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8441_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ! [I2: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bo3990330152332043303nteger )
% 5.82/6.18 => ( ord_less_rat @ ( groups2555765274223993564er_rat @ F @ A ) @ ( groups2555765274223993564er_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8442_prod__mono__strict,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > rat,G: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ! [I2: complex] :
% 5.82/6.18 ( ( member_complex @ I2 @ A )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.82/6.18 & ( ord_less_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.82/6.18 => ( ( A != bot_bot_set_complex )
% 5.82/6.18 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A ) @ ( groups225925009352817453ex_rat @ G @ A ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono_strict
% 5.82/6.18 thf(fact_8443_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_int,F: int > nat] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A ) )
% 5.82/6.18 = ( ? [X3: int] :
% 5.82/6.18 ( ( member_int @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8444_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3190895334310489300er_nat @ F @ A ) )
% 5.82/6.18 = ( ? [X3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8445_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A ) )
% 5.82/6.18 = ( ? [X3: complex] :
% 5.82/6.18 ( ( member_complex @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8446_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > int] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3188404863801439024er_int @ F @ A ) )
% 5.82/6.18 = ( ? [X3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8447_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > int] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A ) )
% 5.82/6.18 = ( ? [X3: complex] :
% 5.82/6.18 ( ( member_complex @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8448_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_nat,F: nat > int] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A ) )
% 5.82/6.18 = ( ? [X3: nat] :
% 5.82/6.18 ( ( member_nat @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8449_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_int,F: int > int] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A ) )
% 5.82/6.18 = ( ? [X3: int] :
% 5.82/6.18 ( ( member_int @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8450_even__prod__iff,axiom,
% 5.82/6.18 ! [A: set_nat,F: nat > nat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A ) )
% 5.82/6.18 = ( ? [X3: nat] :
% 5.82/6.18 ( ( member_nat @ X3 @ A )
% 5.82/6.18 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % even_prod_iff
% 5.82/6.18 thf(fact_8451_floor__unique,axiom,
% 5.82/6.18 ! [Z: int,X2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 )
% 5.82/6.18 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ X2 )
% 5.82/6.18 = Z ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_unique
% 5.82/6.18 thf(fact_8452_floor__unique,axiom,
% 5.82/6.18 ! [Z: int,X2: rat] :
% 5.82/6.18 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 )
% 5.82/6.18 => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.82/6.18 => ( ( archim3151403230148437115or_rat @ X2 )
% 5.82/6.18 = Z ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_unique
% 5.82/6.18 thf(fact_8453_floor__eq__iff,axiom,
% 5.82/6.18 ! [X2: real,A2: int] :
% 5.82/6.18 ( ( ( archim6058952711729229775r_real @ X2 )
% 5.82/6.18 = A2 )
% 5.82/6.18 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A2 ) @ X2 )
% 5.82/6.18 & ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ A2 ) @ one_one_real ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_eq_iff
% 5.82/6.18 thf(fact_8454_floor__eq__iff,axiom,
% 5.82/6.18 ! [X2: rat,A2: int] :
% 5.82/6.18 ( ( ( archim3151403230148437115or_rat @ X2 )
% 5.82/6.18 = A2 )
% 5.82/6.18 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A2 ) @ X2 )
% 5.82/6.18 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A2 ) @ one_one_rat ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_eq_iff
% 5.82/6.18 thf(fact_8455_floor__split,axiom,
% 5.82/6.18 ! [P: int > $o,T: real] :
% 5.82/6.18 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.82/6.18 = ( ! [I4: int] :
% 5.82/6.18 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 5.82/6.18 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 5.82/6.18 => ( P @ I4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_split
% 5.82/6.18 thf(fact_8456_floor__split,axiom,
% 5.82/6.18 ! [P: int > $o,T: rat] :
% 5.82/6.18 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.82/6.18 = ( ! [I4: int] :
% 5.82/6.18 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 5.82/6.18 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 5.82/6.18 => ( P @ I4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_split
% 5.82/6.18 thf(fact_8457_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8458_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_Code_integer,G: code_integer > real,X2: code_integer] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups9004974159866482096r_real @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8459_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_complex,G: complex > real,X2: complex] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8460_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_int,G: int > real,X2: int] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8461_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_nat,G: nat > real,X2: nat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8462_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,G: vEBT_VEBT > rat,X2: vEBT_VEBT] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8463_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_Code_integer,G: code_integer > rat,X2: code_integer] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat @ G @ ( insert_Code_integer @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8464_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_complex,G: complex > rat,X2: complex] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8465_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_int,G: int > rat,X2: int] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8466_prod_Oinsert__remove,axiom,
% 5.82/6.18 ! [A: set_nat,G: nat > rat,X2: nat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.insert_remove
% 5.82/6.18 thf(fact_8467_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8468_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_real,X2: real,G: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ( member_real @ X2 @ A )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8469_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_Code_integer,X2: code_integer,G: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( member_Code_integer @ X2 @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups9004974159866482096r_real @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8470_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_complex,X2: complex,G: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( member_complex @ X2 @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8471_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_int,X2: int,G: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( member_int @ X2 @ A )
% 5.82/6.18 => ( ( groups2316167850115554303t_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8472_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_nat,X2: nat,G: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( member_nat @ X2 @ A )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ A )
% 5.82/6.18 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8473_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( member_VEBT_VEBT @ X2 @ A )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8474_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_real,X2: real,G: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ( member_real @ X2 @ A )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ ( minus_minus_set_real @ A @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8475_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_Code_integer,X2: code_integer,G: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( member_Code_integer @ X2 @ A )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8476_prod_Oremove,axiom,
% 5.82/6.18 ! [A: set_complex,X2: complex,G: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( member_complex @ X2 @ A )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat @ G @ A )
% 5.82/6.18 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.remove
% 5.82/6.18 thf(fact_8477_less__floor__iff,axiom,
% 5.82/6.18 ! [Z: int,X2: real] :
% 5.82/6.18 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.18 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_floor_iff
% 5.82/6.18 thf(fact_8478_less__floor__iff,axiom,
% 5.82/6.18 ! [Z: int,X2: rat] :
% 5.82/6.18 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.82/6.18 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % less_floor_iff
% 5.82/6.18 thf(fact_8479_floor__le__iff,axiom,
% 5.82/6.18 ! [X2: real,Z: int] :
% 5.82/6.18 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.82/6.18 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_le_iff
% 5.82/6.18 thf(fact_8480_floor__le__iff,axiom,
% 5.82/6.18 ! [X2: rat,Z: int] :
% 5.82/6.18 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.82/6.18 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_le_iff
% 5.82/6.18 thf(fact_8481_le__mult__floor,axiom,
% 5.82/6.18 ! [A2: real,B2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.82/6.18 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.82/6.18 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A2 ) @ ( archim6058952711729229775r_real @ B2 ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_mult_floor
% 5.82/6.18 thf(fact_8482_le__mult__floor,axiom,
% 5.82/6.18 ! [A2: rat,B2: rat] :
% 5.82/6.18 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.82/6.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.82/6.18 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A2 ) @ ( archim3151403230148437115or_rat @ B2 ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % le_mult_floor
% 5.82/6.18 thf(fact_8483_floor__correct,axiom,
% 5.82/6.18 ! [X2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 )
% 5.82/6.18 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_correct
% 5.82/6.18 thf(fact_8484_floor__correct,axiom,
% 5.82/6.18 ! [X2: rat] :
% 5.82/6.18 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 5.82/6.18 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_correct
% 5.82/6.18 thf(fact_8485_prod_Oub__add__nat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > real,P6: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ub_add_nat
% 5.82/6.18 thf(fact_8486_prod_Oub__add__nat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > rat,P6: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ub_add_nat
% 5.82/6.18 thf(fact_8487_prod_Oub__add__nat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > int,P6: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ub_add_nat
% 5.82/6.18 thf(fact_8488_prod_Oub__add__nat,axiom,
% 5.82/6.18 ! [M: nat,N: nat,G: nat > nat,P6: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.82/6.18 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.ub_add_nat
% 5.82/6.18 thf(fact_8489_prod_Ohead__if,axiom,
% 5.82/6.18 ! [N: nat,M: nat,G: nat > assn] :
% 5.82/6.18 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = one_one_assn ) )
% 5.82/6.18 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.head_if
% 5.82/6.18 thf(fact_8490_prod_Ohead__if,axiom,
% 5.82/6.18 ! [N: nat,M: nat,G: nat > real] :
% 5.82/6.18 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = one_one_real ) )
% 5.82/6.18 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.head_if
% 5.82/6.18 thf(fact_8491_prod_Ohead__if,axiom,
% 5.82/6.18 ! [N: nat,M: nat,G: nat > rat] :
% 5.82/6.18 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = one_one_rat ) )
% 5.82/6.18 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.head_if
% 5.82/6.18 thf(fact_8492_prod_Ohead__if,axiom,
% 5.82/6.18 ! [N: nat,M: nat,G: nat > int] :
% 5.82/6.18 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = one_one_int ) )
% 5.82/6.18 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.head_if
% 5.82/6.18 thf(fact_8493_prod_Ohead__if,axiom,
% 5.82/6.18 ! [N: nat,M: nat,G: nat > nat] :
% 5.82/6.18 ( ( ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = one_one_nat ) )
% 5.82/6.18 & ( ~ ( ord_less_nat @ N @ M )
% 5.82/6.18 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.18 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.head_if
% 5.82/6.18 thf(fact_8494_floor__eq4,axiom,
% 5.82/6.18 ! [N: nat,X2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.82/6.18 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.82/6.18 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.82/6.18 = N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_eq4
% 5.82/6.18 thf(fact_8495_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.82/6.18 ! [X2: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y3: nat] :
% 5.82/6.18 ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa @ Xb @ Xc )
% 5.82/6.18 = Y3 )
% 5.82/6.18 => ( ( ( ord_less_nat @ Xb @ Xa )
% 5.82/6.18 => ( Y3 = Xc ) )
% 5.82/6.18 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 5.82/6.18 => ( Y3
% 5.82/6.18 = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X2 @ Xa @ Xc ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % fold_atLeastAtMost_nat.elims
% 5.82/6.18 thf(fact_8496_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.82/6.18 ( set_fo2584398358068434914at_nat
% 5.82/6.18 = ( ^ [F7: nat > nat > nat,A5: nat,B6: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B6 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F7 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B6 @ ( F7 @ A5 @ Acc2 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % fold_atLeastAtMost_nat.simps
% 5.82/6.18 thf(fact_8497_Suc__times__gbinomial,axiom,
% 5.82/6.18 ! [K: nat,A2: rat] :
% 5.82/6.18 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( suc @ K ) ) )
% 5.82/6.18 = ( times_times_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( gbinomial_rat @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Suc_times_gbinomial
% 5.82/6.18 thf(fact_8498_Suc__times__gbinomial,axiom,
% 5.82/6.18 ! [K: nat,A2: real] :
% 5.82/6.18 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( suc @ K ) ) )
% 5.82/6.18 = ( times_times_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( gbinomial_real @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Suc_times_gbinomial
% 5.82/6.18 thf(fact_8499_gbinomial__absorption,axiom,
% 5.82/6.18 ! [K: nat,A2: rat] :
% 5.82/6.18 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A2 @ ( suc @ K ) ) )
% 5.82/6.18 = ( times_times_rat @ A2 @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorption
% 5.82/6.18 thf(fact_8500_gbinomial__absorption,axiom,
% 5.82/6.18 ! [K: nat,A2: real] :
% 5.82/6.18 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A2 @ ( suc @ K ) ) )
% 5.82/6.18 = ( times_times_real @ A2 @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorption
% 5.82/6.18 thf(fact_8501_floor__eq2,axiom,
% 5.82/6.18 ! [N: int,X2: real] :
% 5.82/6.18 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.82/6.18 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ X2 )
% 5.82/6.18 = N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_eq2
% 5.82/6.18 thf(fact_8502_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > real,C2: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.18 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.18 => ( ( groups2703838992350267259T_real
% 5.82/6.18 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_real @ ( B2 @ A2 ) @ ( groups2703838992350267259T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.18 => ( ( groups2703838992350267259T_real
% 5.82/6.18 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups2703838992350267259T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8503_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_real,A2: real,B2: real > real,C2: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ S )
% 5.82/6.18 => ( ( ( member_real @ A2 @ S )
% 5.82/6.18 => ( ( groups1681761925125756287l_real
% 5.82/6.18 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_real @ ( B2 @ A2 ) @ ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.18 => ( ( groups1681761925125756287l_real
% 5.82/6.18 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8504_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > real,C2: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.18 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.18 => ( ( groups9004974159866482096r_real
% 5.82/6.18 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_real @ ( B2 @ A2 ) @ ( groups9004974159866482096r_real @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.18 => ( ( groups9004974159866482096r_real
% 5.82/6.18 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups9004974159866482096r_real @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8505_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_complex,A2: complex,B2: complex > real,C2: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.18 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.18 => ( ( groups766887009212190081x_real
% 5.82/6.18 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_real @ ( B2 @ A2 ) @ ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.18 => ( ( groups766887009212190081x_real
% 5.82/6.18 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8506_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_int,A2: int,B2: int > real,C2: int > real] :
% 5.82/6.18 ( ( finite_finite_int @ S )
% 5.82/6.18 => ( ( ( member_int @ A2 @ S )
% 5.82/6.18 => ( ( groups2316167850115554303t_real
% 5.82/6.18 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_real @ ( B2 @ A2 ) @ ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_int @ A2 @ S )
% 5.82/6.18 => ( ( groups2316167850115554303t_real
% 5.82/6.18 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8507_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_nat,A2: nat,B2: nat > real,C2: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ S )
% 5.82/6.18 => ( ( ( member_nat @ A2 @ S )
% 5.82/6.18 => ( ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [K3: nat] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_real @ ( B2 @ A2 ) @ ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_nat @ A2 @ S )
% 5.82/6.18 => ( ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [K3: nat] : ( if_real @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8508_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_VEBT_VEBT,A2: vEBT_VEBT,B2: vEBT_VEBT > rat,C2: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ S )
% 5.82/6.18 => ( ( ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat
% 5.82/6.18 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_rat @ ( B2 @ A2 ) @ ( groups5726676334696518183BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_VEBT_VEBT @ A2 @ S )
% 5.82/6.18 => ( ( groups5726676334696518183BT_rat
% 5.82/6.18 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups5726676334696518183BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8509_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_real,A2: real,B2: real > rat,C2: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ S )
% 5.82/6.18 => ( ( ( member_real @ A2 @ S )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat
% 5.82/6.18 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_rat @ ( B2 @ A2 ) @ ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_real @ A2 @ S )
% 5.82/6.18 => ( ( groups4061424788464935467al_rat
% 5.82/6.18 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8510_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_Code_integer,A2: code_integer,B2: code_integer > rat,C2: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ S )
% 5.82/6.18 => ( ( ( member_Code_integer @ A2 @ S )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat
% 5.82/6.18 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_rat @ ( B2 @ A2 ) @ ( groups2555765274223993564er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_Code_integer @ A2 @ S )
% 5.82/6.18 => ( ( groups2555765274223993564er_rat
% 5.82/6.18 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups2555765274223993564er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8511_prod_Odelta__remove,axiom,
% 5.82/6.18 ! [S: set_complex,A2: complex,B2: complex > rat,C2: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ S )
% 5.82/6.18 => ( ( ( member_complex @ A2 @ S )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat
% 5.82/6.18 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( times_times_rat @ ( B2 @ A2 ) @ ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.82/6.18 & ( ~ ( member_complex @ A2 @ S )
% 5.82/6.18 => ( ( groups225925009352817453ex_rat
% 5.82/6.18 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B2 @ K3 ) @ ( C2 @ K3 ) )
% 5.82/6.18 @ S )
% 5.82/6.18 = ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.delta_remove
% 5.82/6.18 thf(fact_8512_floor__divide__real__eq__div,axiom,
% 5.82/6.18 ! [B2: int,A2: real] :
% 5.82/6.18 ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A2 @ ( ring_1_of_int_real @ B2 ) ) )
% 5.82/6.18 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A2 ) @ B2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_real_eq_div
% 5.82/6.18 thf(fact_8513_gbinomial__trinomial__revision,axiom,
% 5.82/6.18 ! [K: nat,M: nat,A2: rat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.18 => ( ( times_times_rat @ ( gbinomial_rat @ A2 @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.82/6.18 = ( times_times_rat @ ( gbinomial_rat @ A2 @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_trinomial_revision
% 5.82/6.18 thf(fact_8514_gbinomial__trinomial__revision,axiom,
% 5.82/6.18 ! [K: nat,M: nat,A2: real] :
% 5.82/6.18 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.18 => ( ( times_times_real @ ( gbinomial_real @ A2 @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.82/6.18 = ( times_times_real @ ( gbinomial_real @ A2 @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_trinomial_revision
% 5.82/6.18 thf(fact_8515_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_VEBT_VEBT,Z: vEBT_VEBT > real,W: vEBT_VEBT > real] :
% 5.82/6.18 ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2703838992350267259T_real @ Z @ I6 ) @ ( groups2703838992350267259T_real @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups2240296850493347238T_real
% 5.82/6.18 @ ^ [I4: vEBT_VEBT] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8516_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_real,Z: real > real,W: real > real] :
% 5.82/6.18 ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I6 ) @ ( groups1681761925125756287l_real @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups8097168146408367636l_real
% 5.82/6.18 @ ^ [I4: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8517_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_int,Z: int > real,W: int > real] :
% 5.82/6.18 ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I6 ) @ ( groups2316167850115554303t_real @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups8778361861064173332t_real
% 5.82/6.18 @ ^ [I4: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8518_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_VEBT_VEBT,Z: vEBT_VEBT > complex,W: vEBT_VEBT > complex] :
% 5.82/6.18 ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups127312072573709053omplex @ Z @ I6 ) @ ( groups127312072573709053omplex @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups2240296850493347238T_real
% 5.82/6.18 @ ^ [I4: vEBT_VEBT] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8519_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_real,Z: real > complex,W: real > complex] :
% 5.82/6.18 ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: real] :
% 5.82/6.18 ( ( member_real @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I6 ) @ ( groups713298508707869441omplex @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups8097168146408367636l_real
% 5.82/6.18 @ ^ [I4: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8520_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_int,Z: int > complex,W: int > complex] :
% 5.82/6.18 ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: int] :
% 5.82/6.18 ( ( member_int @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I6 ) @ ( groups7440179247065528705omplex @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups8778361861064173332t_real
% 5.82/6.18 @ ^ [I4: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8521_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_nat,Z: nat > real,W: nat > real] :
% 5.82/6.18 ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I6 ) @ ( groups129246275422532515t_real @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8522_norm__prod__diff,axiom,
% 5.82/6.18 ! [I6: set_nat,Z: nat > complex,W: nat > complex] :
% 5.82/6.18 ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ! [I2: nat] :
% 5.82/6.18 ( ( member_nat @ I2 @ I6 )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I6 ) @ ( groups6464643781859351333omplex @ W @ I6 ) ) )
% 5.82/6.18 @ ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I4 ) @ ( W @ I4 ) ) )
% 5.82/6.18 @ I6 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % norm_prod_diff
% 5.82/6.18 thf(fact_8523_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat,M: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 5.82/6.18 thf(fact_8524_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat,M: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 5.82/6.18 thf(fact_8525_pochhammer__prod,axiom,
% 5.82/6.18 ( comm_s4028243227959126397er_rat
% 5.82/6.18 = ( ^ [A5: rat,N4: nat] :
% 5.82/6.18 ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod
% 5.82/6.18 thf(fact_8526_pochhammer__prod,axiom,
% 5.82/6.18 ( comm_s7457072308508201937r_real
% 5.82/6.18 = ( ^ [A5: real,N4: nat] :
% 5.82/6.18 ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ I4 ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod
% 5.82/6.18 thf(fact_8527_pochhammer__prod,axiom,
% 5.82/6.18 ( comm_s4660882817536571857er_int
% 5.82/6.18 = ( ^ [A5: int,N4: nat] :
% 5.82/6.18 ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod
% 5.82/6.18 thf(fact_8528_pochhammer__prod,axiom,
% 5.82/6.18 ( comm_s4663373288045622133er_nat
% 5.82/6.18 = ( ^ [A5: nat,N4: nat] :
% 5.82/6.18 ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.82/6.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod
% 5.82/6.18 thf(fact_8529_floor__divide__lower,axiom,
% 5.82/6.18 ! [Q3: real,P6: real] :
% 5.82/6.18 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.82/6.18 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_lower
% 5.82/6.18 thf(fact_8530_floor__divide__lower,axiom,
% 5.82/6.18 ! [Q3: rat,P6: rat] :
% 5.82/6.18 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.82/6.18 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_lower
% 5.82/6.18 thf(fact_8531_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A ) @ ( groups2703838992350267259T_real @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8532_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_real,A: set_real,F: real > real] :
% 5.82/6.18 ( ( finite_finite_real @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A ) @ ( groups1681761925125756287l_real @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8533_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > real] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( groups9004974159866482096r_real @ F @ A ) @ ( groups9004974159866482096r_real @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8534_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,F: complex > real] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A ) @ ( groups766887009212190081x_real @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8535_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,F: nat > real] :
% 5.82/6.18 ( ( finite_finite_nat @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.18 => ( ! [B3: nat] :
% 5.82/6.18 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: nat] :
% 5.82/6.18 ( ( member_nat @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A ) @ ( groups129246275422532515t_real @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8536_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_VEBT_VEBT,A: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ B )
% 5.82/6.18 => ( ( ord_le4337996190870823476T_VEBT @ A @ B )
% 5.82/6.18 => ( ! [B3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: vEBT_VEBT] :
% 5.82/6.18 ( ( member_VEBT_VEBT @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A ) @ ( groups5726676334696518183BT_rat @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8537_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_real,A: set_real,F: real > rat] :
% 5.82/6.18 ( ( finite_finite_real @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_real @ A @ B )
% 5.82/6.18 => ( ! [B3: real] :
% 5.82/6.18 ( ( member_real @ B3 @ ( minus_minus_set_real @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: real] :
% 5.82/6.18 ( ( member_real @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A ) @ ( groups4061424788464935467al_rat @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8538_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_Code_integer,A: set_Code_integer,F: code_integer > rat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ B )
% 5.82/6.18 => ( ( ord_le7084787975880047091nteger @ A @ B )
% 5.82/6.18 => ( ! [B3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A ) @ ( groups2555765274223993564er_rat @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8539_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_complex,A: set_complex,F: complex > rat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ B )
% 5.82/6.18 => ( ( ord_le211207098394363844omplex @ A @ B )
% 5.82/6.18 => ( ! [B3: complex] :
% 5.82/6.18 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: complex] :
% 5.82/6.18 ( ( member_complex @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A ) @ ( groups225925009352817453ex_rat @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8540_prod__mono2,axiom,
% 5.82/6.18 ! [B: set_nat,A: set_nat,F: nat > rat] :
% 5.82/6.18 ( ( finite_finite_nat @ B )
% 5.82/6.18 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.82/6.18 => ( ! [B3: nat] :
% 5.82/6.18 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B @ A ) )
% 5.82/6.18 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 5.82/6.18 => ( ! [A3: nat] :
% 5.82/6.18 ( ( member_nat @ A3 @ A )
% 5.82/6.18 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.82/6.18 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A ) @ ( groups73079841787564623at_rat @ F @ B ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_mono2
% 5.82/6.18 thf(fact_8541_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > complex,A2: vEBT_VEBT] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_complex )
% 5.82/6.18 => ( ( ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.18 => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.18 = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.18 => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.18 = ( groups127312072573709053omplex @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8542_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_real,F: real > complex,A2: real] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_complex )
% 5.82/6.18 => ( ( ( member_real @ A2 @ A )
% 5.82/6.18 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.18 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_real @ A2 @ A )
% 5.82/6.18 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.18 = ( groups713298508707869441omplex @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8543_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > complex,A2: code_integer] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_complex )
% 5.82/6.18 => ( ( ( member_Code_integer @ A2 @ A )
% 5.82/6.18 => ( ( groups862514429393162674omplex @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.18 = ( divide1717551699836669952omplex @ ( groups862514429393162674omplex @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_Code_integer @ A2 @ A )
% 5.82/6.18 => ( ( groups862514429393162674omplex @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.18 = ( groups862514429393162674omplex @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8544_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > complex,A2: complex] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_complex )
% 5.82/6.18 => ( ( ( member_complex @ A2 @ A )
% 5.82/6.18 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.18 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_complex @ A2 @ A )
% 5.82/6.18 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.18 = ( groups3708469109370488835omplex @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8545_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_int,F: int > complex,A2: int] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_complex )
% 5.82/6.18 => ( ( ( member_int @ A2 @ A )
% 5.82/6.18 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.18 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_int @ A2 @ A )
% 5.82/6.18 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.82/6.18 = ( groups7440179247065528705omplex @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8546_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_nat,F: nat > complex,A2: nat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_complex )
% 5.82/6.18 => ( ( ( member_nat @ A2 @ A )
% 5.82/6.18 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.18 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_nat @ A2 @ A )
% 5.82/6.18 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.82/6.18 = ( groups6464643781859351333omplex @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8547_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_VEBT_VEBT,F: vEBT_VEBT > real,A2: vEBT_VEBT] :
% 5.82/6.18 ( ( finite5795047828879050333T_VEBT @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_real )
% 5.82/6.18 => ( ( ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.18 = ( divide_divide_real @ ( groups2703838992350267259T_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_VEBT_VEBT @ A2 @ A )
% 5.82/6.18 => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A @ ( insert_VEBT_VEBT @ A2 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.82/6.18 = ( groups2703838992350267259T_real @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8548_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_real,F: real > real,A2: real] :
% 5.82/6.18 ( ( finite_finite_real @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_real )
% 5.82/6.18 => ( ( ( member_real @ A2 @ A )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.18 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_real @ A2 @ A )
% 5.82/6.18 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.82/6.18 = ( groups1681761925125756287l_real @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8549_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > real,A2: code_integer] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_real )
% 5.82/6.18 => ( ( ( member_Code_integer @ A2 @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.18 = ( divide_divide_real @ ( groups9004974159866482096r_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_Code_integer @ A2 @ A )
% 5.82/6.18 => ( ( groups9004974159866482096r_real @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 5.82/6.18 = ( groups9004974159866482096r_real @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8550_prod__diff1,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > real,A2: complex] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( ( F @ A2 )
% 5.82/6.18 != zero_zero_real )
% 5.82/6.18 => ( ( ( member_complex @ A2 @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.18 = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A ) @ ( F @ A2 ) ) ) )
% 5.82/6.18 & ( ~ ( member_complex @ A2 @ A )
% 5.82/6.18 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.82/6.18 = ( groups766887009212190081x_real @ F @ A ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_diff1
% 5.82/6.18 thf(fact_8551_gbinomial__factors,axiom,
% 5.82/6.18 ! [A2: complex,K: nat] :
% 5.82/6.18 ( ( gbinomial_complex @ ( plus_plus_complex @ A2 @ one_one_complex ) @ ( suc @ K ) )
% 5.82/6.18 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A2 @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_factors
% 5.82/6.18 thf(fact_8552_gbinomial__factors,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( gbinomial_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( suc @ K ) )
% 5.82/6.18 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_factors
% 5.82/6.18 thf(fact_8553_gbinomial__factors,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( gbinomial_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( suc @ K ) )
% 5.82/6.18 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A2 @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_factors
% 5.82/6.18 thf(fact_8554_gbinomial__rec,axiom,
% 5.82/6.18 ! [A2: complex,K: nat] :
% 5.82/6.18 ( ( gbinomial_complex @ ( plus_plus_complex @ A2 @ one_one_complex ) @ ( suc @ K ) )
% 5.82/6.18 = ( times_times_complex @ ( gbinomial_complex @ A2 @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A2 @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_rec
% 5.82/6.18 thf(fact_8555_gbinomial__rec,axiom,
% 5.82/6.18 ! [A2: rat,K: nat] :
% 5.82/6.18 ( ( gbinomial_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( suc @ K ) )
% 5.82/6.18 = ( times_times_rat @ ( gbinomial_rat @ A2 @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_rec
% 5.82/6.18 thf(fact_8556_gbinomial__rec,axiom,
% 5.82/6.18 ! [A2: real,K: nat] :
% 5.82/6.18 ( ( gbinomial_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( suc @ K ) )
% 5.82/6.18 = ( times_times_real @ ( gbinomial_real @ A2 @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_rec
% 5.82/6.18 thf(fact_8557_pochhammer__Suc__prod,axiom,
% 5.82/6.18 ! [A2: rat,N: nat] :
% 5.82/6.18 ( ( comm_s4028243227959126397er_rat @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod
% 5.82/6.18 thf(fact_8558_pochhammer__Suc__prod,axiom,
% 5.82/6.18 ! [A2: real,N: nat] :
% 5.82/6.18 ( ( comm_s7457072308508201937r_real @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_real @ A2 @ ( semiri5074537144036343181t_real @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod
% 5.82/6.18 thf(fact_8559_pochhammer__Suc__prod,axiom,
% 5.82/6.18 ! [A2: int,N: nat] :
% 5.82/6.18 ( ( comm_s4660882817536571857er_int @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_int @ A2 @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod
% 5.82/6.18 thf(fact_8560_pochhammer__Suc__prod,axiom,
% 5.82/6.18 ! [A2: nat,N: nat] :
% 5.82/6.18 ( ( comm_s4663373288045622133er_nat @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod
% 5.82/6.18 thf(fact_8561_pochhammer__prod__rev,axiom,
% 5.82/6.18 ( comm_s4028243227959126397er_rat
% 5.82/6.18 = ( ^ [A5: rat,N4: nat] :
% 5.82/6.18 ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod_rev
% 5.82/6.18 thf(fact_8562_pochhammer__prod__rev,axiom,
% 5.82/6.18 ( comm_s7457072308508201937r_real
% 5.82/6.18 = ( ^ [A5: real,N4: nat] :
% 5.82/6.18 ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod_rev
% 5.82/6.18 thf(fact_8563_pochhammer__prod__rev,axiom,
% 5.82/6.18 ( comm_s4660882817536571857er_int
% 5.82/6.18 = ( ^ [A5: int,N4: nat] :
% 5.82/6.18 ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod_rev
% 5.82/6.18 thf(fact_8564_pochhammer__prod__rev,axiom,
% 5.82/6.18 ( comm_s4663373288045622133er_nat
% 5.82/6.18 = ( ^ [A5: nat,N4: nat] :
% 5.82/6.18 ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_prod_rev
% 5.82/6.18 thf(fact_8565_floor__divide__upper,axiom,
% 5.82/6.18 ! [Q3: real,P6: real] :
% 5.82/6.18 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.82/6.18 => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_upper
% 5.82/6.18 thf(fact_8566_floor__divide__upper,axiom,
% 5.82/6.18 ! [Q3: rat,P6: rat] :
% 5.82/6.18 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.82/6.18 => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_divide_upper
% 5.82/6.18 thf(fact_8567_round__def,axiom,
% 5.82/6.18 ( archim8280529875227126926d_real
% 5.82/6.18 = ( ^ [X3: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % round_def
% 5.82/6.18 thf(fact_8568_round__def,axiom,
% 5.82/6.18 ( archim7778729529865785530nd_rat
% 5.82/6.18 = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % round_def
% 5.82/6.18 thf(fact_8569_prod_Oin__pairs,axiom,
% 5.82/6.18 ! [G: nat > real,M: nat,N: nat] :
% 5.82/6.18 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.18 = ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.in_pairs
% 5.82/6.18 thf(fact_8570_prod_Oin__pairs,axiom,
% 5.82/6.18 ! [G: nat > rat,M: nat,N: nat] :
% 5.82/6.18 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.18 = ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.in_pairs
% 5.82/6.18 thf(fact_8571_prod_Oin__pairs,axiom,
% 5.82/6.18 ! [G: nat > int,M: nat,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.in_pairs
% 5.82/6.18 thf(fact_8572_prod_Oin__pairs,axiom,
% 5.82/6.18 ! [G: nat > nat,M: nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.in_pairs
% 5.82/6.18 thf(fact_8573_gbinomial__reduce__nat,axiom,
% 5.82/6.18 ! [K: nat,A2: real] :
% 5.82/6.18 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.18 => ( ( gbinomial_real @ A2 @ K )
% 5.82/6.18 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_reduce_nat
% 5.82/6.18 thf(fact_8574_gbinomial__reduce__nat,axiom,
% 5.82/6.18 ! [K: nat,A2: rat] :
% 5.82/6.18 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.18 => ( ( gbinomial_rat @ A2 @ K )
% 5.82/6.18 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_reduce_nat
% 5.82/6.18 thf(fact_8575_sum__atLeastAtMost__code,axiom,
% 5.82/6.18 ! [F: nat > complex,A2: nat,B2: nat] :
% 5.82/6.18 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( set_fo1517530859248394432omplex
% 5.82/6.18 @ ^ [A5: nat] : ( plus_plus_complex @ ( F @ A5 ) )
% 5.82/6.18 @ A2
% 5.82/6.18 @ B2
% 5.82/6.18 @ zero_zero_complex ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_atLeastAtMost_code
% 5.82/6.18 thf(fact_8576_sum__atLeastAtMost__code,axiom,
% 5.82/6.18 ! [F: nat > rat,A2: nat,B2: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( set_fo1949268297981939178at_rat
% 5.82/6.18 @ ^ [A5: nat] : ( plus_plus_rat @ ( F @ A5 ) )
% 5.82/6.18 @ A2
% 5.82/6.18 @ B2
% 5.82/6.18 @ zero_zero_rat ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_atLeastAtMost_code
% 5.82/6.18 thf(fact_8577_sum__atLeastAtMost__code,axiom,
% 5.82/6.18 ! [F: nat > int,A2: nat,B2: nat] :
% 5.82/6.18 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( set_fo2581907887559384638at_int
% 5.82/6.18 @ ^ [A5: nat] : ( plus_plus_int @ ( F @ A5 ) )
% 5.82/6.18 @ A2
% 5.82/6.18 @ B2
% 5.82/6.18 @ zero_zero_int ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_atLeastAtMost_code
% 5.82/6.18 thf(fact_8578_sum__atLeastAtMost__code,axiom,
% 5.82/6.18 ! [F: nat > nat,A2: nat,B2: nat] :
% 5.82/6.18 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( set_fo2584398358068434914at_nat
% 5.82/6.18 @ ^ [A5: nat] : ( plus_plus_nat @ ( F @ A5 ) )
% 5.82/6.18 @ A2
% 5.82/6.18 @ B2
% 5.82/6.18 @ zero_zero_nat ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_atLeastAtMost_code
% 5.82/6.18 thf(fact_8579_sum__atLeastAtMost__code,axiom,
% 5.82/6.18 ! [F: nat > real,A2: nat,B2: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A2 @ B2 ) )
% 5.82/6.18 = ( set_fo3111899725591712190t_real
% 5.82/6.18 @ ^ [A5: nat] : ( plus_plus_real @ ( F @ A5 ) )
% 5.82/6.18 @ A2
% 5.82/6.18 @ B2
% 5.82/6.18 @ zero_zero_real ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_atLeastAtMost_code
% 5.82/6.18 thf(fact_8580_pochhammer__Suc__prod__rev,axiom,
% 5.82/6.18 ! [A2: rat,N: nat] :
% 5.82/6.18 ( ( comm_s4028243227959126397er_rat @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod_rev
% 5.82/6.18 thf(fact_8581_pochhammer__Suc__prod__rev,axiom,
% 5.82/6.18 ! [A2: real,N: nat] :
% 5.82/6.18 ( ( comm_s7457072308508201937r_real @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_real @ A2 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod_rev
% 5.82/6.18 thf(fact_8582_pochhammer__Suc__prod__rev,axiom,
% 5.82/6.18 ! [A2: int,N: nat] :
% 5.82/6.18 ( ( comm_s4660882817536571857er_int @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_int @ A2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod_rev
% 5.82/6.18 thf(fact_8583_pochhammer__Suc__prod__rev,axiom,
% 5.82/6.18 ! [A2: nat,N: nat] :
% 5.82/6.18 ( ( comm_s4663373288045622133er_nat @ A2 @ ( suc @ N ) )
% 5.82/6.18 = ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % pochhammer_Suc_prod_rev
% 5.82/6.18 thf(fact_8584_gbinomial__sum__up__index,axiom,
% 5.82/6.18 ! [K: nat,N: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat
% 5.82/6.18 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.18 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_sum_up_index
% 5.82/6.18 thf(fact_8585_gbinomial__sum__up__index,axiom,
% 5.82/6.18 ! [K: nat,N: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.82/6.18 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.82/6.18 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_sum_up_index
% 5.82/6.18 thf(fact_8586_gbinomial__absorption_H,axiom,
% 5.82/6.18 ! [K: nat,A2: complex] :
% 5.82/6.18 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.18 => ( ( gbinomial_complex @ A2 @ K )
% 5.82/6.18 = ( times_times_complex @ ( divide1717551699836669952omplex @ A2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A2 @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorption'
% 5.82/6.18 thf(fact_8587_gbinomial__absorption_H,axiom,
% 5.82/6.18 ! [K: nat,A2: rat] :
% 5.82/6.18 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.18 => ( ( gbinomial_rat @ A2 @ K )
% 5.82/6.18 = ( times_times_rat @ ( divide_divide_rat @ A2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorption'
% 5.82/6.18 thf(fact_8588_gbinomial__absorption_H,axiom,
% 5.82/6.18 ! [K: nat,A2: real] :
% 5.82/6.18 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.18 => ( ( gbinomial_real @ A2 @ K )
% 5.82/6.18 = ( times_times_real @ ( divide_divide_real @ A2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A2 @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_absorption'
% 5.82/6.18 thf(fact_8589_floor__log__eq__powr__iff,axiom,
% 5.82/6.18 ! [X2: real,B2: real,K: int] :
% 5.82/6.18 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.18 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.18 => ( ( ( archim6058952711729229775r_real @ ( log @ B2 @ X2 ) )
% 5.82/6.18 = K )
% 5.82/6.18 = ( ( ord_less_eq_real @ ( powr_real @ B2 @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.82/6.18 & ( ord_less_real @ X2 @ ( powr_real @ B2 @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_log_eq_powr_iff
% 5.82/6.18 thf(fact_8590_floor__log2__div2,axiom,
% 5.82/6.18 ! [N: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.82/6.18 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_log2_div2
% 5.82/6.18 thf(fact_8591_floor__log__nat__eq__if,axiom,
% 5.82/6.18 ! [B2: nat,N: nat,K: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.82/6.18 => ( ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.82/6.18 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.82/6.18 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.82/6.18 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % floor_log_nat_eq_if
% 5.82/6.18 thf(fact_8592_gbinomial__partial__row__sum,axiom,
% 5.82/6.18 ! [A2: complex,M: nat] :
% 5.82/6.18 ( ( groups2073611262835488442omplex
% 5.82/6.18 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.18 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A2 @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_partial_row_sum
% 5.82/6.18 thf(fact_8593_gbinomial__partial__row__sum,axiom,
% 5.82/6.18 ! [A2: rat,M: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat
% 5.82/6.18 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.18 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A2 @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_partial_row_sum
% 5.82/6.18 thf(fact_8594_gbinomial__partial__row__sum,axiom,
% 5.82/6.18 ! [A2: real,M: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.18 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A2 @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_partial_row_sum
% 5.82/6.18 thf(fact_8595_round__altdef,axiom,
% 5.82/6.18 ( archim8280529875227126926d_real
% 5.82/6.18 = ( ^ [X3: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X3 ) ) @ ( archim7802044766580827645g_real @ X3 ) @ ( archim6058952711729229775r_real @ X3 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % round_altdef
% 5.82/6.18 thf(fact_8596_round__altdef,axiom,
% 5.82/6.18 ( archim7778729529865785530nd_rat
% 5.82/6.18 = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % round_altdef
% 5.82/6.18 thf(fact_8597_gbinomial__r__part__sum,axiom,
% 5.82/6.18 ! [M: nat] :
% 5.82/6.18 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.18 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_r_part_sum
% 5.82/6.18 thf(fact_8598_gbinomial__r__part__sum,axiom,
% 5.82/6.18 ! [M: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.18 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_r_part_sum
% 5.82/6.18 thf(fact_8599_gbinomial__r__part__sum,axiom,
% 5.82/6.18 ! [M: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.18 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % gbinomial_r_part_sum
% 5.82/6.18 thf(fact_8600_prod_Oinject,axiom,
% 5.82/6.18 ! [X1: code_integer,X22: code_integer,Y15: code_integer,Y2: code_integer] :
% 5.82/6.18 ( ( ( produc1086072967326762835nteger @ X1 @ X22 )
% 5.82/6.18 = ( produc1086072967326762835nteger @ Y15 @ Y2 ) )
% 5.82/6.18 = ( ( X1 = Y15 )
% 5.82/6.18 & ( X22 = Y2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.inject
% 5.82/6.18 thf(fact_8601_prod_Oinject,axiom,
% 5.82/6.18 ! [X1: heap_e7401611519738050253t_unit,X22: set_nat,Y15: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 5.82/6.18 ( ( ( produc7507926704131184380et_nat @ X1 @ X22 )
% 5.82/6.18 = ( produc7507926704131184380et_nat @ Y15 @ Y2 ) )
% 5.82/6.18 = ( ( X1 = Y15 )
% 5.82/6.18 & ( X22 = Y2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.inject
% 5.82/6.18 thf(fact_8602_prod_Oinject,axiom,
% 5.82/6.18 ! [X1: num,X22: num,Y15: num,Y2: num] :
% 5.82/6.18 ( ( ( product_Pair_num_num @ X1 @ X22 )
% 5.82/6.18 = ( product_Pair_num_num @ Y15 @ Y2 ) )
% 5.82/6.18 = ( ( X1 = Y15 )
% 5.82/6.18 & ( X22 = Y2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.inject
% 5.82/6.18 thf(fact_8603_prod_Oinject,axiom,
% 5.82/6.18 ! [X1: nat,X22: nat,Y15: nat,Y2: nat] :
% 5.82/6.18 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 5.82/6.18 = ( product_Pair_nat_nat @ Y15 @ Y2 ) )
% 5.82/6.18 = ( ( X1 = Y15 )
% 5.82/6.18 & ( X22 = Y2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.inject
% 5.82/6.18 thf(fact_8604_prod_Oinject,axiom,
% 5.82/6.18 ! [X1: int,X22: int,Y15: int,Y2: int] :
% 5.82/6.18 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.82/6.18 = ( product_Pair_int_int @ Y15 @ Y2 ) )
% 5.82/6.18 = ( ( X1 = Y15 )
% 5.82/6.18 & ( X22 = Y2 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.inject
% 5.82/6.18 thf(fact_8605_old_Oprod_Oinject,axiom,
% 5.82/6.18 ! [A2: code_integer,B2: code_integer,A4: code_integer,B4: code_integer] :
% 5.82/6.18 ( ( ( produc1086072967326762835nteger @ A2 @ B2 )
% 5.82/6.18 = ( produc1086072967326762835nteger @ A4 @ B4 ) )
% 5.82/6.18 = ( ( A2 = A4 )
% 5.82/6.18 & ( B2 = B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.inject
% 5.82/6.18 thf(fact_8606_old_Oprod_Oinject,axiom,
% 5.82/6.18 ! [A2: heap_e7401611519738050253t_unit,B2: set_nat,A4: heap_e7401611519738050253t_unit,B4: set_nat] :
% 5.82/6.18 ( ( ( produc7507926704131184380et_nat @ A2 @ B2 )
% 5.82/6.18 = ( produc7507926704131184380et_nat @ A4 @ B4 ) )
% 5.82/6.18 = ( ( A2 = A4 )
% 5.82/6.18 & ( B2 = B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.inject
% 5.82/6.18 thf(fact_8607_old_Oprod_Oinject,axiom,
% 5.82/6.18 ! [A2: num,B2: num,A4: num,B4: num] :
% 5.82/6.18 ( ( ( product_Pair_num_num @ A2 @ B2 )
% 5.82/6.18 = ( product_Pair_num_num @ A4 @ B4 ) )
% 5.82/6.18 = ( ( A2 = A4 )
% 5.82/6.18 & ( B2 = B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.inject
% 5.82/6.18 thf(fact_8608_old_Oprod_Oinject,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat,A4: nat,B4: nat] :
% 5.82/6.18 ( ( ( product_Pair_nat_nat @ A2 @ B2 )
% 5.82/6.18 = ( product_Pair_nat_nat @ A4 @ B4 ) )
% 5.82/6.18 = ( ( A2 = A4 )
% 5.82/6.18 & ( B2 = B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.inject
% 5.82/6.18 thf(fact_8609_old_Oprod_Oinject,axiom,
% 5.82/6.18 ! [A2: int,B2: int,A4: int,B4: int] :
% 5.82/6.18 ( ( ( product_Pair_int_int @ A2 @ B2 )
% 5.82/6.18 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.82/6.18 = ( ( A2 = A4 )
% 5.82/6.18 & ( B2 = B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.inject
% 5.82/6.18 thf(fact_8610_atMost__iff,axiom,
% 5.82/6.18 ! [I: real,K: real] :
% 5.82/6.18 ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 5.82/6.18 = ( ord_less_eq_real @ I @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_iff
% 5.82/6.18 thf(fact_8611_atMost__iff,axiom,
% 5.82/6.18 ! [I: set_int,K: set_int] :
% 5.82/6.18 ( ( member_set_int @ I @ ( set_or58775011639299419et_int @ K ) )
% 5.82/6.18 = ( ord_less_eq_set_int @ I @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_iff
% 5.82/6.18 thf(fact_8612_atMost__iff,axiom,
% 5.82/6.18 ! [I: rat,K: rat] :
% 5.82/6.18 ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 5.82/6.18 = ( ord_less_eq_rat @ I @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_iff
% 5.82/6.18 thf(fact_8613_atMost__iff,axiom,
% 5.82/6.18 ! [I: num,K: num] :
% 5.82/6.18 ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 5.82/6.18 = ( ord_less_eq_num @ I @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_iff
% 5.82/6.18 thf(fact_8614_atMost__iff,axiom,
% 5.82/6.18 ! [I: nat,K: nat] :
% 5.82/6.18 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 5.82/6.18 = ( ord_less_eq_nat @ I @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_iff
% 5.82/6.18 thf(fact_8615_atMost__iff,axiom,
% 5.82/6.18 ! [I: int,K: int] :
% 5.82/6.18 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 5.82/6.18 = ( ord_less_eq_int @ I @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_iff
% 5.82/6.18 thf(fact_8616_atMost__subset__iff,axiom,
% 5.82/6.18 ! [X2: set_int,Y3: set_int] :
% 5.82/6.18 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X2 ) @ ( set_or58775011639299419et_int @ Y3 ) )
% 5.82/6.18 = ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_subset_iff
% 5.82/6.18 thf(fact_8617_atMost__subset__iff,axiom,
% 5.82/6.18 ! [X2: rat,Y3: rat] :
% 5.82/6.18 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X2 ) @ ( set_ord_atMost_rat @ Y3 ) )
% 5.82/6.18 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_subset_iff
% 5.82/6.18 thf(fact_8618_atMost__subset__iff,axiom,
% 5.82/6.18 ! [X2: num,Y3: num] :
% 5.82/6.18 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X2 ) @ ( set_ord_atMost_num @ Y3 ) )
% 5.82/6.18 = ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_subset_iff
% 5.82/6.18 thf(fact_8619_atMost__subset__iff,axiom,
% 5.82/6.18 ! [X2: nat,Y3: nat] :
% 5.82/6.18 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X2 ) @ ( set_ord_atMost_nat @ Y3 ) )
% 5.82/6.18 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_subset_iff
% 5.82/6.18 thf(fact_8620_atMost__subset__iff,axiom,
% 5.82/6.18 ! [X2: int,Y3: int] :
% 5.82/6.18 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X2 ) @ ( set_ord_atMost_int @ Y3 ) )
% 5.82/6.18 = ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_subset_iff
% 5.82/6.18 thf(fact_8621_prod__eq__1__iff,axiom,
% 5.82/6.18 ! [A: set_int,F: int > nat] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( ( groups1707563613775114915nt_nat @ F @ A )
% 5.82/6.18 = one_one_nat )
% 5.82/6.18 = ( ! [X3: int] :
% 5.82/6.18 ( ( member_int @ X3 @ A )
% 5.82/6.18 => ( ( F @ X3 )
% 5.82/6.18 = one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_eq_1_iff
% 5.82/6.18 thf(fact_8622_prod__eq__1__iff,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( ( groups3190895334310489300er_nat @ F @ A )
% 5.82/6.18 = one_one_nat )
% 5.82/6.18 = ( ! [X3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.18 => ( ( F @ X3 )
% 5.82/6.18 = one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_eq_1_iff
% 5.82/6.18 thf(fact_8623_prod__eq__1__iff,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( ( groups861055069439313189ex_nat @ F @ A )
% 5.82/6.18 = one_one_nat )
% 5.82/6.18 = ( ! [X3: complex] :
% 5.82/6.18 ( ( member_complex @ X3 @ A )
% 5.82/6.18 => ( ( F @ X3 )
% 5.82/6.18 = one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_eq_1_iff
% 5.82/6.18 thf(fact_8624_prod__eq__1__iff,axiom,
% 5.82/6.18 ! [A: set_nat,F: nat > nat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( ( groups708209901874060359at_nat @ F @ A )
% 5.82/6.18 = one_one_nat )
% 5.82/6.18 = ( ! [X3: nat] :
% 5.82/6.18 ( ( member_nat @ X3 @ A )
% 5.82/6.18 => ( ( F @ X3 )
% 5.82/6.18 = one_one_nat ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_eq_1_iff
% 5.82/6.18 thf(fact_8625_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: set_int,H2: set_int,H4: set_int] :
% 5.82/6.18 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H2 ) @ ( set_or58775011639299419et_int @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 5.82/6.18 | ( ord_less_eq_set_int @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8626_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: rat,H2: rat,H4: rat] :
% 5.82/6.18 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.82/6.18 | ( ord_less_eq_rat @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8627_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: num,H2: num,H4: num] :
% 5.82/6.18 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.82/6.18 | ( ord_less_eq_num @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8628_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: nat,H2: nat,H4: nat] :
% 5.82/6.18 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.82/6.18 | ( ord_less_eq_nat @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8629_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: int,H2: int,H4: int] :
% 5.82/6.18 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.82/6.18 | ( ord_less_eq_int @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8630_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: code_integer,H2: code_integer,H4: code_integer] :
% 5.82/6.18 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ L @ H2 ) @ ( set_or9101266186257409494nteger @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_le3102999989581377725nteger @ L @ H2 )
% 5.82/6.18 | ( ord_le3102999989581377725nteger @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8631_Icc__subset__Iic__iff,axiom,
% 5.82/6.18 ! [L: real,H2: real,H4: real] :
% 5.82/6.18 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H4 ) )
% 5.82/6.18 = ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.82/6.18 | ( ord_less_eq_real @ H2 @ H4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Icc_subset_Iic_iff
% 5.82/6.18 thf(fact_8632_sum_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc
% 5.82/6.18 thf(fact_8633_sum_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc
% 5.82/6.18 thf(fact_8634_sum_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc
% 5.82/6.18 thf(fact_8635_sum_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc
% 5.82/6.18 thf(fact_8636_prod_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc
% 5.82/6.18 thf(fact_8637_prod_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc
% 5.82/6.18 thf(fact_8638_prod_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc
% 5.82/6.18 thf(fact_8639_prod_OatMost__Suc,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc
% 5.82/6.18 thf(fact_8640_prod__pos__nat__iff,axiom,
% 5.82/6.18 ! [A: set_int,F: int > nat] :
% 5.82/6.18 ( ( finite_finite_int @ A )
% 5.82/6.18 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A ) )
% 5.82/6.18 = ( ! [X3: int] :
% 5.82/6.18 ( ( member_int @ X3 @ A )
% 5.82/6.18 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_pos_nat_iff
% 5.82/6.18 thf(fact_8641_prod__pos__nat__iff,axiom,
% 5.82/6.18 ! [A: set_Code_integer,F: code_integer > nat] :
% 5.82/6.18 ( ( finite6017078050557962740nteger @ A )
% 5.82/6.18 => ( ( ord_less_nat @ zero_zero_nat @ ( groups3190895334310489300er_nat @ F @ A ) )
% 5.82/6.18 = ( ! [X3: code_integer] :
% 5.82/6.18 ( ( member_Code_integer @ X3 @ A )
% 5.82/6.18 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_pos_nat_iff
% 5.82/6.18 thf(fact_8642_prod__pos__nat__iff,axiom,
% 5.82/6.18 ! [A: set_complex,F: complex > nat] :
% 5.82/6.18 ( ( finite3207457112153483333omplex @ A )
% 5.82/6.18 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A ) )
% 5.82/6.18 = ( ! [X3: complex] :
% 5.82/6.18 ( ( member_complex @ X3 @ A )
% 5.82/6.18 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_pos_nat_iff
% 5.82/6.18 thf(fact_8643_prod__pos__nat__iff,axiom,
% 5.82/6.18 ! [A: set_nat,F: nat > nat] :
% 5.82/6.18 ( ( finite_finite_nat @ A )
% 5.82/6.18 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A ) )
% 5.82/6.18 = ( ! [X3: nat] :
% 5.82/6.18 ( ( member_nat @ X3 @ A )
% 5.82/6.18 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_pos_nat_iff
% 5.82/6.18 thf(fact_8644_int__prod,axiom,
% 5.82/6.18 ! [F: int > nat,A: set_int] :
% 5.82/6.18 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A ) )
% 5.82/6.18 = ( groups1705073143266064639nt_int
% 5.82/6.18 @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.18 @ A ) ) ).
% 5.82/6.18
% 5.82/6.18 % int_prod
% 5.82/6.18 thf(fact_8645_int__prod,axiom,
% 5.82/6.18 ! [F: nat > nat,A: set_nat] :
% 5.82/6.18 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A ) )
% 5.82/6.18 = ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F @ X3 ) )
% 5.82/6.18 @ A ) ) ).
% 5.82/6.18
% 5.82/6.18 % int_prod
% 5.82/6.18 thf(fact_8646_atMost__def,axiom,
% 5.82/6.18 ( set_or58775011639299419et_int
% 5.82/6.18 = ( ^ [U2: set_int] :
% 5.82/6.18 ( collect_set_int
% 5.82/6.18 @ ^ [X3: set_int] : ( ord_less_eq_set_int @ X3 @ U2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_def
% 5.82/6.18 thf(fact_8647_atMost__def,axiom,
% 5.82/6.18 ( set_ord_atMost_rat
% 5.82/6.18 = ( ^ [U2: rat] :
% 5.82/6.18 ( collect_rat
% 5.82/6.18 @ ^ [X3: rat] : ( ord_less_eq_rat @ X3 @ U2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_def
% 5.82/6.18 thf(fact_8648_atMost__def,axiom,
% 5.82/6.18 ( set_ord_atMost_num
% 5.82/6.18 = ( ^ [U2: num] :
% 5.82/6.18 ( collect_num
% 5.82/6.18 @ ^ [X3: num] : ( ord_less_eq_num @ X3 @ U2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_def
% 5.82/6.18 thf(fact_8649_atMost__def,axiom,
% 5.82/6.18 ( set_ord_atMost_nat
% 5.82/6.18 = ( ^ [U2: nat] :
% 5.82/6.18 ( collect_nat
% 5.82/6.18 @ ^ [X3: nat] : ( ord_less_eq_nat @ X3 @ U2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_def
% 5.82/6.18 thf(fact_8650_atMost__def,axiom,
% 5.82/6.18 ( set_ord_atMost_int
% 5.82/6.18 = ( ^ [U2: int] :
% 5.82/6.18 ( collect_int
% 5.82/6.18 @ ^ [X3: int] : ( ord_less_eq_int @ X3 @ U2 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_def
% 5.82/6.18 thf(fact_8651_lessThan__Suc__atMost,axiom,
% 5.82/6.18 ! [K: nat] :
% 5.82/6.18 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.82/6.18 = ( set_ord_atMost_nat @ K ) ) ).
% 5.82/6.18
% 5.82/6.18 % lessThan_Suc_atMost
% 5.82/6.18 thf(fact_8652_atMost__Suc,axiom,
% 5.82/6.18 ! [K: nat] :
% 5.82/6.18 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.82/6.18 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % atMost_Suc
% 5.82/6.18 thf(fact_8653_not__UNIV__le__Iic,axiom,
% 5.82/6.18 ! [H2: real] :
% 5.82/6.18 ~ ( ord_less_eq_set_real @ top_top_set_real @ ( set_ord_atMost_real @ H2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % not_UNIV_le_Iic
% 5.82/6.18 thf(fact_8654_not__UNIV__le__Iic,axiom,
% 5.82/6.18 ! [H2: nat] :
% 5.82/6.18 ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_ord_atMost_nat @ H2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % not_UNIV_le_Iic
% 5.82/6.18 thf(fact_8655_not__UNIV__le__Iic,axiom,
% 5.82/6.18 ! [H2: int] :
% 5.82/6.18 ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_ord_atMost_int @ H2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % not_UNIV_le_Iic
% 5.82/6.18 thf(fact_8656_not__Iic__le__Icc,axiom,
% 5.82/6.18 ! [H2: int,L4: int,H4: int] :
% 5.82/6.18 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L4 @ H4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % not_Iic_le_Icc
% 5.82/6.18 thf(fact_8657_not__Iic__le__Icc,axiom,
% 5.82/6.18 ! [H2: real,L4: real,H4: real] :
% 5.82/6.18 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L4 @ H4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % not_Iic_le_Icc
% 5.82/6.18 thf(fact_8658_finite__nat__iff__bounded__le,axiom,
% 5.82/6.18 ( finite_finite_nat
% 5.82/6.18 = ( ^ [S8: set_nat] :
% 5.82/6.18 ? [K3: nat] : ( ord_less_eq_set_nat @ S8 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % finite_nat_iff_bounded_le
% 5.82/6.18 thf(fact_8659_frac__ge__0,axiom,
% 5.82/6.18 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % frac_ge_0
% 5.82/6.18 thf(fact_8660_frac__ge__0,axiom,
% 5.82/6.18 ! [X2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % frac_ge_0
% 5.82/6.18 thf(fact_8661_frac__lt__1,axiom,
% 5.82/6.18 ! [X2: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X2 ) @ one_one_real ) ).
% 5.82/6.18
% 5.82/6.18 % frac_lt_1
% 5.82/6.18 thf(fact_8662_frac__lt__1,axiom,
% 5.82/6.18 ! [X2: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X2 ) @ one_one_rat ) ).
% 5.82/6.18
% 5.82/6.18 % frac_lt_1
% 5.82/6.18 thf(fact_8663_frac__1__eq,axiom,
% 5.82/6.18 ! [X2: real] :
% 5.82/6.18 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.82/6.18 = ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % frac_1_eq
% 5.82/6.18 thf(fact_8664_frac__1__eq,axiom,
% 5.82/6.18 ! [X2: rat] :
% 5.82/6.18 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.82/6.18 = ( archimedean_frac_rat @ X2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % frac_1_eq
% 5.82/6.18 thf(fact_8665_old_Oprod_Oexhaust,axiom,
% 5.82/6.18 ! [Y3: produc8923325533196201883nteger] :
% 5.82/6.18 ~ ! [A3: code_integer,B3: code_integer] :
% 5.82/6.18 ( Y3
% 5.82/6.18 != ( produc1086072967326762835nteger @ A3 @ B3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.exhaust
% 5.82/6.18 thf(fact_8666_old_Oprod_Oexhaust,axiom,
% 5.82/6.18 ! [Y3: produc3658429121746597890et_nat] :
% 5.82/6.18 ~ ! [A3: heap_e7401611519738050253t_unit,B3: set_nat] :
% 5.82/6.18 ( Y3
% 5.82/6.18 != ( produc7507926704131184380et_nat @ A3 @ B3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.exhaust
% 5.82/6.18 thf(fact_8667_old_Oprod_Oexhaust,axiom,
% 5.82/6.18 ! [Y3: product_prod_num_num] :
% 5.82/6.18 ~ ! [A3: num,B3: num] :
% 5.82/6.18 ( Y3
% 5.82/6.18 != ( product_Pair_num_num @ A3 @ B3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.exhaust
% 5.82/6.18 thf(fact_8668_old_Oprod_Oexhaust,axiom,
% 5.82/6.18 ! [Y3: product_prod_nat_nat] :
% 5.82/6.18 ~ ! [A3: nat,B3: nat] :
% 5.82/6.18 ( Y3
% 5.82/6.18 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.exhaust
% 5.82/6.18 thf(fact_8669_old_Oprod_Oexhaust,axiom,
% 5.82/6.18 ! [Y3: product_prod_int_int] :
% 5.82/6.18 ~ ! [A3: int,B3: int] :
% 5.82/6.18 ( Y3
% 5.82/6.18 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 5.82/6.18
% 5.82/6.18 % old.prod.exhaust
% 5.82/6.18 thf(fact_8670_surj__pair,axiom,
% 5.82/6.18 ! [P6: produc8923325533196201883nteger] :
% 5.82/6.18 ? [X4: code_integer,Y4: code_integer] :
% 5.82/6.18 ( P6
% 5.82/6.18 = ( produc1086072967326762835nteger @ X4 @ Y4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % surj_pair
% 5.82/6.18 thf(fact_8671_surj__pair,axiom,
% 5.82/6.18 ! [P6: produc3658429121746597890et_nat] :
% 5.82/6.18 ? [X4: heap_e7401611519738050253t_unit,Y4: set_nat] :
% 5.82/6.18 ( P6
% 5.82/6.18 = ( produc7507926704131184380et_nat @ X4 @ Y4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % surj_pair
% 5.82/6.18 thf(fact_8672_surj__pair,axiom,
% 5.82/6.18 ! [P6: product_prod_num_num] :
% 5.82/6.18 ? [X4: num,Y4: num] :
% 5.82/6.18 ( P6
% 5.82/6.18 = ( product_Pair_num_num @ X4 @ Y4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % surj_pair
% 5.82/6.18 thf(fact_8673_surj__pair,axiom,
% 5.82/6.18 ! [P6: product_prod_nat_nat] :
% 5.82/6.18 ? [X4: nat,Y4: nat] :
% 5.82/6.18 ( P6
% 5.82/6.18 = ( product_Pair_nat_nat @ X4 @ Y4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % surj_pair
% 5.82/6.18 thf(fact_8674_surj__pair,axiom,
% 5.82/6.18 ! [P6: product_prod_int_int] :
% 5.82/6.18 ? [X4: int,Y4: int] :
% 5.82/6.18 ( P6
% 5.82/6.18 = ( product_Pair_int_int @ X4 @ Y4 ) ) ).
% 5.82/6.18
% 5.82/6.18 % surj_pair
% 5.82/6.18 thf(fact_8675_prod__cases,axiom,
% 5.82/6.18 ! [P: produc8923325533196201883nteger > $o,P6: produc8923325533196201883nteger] :
% 5.82/6.18 ( ! [A3: code_integer,B3: code_integer] : ( P @ ( produc1086072967326762835nteger @ A3 @ B3 ) )
% 5.82/6.18 => ( P @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_cases
% 5.82/6.18 thf(fact_8676_prod__cases,axiom,
% 5.82/6.18 ! [P: produc3658429121746597890et_nat > $o,P6: produc3658429121746597890et_nat] :
% 5.82/6.18 ( ! [A3: heap_e7401611519738050253t_unit,B3: set_nat] : ( P @ ( produc7507926704131184380et_nat @ A3 @ B3 ) )
% 5.82/6.18 => ( P @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_cases
% 5.82/6.18 thf(fact_8677_prod__cases,axiom,
% 5.82/6.18 ! [P: product_prod_num_num > $o,P6: product_prod_num_num] :
% 5.82/6.18 ( ! [A3: num,B3: num] : ( P @ ( product_Pair_num_num @ A3 @ B3 ) )
% 5.82/6.18 => ( P @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_cases
% 5.82/6.18 thf(fact_8678_prod__cases,axiom,
% 5.82/6.18 ! [P: product_prod_nat_nat > $o,P6: product_prod_nat_nat] :
% 5.82/6.18 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 5.82/6.18 => ( P @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_cases
% 5.82/6.18 thf(fact_8679_prod__cases,axiom,
% 5.82/6.18 ! [P: product_prod_int_int > $o,P6: product_prod_int_int] :
% 5.82/6.18 ( ! [A3: int,B3: int] : ( P @ ( product_Pair_int_int @ A3 @ B3 ) )
% 5.82/6.18 => ( P @ P6 ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_cases
% 5.82/6.18 thf(fact_8680_Pair__inject,axiom,
% 5.82/6.18 ! [A2: code_integer,B2: code_integer,A4: code_integer,B4: code_integer] :
% 5.82/6.18 ( ( ( produc1086072967326762835nteger @ A2 @ B2 )
% 5.82/6.18 = ( produc1086072967326762835nteger @ A4 @ B4 ) )
% 5.82/6.18 => ~ ( ( A2 = A4 )
% 5.82/6.18 => ( B2 != B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Pair_inject
% 5.82/6.18 thf(fact_8681_Pair__inject,axiom,
% 5.82/6.18 ! [A2: heap_e7401611519738050253t_unit,B2: set_nat,A4: heap_e7401611519738050253t_unit,B4: set_nat] :
% 5.82/6.18 ( ( ( produc7507926704131184380et_nat @ A2 @ B2 )
% 5.82/6.18 = ( produc7507926704131184380et_nat @ A4 @ B4 ) )
% 5.82/6.18 => ~ ( ( A2 = A4 )
% 5.82/6.18 => ( B2 != B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Pair_inject
% 5.82/6.18 thf(fact_8682_Pair__inject,axiom,
% 5.82/6.18 ! [A2: num,B2: num,A4: num,B4: num] :
% 5.82/6.18 ( ( ( product_Pair_num_num @ A2 @ B2 )
% 5.82/6.18 = ( product_Pair_num_num @ A4 @ B4 ) )
% 5.82/6.18 => ~ ( ( A2 = A4 )
% 5.82/6.18 => ( B2 != B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Pair_inject
% 5.82/6.18 thf(fact_8683_Pair__inject,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat,A4: nat,B4: nat] :
% 5.82/6.18 ( ( ( product_Pair_nat_nat @ A2 @ B2 )
% 5.82/6.18 = ( product_Pair_nat_nat @ A4 @ B4 ) )
% 5.82/6.18 => ~ ( ( A2 = A4 )
% 5.82/6.18 => ( B2 != B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Pair_inject
% 5.82/6.18 thf(fact_8684_Pair__inject,axiom,
% 5.82/6.18 ! [A2: int,B2: int,A4: int,B4: int] :
% 5.82/6.18 ( ( ( product_Pair_int_int @ A2 @ B2 )
% 5.82/6.18 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.82/6.18 => ~ ( ( A2 = A4 )
% 5.82/6.18 => ( B2 != B4 ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % Pair_inject
% 5.82/6.18 thf(fact_8685_Iic__subset__Iio__iff,axiom,
% 5.82/6.18 ! [A2: rat,B2: rat] :
% 5.82/6.18 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A2 ) @ ( set_ord_lessThan_rat @ B2 ) )
% 5.82/6.18 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % Iic_subset_Iio_iff
% 5.82/6.18 thf(fact_8686_Iic__subset__Iio__iff,axiom,
% 5.82/6.18 ! [A2: num,B2: num] :
% 5.82/6.18 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A2 ) @ ( set_ord_lessThan_num @ B2 ) )
% 5.82/6.18 = ( ord_less_num @ A2 @ B2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % Iic_subset_Iio_iff
% 5.82/6.18 thf(fact_8687_Iic__subset__Iio__iff,axiom,
% 5.82/6.18 ! [A2: nat,B2: nat] :
% 5.82/6.18 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A2 ) @ ( set_ord_lessThan_nat @ B2 ) )
% 5.82/6.18 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % Iic_subset_Iio_iff
% 5.82/6.18 thf(fact_8688_Iic__subset__Iio__iff,axiom,
% 5.82/6.18 ! [A2: int,B2: int] :
% 5.82/6.18 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A2 ) @ ( set_ord_lessThan_int @ B2 ) )
% 5.82/6.18 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % Iic_subset_Iio_iff
% 5.82/6.18 thf(fact_8689_Iic__subset__Iio__iff,axiom,
% 5.82/6.18 ! [A2: real,B2: real] :
% 5.82/6.18 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A2 ) @ ( set_or5984915006950818249n_real @ B2 ) )
% 5.82/6.18 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.18
% 5.82/6.18 % Iic_subset_Iio_iff
% 5.82/6.18 thf(fact_8690_prod__int__eq,axiom,
% 5.82/6.18 ! [I: nat,J: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.82/6.18 = ( groups1705073143266064639nt_int
% 5.82/6.18 @ ^ [X3: int] : X3
% 5.82/6.18 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_int_eq
% 5.82/6.18 thf(fact_8691_frac__def,axiom,
% 5.82/6.18 ( archim2898591450579166408c_real
% 5.82/6.18 = ( ^ [X3: real] : ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % frac_def
% 5.82/6.18 thf(fact_8692_frac__def,axiom,
% 5.82/6.18 ( archimedean_frac_rat
% 5.82/6.18 = ( ^ [X3: rat] : ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % frac_def
% 5.82/6.18 thf(fact_8693_sum_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups2906978787729119204at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc_shift
% 5.82/6.18 thf(fact_8694_sum_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups3539618377306564664at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc_shift
% 5.82/6.18 thf(fact_8695_sum_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups3542108847815614940at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc_shift
% 5.82/6.18 thf(fact_8696_sum_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum.atMost_Suc_shift
% 5.82/6.18 thf(fact_8697_sum__telescope,axiom,
% 5.82/6.18 ! [F: nat > rat,I: nat] :
% 5.82/6.18 ( ( groups2906978787729119204at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ I ) )
% 5.82/6.18 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_telescope
% 5.82/6.18 thf(fact_8698_sum__telescope,axiom,
% 5.82/6.18 ! [F: nat > int,I: nat] :
% 5.82/6.18 ( ( groups3539618377306564664at_int
% 5.82/6.18 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ I ) )
% 5.82/6.18 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_telescope
% 5.82/6.18 thf(fact_8699_sum__telescope,axiom,
% 5.82/6.18 ! [F: nat > real,I: nat] :
% 5.82/6.18 ( ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ I ) )
% 5.82/6.18 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % sum_telescope
% 5.82/6.18 thf(fact_8700_polyfun__eq__coeffs,axiom,
% 5.82/6.18 ! [C2: nat > complex,N: nat,D2: nat > complex] :
% 5.82/6.18 ( ( ! [X3: complex] :
% 5.82/6.18 ( ( groups2073611262835488442omplex
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.18 = ( groups2073611262835488442omplex
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_complex @ ( D2 @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.82/6.18 = ( ! [I4: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ I4 @ N )
% 5.82/6.18 => ( ( C2 @ I4 )
% 5.82/6.18 = ( D2 @ I4 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % polyfun_eq_coeffs
% 5.82/6.18 thf(fact_8701_polyfun__eq__coeffs,axiom,
% 5.82/6.18 ! [C2: nat > real,N: nat,D2: nat > real] :
% 5.82/6.18 ( ( ! [X3: real] :
% 5.82/6.18 ( ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.18 = ( groups6591440286371151544t_real
% 5.82/6.18 @ ^ [I4: nat] : ( times_times_real @ ( D2 @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.82/6.18 = ( ! [I4: nat] :
% 5.82/6.18 ( ( ord_less_eq_nat @ I4 @ N )
% 5.82/6.18 => ( ( C2 @ I4 )
% 5.82/6.18 = ( D2 @ I4 ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % polyfun_eq_coeffs
% 5.82/6.18 thf(fact_8702_prod_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > real,N: nat] :
% 5.82/6.18 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups129246275422532515t_real
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc_shift
% 5.82/6.18 thf(fact_8703_prod_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > rat,N: nat] :
% 5.82/6.18 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups73079841787564623at_rat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc_shift
% 5.82/6.18 thf(fact_8704_prod_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > int,N: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups705719431365010083at_int
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc_shift
% 5.82/6.18 thf(fact_8705_prod_OatMost__Suc__shift,axiom,
% 5.82/6.18 ! [G: nat > nat,N: nat] :
% 5.82/6.18 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.82/6.18 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.82/6.18 @ ( groups708209901874060359at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.18 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod.atMost_Suc_shift
% 5.82/6.18 thf(fact_8706_prod__int__plus__eq,axiom,
% 5.82/6.18 ! [I: nat,J: nat] :
% 5.82/6.18 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.82/6.18 = ( groups1705073143266064639nt_int
% 5.82/6.18 @ ^ [X3: int] : X3
% 5.82/6.18 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.82/6.18
% 5.82/6.18 % prod_int_plus_eq
% 5.82/6.18 thf(fact_8707_sum_Onested__swap_H,axiom,
% 5.82/6.18 ! [A2: nat > nat > nat,N: nat] :
% 5.82/6.18 ( ( groups3542108847815614940at_nat
% 5.82/6.18 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( A2 @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.nested_swap'
% 5.82/6.19 thf(fact_8708_sum_Onested__swap_H,axiom,
% 5.82/6.19 ! [A2: nat > nat > real,N: nat] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ ( A2 @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.nested_swap'
% 5.82/6.19 thf(fact_8709_prod_Onested__swap_H,axiom,
% 5.82/6.19 ! [A2: nat > nat > int,N: nat] :
% 5.82/6.19 ( ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A2 @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.nested_swap'
% 5.82/6.19 thf(fact_8710_prod_Onested__swap_H,axiom,
% 5.82/6.19 ! [A2: nat > nat > nat,N: nat] :
% 5.82/6.19 ( ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A2 @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( A2 @ I4 @ J3 )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.nested_swap'
% 5.82/6.19 thf(fact_8711_frac__eq,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.82/6.19 = X2 )
% 5.82/6.19 = ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 & ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % frac_eq
% 5.82/6.19 thf(fact_8712_frac__eq,axiom,
% 5.82/6.19 ! [X2: rat] :
% 5.82/6.19 ( ( ( archimedean_frac_rat @ X2 )
% 5.82/6.19 = X2 )
% 5.82/6.19 = ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.82/6.19 & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % frac_eq
% 5.82/6.19 thf(fact_8713_frac__add,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.82/6.19 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) ) )
% 5.82/6.19 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.82/6.19 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % frac_add
% 5.82/6.19 thf(fact_8714_frac__add,axiom,
% 5.82/6.19 ! [X2: rat,Y3: rat] :
% 5.82/6.19 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.82/6.19 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) ) )
% 5.82/6.19 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.82/6.19 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y3 ) )
% 5.82/6.19 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % frac_add
% 5.82/6.19 thf(fact_8715_zero__polynom__imp__zero__coeffs,axiom,
% 5.82/6.19 ! [C2: nat > complex,N: nat,K: nat] :
% 5.82/6.19 ( ! [W3: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ W3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_complex )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( C2 @ K )
% 5.82/6.19 = zero_zero_complex ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zero_polynom_imp_zero_coeffs
% 5.82/6.19 thf(fact_8716_zero__polynom__imp__zero__coeffs,axiom,
% 5.82/6.19 ! [C2: nat > real,N: nat,K: nat] :
% 5.82/6.19 ( ! [W3: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ W3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( C2 @ K )
% 5.82/6.19 = zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zero_polynom_imp_zero_coeffs
% 5.82/6.19 thf(fact_8717_polyfun__eq__0,axiom,
% 5.82/6.19 ! [C2: nat > complex,N: nat] :
% 5.82/6.19 ( ( ! [X3: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_complex ) )
% 5.82/6.19 = ( ! [I4: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ I4 @ N )
% 5.82/6.19 => ( ( C2 @ I4 )
% 5.82/6.19 = zero_zero_complex ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_eq_0
% 5.82/6.19 thf(fact_8718_polyfun__eq__0,axiom,
% 5.82/6.19 ! [C2: nat > real,N: nat] :
% 5.82/6.19 ( ( ! [X3: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_real ) )
% 5.82/6.19 = ( ! [I4: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ I4 @ N )
% 5.82/6.19 => ( ( C2 @ I4 )
% 5.82/6.19 = zero_zero_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_eq_0
% 5.82/6.19 thf(fact_8719_sum_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > rat,N: nat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.atMost_shift
% 5.82/6.19 thf(fact_8720_sum_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > int,N: nat] :
% 5.82/6.19 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.atMost_shift
% 5.82/6.19 thf(fact_8721_sum_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > nat,N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.atMost_shift
% 5.82/6.19 thf(fact_8722_sum_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > real,N: nat] :
% 5.82/6.19 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.atMost_shift
% 5.82/6.19 thf(fact_8723_sum__up__index__split,axiom,
% 5.82/6.19 ! [F: nat > rat,M: nat,N: nat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.19 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_up_index_split
% 5.82/6.19 thf(fact_8724_sum__up__index__split,axiom,
% 5.82/6.19 ! [F: nat > int,M: nat,N: nat] :
% 5.82/6.19 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.19 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_up_index_split
% 5.82/6.19 thf(fact_8725_sum__up__index__split,axiom,
% 5.82/6.19 ! [F: nat > nat,M: nat,N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.19 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_up_index_split
% 5.82/6.19 thf(fact_8726_sum__up__index__split,axiom,
% 5.82/6.19 ! [F: nat > real,M: nat,N: nat] :
% 5.82/6.19 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.82/6.19 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_up_index_split
% 5.82/6.19 thf(fact_8727_prod_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > real,N: nat] :
% 5.82/6.19 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups129246275422532515t_real
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.atMost_shift
% 5.82/6.19 thf(fact_8728_prod_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > rat,N: nat] :
% 5.82/6.19 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups73079841787564623at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.atMost_shift
% 5.82/6.19 thf(fact_8729_prod_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > int,N: nat] :
% 5.82/6.19 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.atMost_shift
% 5.82/6.19 thf(fact_8730_prod_OatMost__shift,axiom,
% 5.82/6.19 ! [G: nat > nat,N: nat] :
% 5.82/6.19 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.82/6.19 @ ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.atMost_shift
% 5.82/6.19 thf(fact_8731_gbinomial__parallel__sum,axiom,
% 5.82/6.19 ! [A2: rat,N: nat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_parallel_sum
% 5.82/6.19 thf(fact_8732_gbinomial__parallel__sum,axiom,
% 5.82/6.19 ! [A2: real,N: nat] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A2 @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A2 @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_parallel_sum
% 5.82/6.19 thf(fact_8733_sum__gp__basic,axiom,
% 5.82/6.19 ! [X2: complex,N: nat] :
% 5.82/6.19 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp_basic
% 5.82/6.19 thf(fact_8734_sum__gp__basic,axiom,
% 5.82/6.19 ! [X2: code_integer,N: nat] :
% 5.82/6.19 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X2 ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp_basic
% 5.82/6.19 thf(fact_8735_sum__gp__basic,axiom,
% 5.82/6.19 ! [X2: rat,N: nat] :
% 5.82/6.19 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp_basic
% 5.82/6.19 thf(fact_8736_sum__gp__basic,axiom,
% 5.82/6.19 ! [X2: int,N: nat] :
% 5.82/6.19 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp_basic
% 5.82/6.19 thf(fact_8737_sum__gp__basic,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp_basic
% 5.82/6.19 thf(fact_8738_polyfun__roots__finite,axiom,
% 5.82/6.19 ! [C2: nat > complex,K: nat,N: nat] :
% 5.82/6.19 ( ( ( C2 @ K )
% 5.82/6.19 != zero_zero_complex )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( finite3207457112153483333omplex
% 5.82/6.19 @ ( collect_complex
% 5.82/6.19 @ ^ [Z4: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ Z4 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_complex ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_roots_finite
% 5.82/6.19 thf(fact_8739_polyfun__roots__finite,axiom,
% 5.82/6.19 ! [C2: nat > real,K: nat,N: nat] :
% 5.82/6.19 ( ( ( C2 @ K )
% 5.82/6.19 != zero_zero_real )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( finite_finite_real
% 5.82/6.19 @ ( collect_real
% 5.82/6.19 @ ^ [Z4: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ Z4 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_roots_finite
% 5.82/6.19 thf(fact_8740_polyfun__finite__roots,axiom,
% 5.82/6.19 ! [C2: nat > complex,N: nat] :
% 5.82/6.19 ( ( finite3207457112153483333omplex
% 5.82/6.19 @ ( collect_complex
% 5.82/6.19 @ ^ [X3: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_complex ) ) )
% 5.82/6.19 = ( ? [I4: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ I4 @ N )
% 5.82/6.19 & ( ( C2 @ I4 )
% 5.82/6.19 != zero_zero_complex ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_finite_roots
% 5.82/6.19 thf(fact_8741_polyfun__finite__roots,axiom,
% 5.82/6.19 ! [C2: nat > real,N: nat] :
% 5.82/6.19 ( ( finite_finite_real
% 5.82/6.19 @ ( collect_real
% 5.82/6.19 @ ^ [X3: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_real ) ) )
% 5.82/6.19 = ( ? [I4: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ I4 @ N )
% 5.82/6.19 & ( ( C2 @ I4 )
% 5.82/6.19 != zero_zero_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_finite_roots
% 5.82/6.19 thf(fact_8742_polyfun__linear__factor__root,axiom,
% 5.82/6.19 ! [C2: nat > complex,A2: complex,N: nat] :
% 5.82/6.19 ( ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_complex )
% 5.82/6.19 => ~ ! [B3: nat > complex] :
% 5.82/6.19 ~ ! [Z5: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A2 )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( B3 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor_root
% 5.82/6.19 thf(fact_8743_polyfun__linear__factor__root,axiom,
% 5.82/6.19 ! [C2: nat > code_integer,A2: code_integer,N: nat] :
% 5.82/6.19 ( ( ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( C2 @ I4 ) @ ( power_8256067586552552935nteger @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_z3403309356797280102nteger )
% 5.82/6.19 => ~ ! [B3: nat > code_integer] :
% 5.82/6.19 ~ ! [Z5: code_integer] :
% 5.82/6.19 ( ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( C2 @ I4 ) @ ( power_8256067586552552935nteger @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ Z5 @ A2 )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( B3 @ I4 ) @ ( power_8256067586552552935nteger @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor_root
% 5.82/6.19 thf(fact_8744_polyfun__linear__factor__root,axiom,
% 5.82/6.19 ! [C2: nat > rat,A2: rat,N: nat] :
% 5.82/6.19 ( ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_rat )
% 5.82/6.19 => ~ ! [B3: nat > rat] :
% 5.82/6.19 ~ ! [Z5: rat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A2 )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( B3 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor_root
% 5.82/6.19 thf(fact_8745_polyfun__linear__factor__root,axiom,
% 5.82/6.19 ! [C2: nat > int,A2: int,N: nat] :
% 5.82/6.19 ( ( ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( C2 @ I4 ) @ ( power_power_int @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_int )
% 5.82/6.19 => ~ ! [B3: nat > int] :
% 5.82/6.19 ~ ! [Z5: int] :
% 5.82/6.19 ( ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( C2 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_int @ ( minus_minus_int @ Z5 @ A2 )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( B3 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor_root
% 5.82/6.19 thf(fact_8746_polyfun__linear__factor__root,axiom,
% 5.82/6.19 ! [C2: nat > real,A2: real,N: nat] :
% 5.82/6.19 ( ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 => ~ ! [B3: nat > real] :
% 5.82/6.19 ~ ! [Z5: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_real @ ( minus_minus_real @ Z5 @ A2 )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( B3 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor_root
% 5.82/6.19 thf(fact_8747_polyfun__linear__factor,axiom,
% 5.82/6.19 ! [C2: nat > complex,N: nat,A2: complex] :
% 5.82/6.19 ? [B3: nat > complex] :
% 5.82/6.19 ! [Z5: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_complex
% 5.82/6.19 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A2 )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( B3 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor
% 5.82/6.19 thf(fact_8748_polyfun__linear__factor,axiom,
% 5.82/6.19 ! [C2: nat > code_integer,N: nat,A2: code_integer] :
% 5.82/6.19 ? [B3: nat > code_integer] :
% 5.82/6.19 ! [Z5: code_integer] :
% 5.82/6.19 ( ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( C2 @ I4 ) @ ( power_8256067586552552935nteger @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_p5714425477246183910nteger
% 5.82/6.19 @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ Z5 @ A2 )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( B3 @ I4 ) @ ( power_8256067586552552935nteger @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( C2 @ I4 ) @ ( power_8256067586552552935nteger @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor
% 5.82/6.19 thf(fact_8749_polyfun__linear__factor,axiom,
% 5.82/6.19 ! [C2: nat > rat,N: nat,A2: rat] :
% 5.82/6.19 ? [B3: nat > rat] :
% 5.82/6.19 ! [Z5: rat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_rat
% 5.82/6.19 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A2 )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( B3 @ I4 ) @ ( power_power_rat @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( C2 @ I4 ) @ ( power_power_rat @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor
% 5.82/6.19 thf(fact_8750_polyfun__linear__factor,axiom,
% 5.82/6.19 ! [C2: nat > int,N: nat,A2: int] :
% 5.82/6.19 ? [B3: nat > int] :
% 5.82/6.19 ! [Z5: int] :
% 5.82/6.19 ( ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( C2 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_int
% 5.82/6.19 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A2 )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( B3 @ I4 ) @ ( power_power_int @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( C2 @ I4 ) @ ( power_power_int @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor
% 5.82/6.19 thf(fact_8751_polyfun__linear__factor,axiom,
% 5.82/6.19 ! [C2: nat > real,N: nat,A2: real] :
% 5.82/6.19 ? [B3: nat > real] :
% 5.82/6.19 ! [Z5: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A2 )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( B3 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ A2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_linear_factor
% 5.82/6.19 thf(fact_8752_sum__power__shift,axiom,
% 5.82/6.19 ! [M: nat,N: nat,X2: complex] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.19 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_power_shift
% 5.82/6.19 thf(fact_8753_sum__power__shift,axiom,
% 5.82/6.19 ! [M: nat,N: nat,X2: code_integer] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.19 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_power_shift
% 5.82/6.19 thf(fact_8754_sum__power__shift,axiom,
% 5.82/6.19 ! [M: nat,N: nat,X2: rat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.19 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_power_shift
% 5.82/6.19 thf(fact_8755_sum__power__shift,axiom,
% 5.82/6.19 ! [M: nat,N: nat,X2: int] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.19 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_power_shift
% 5.82/6.19 thf(fact_8756_sum__power__shift,axiom,
% 5.82/6.19 ! [M: nat,N: nat,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.82/6.19 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_power_shift
% 5.82/6.19 thf(fact_8757_atLeast1__atMost__eq__remove0,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.19 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % atLeast1_atMost_eq_remove0
% 5.82/6.19 thf(fact_8758_sum_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > rat,N: nat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.in_pairs_0
% 5.82/6.19 thf(fact_8759_sum_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > int,N: nat] :
% 5.82/6.19 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.in_pairs_0
% 5.82/6.19 thf(fact_8760_sum_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > nat,N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.in_pairs_0
% 5.82/6.19 thf(fact_8761_sum_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > real,N: nat] :
% 5.82/6.19 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.in_pairs_0
% 5.82/6.19 thf(fact_8762_polynomial__product,axiom,
% 5.82/6.19 ! [M: nat,A2: nat > complex,N: nat,B2: nat > complex,X2: complex] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ M @ I2 )
% 5.82/6.19 => ( ( A2 @ I2 )
% 5.82/6.19 = zero_zero_complex ) )
% 5.82/6.19 => ( ! [J2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ J2 )
% 5.82/6.19 => ( ( B2 @ J2 )
% 5.82/6.19 = zero_zero_complex ) )
% 5.82/6.19 => ( ( times_times_complex
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( A2 @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [J3: nat] : ( times_times_complex @ ( B2 @ J3 ) @ ( power_power_complex @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [R5: nat] :
% 5.82/6.19 ( times_times_complex
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_complex @ ( A2 @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R5 ) )
% 5.82/6.19 @ ( power_power_complex @ X2 @ R5 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polynomial_product
% 5.82/6.19 thf(fact_8763_polynomial__product,axiom,
% 5.82/6.19 ! [M: nat,A2: nat > code_integer,N: nat,B2: nat > code_integer,X2: code_integer] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ M @ I2 )
% 5.82/6.19 => ( ( A2 @ I2 )
% 5.82/6.19 = zero_z3403309356797280102nteger ) )
% 5.82/6.19 => ( ! [J2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ J2 )
% 5.82/6.19 => ( ( B2 @ J2 )
% 5.82/6.19 = zero_z3403309356797280102nteger ) )
% 5.82/6.19 => ( ( times_3573771949741848930nteger
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( power_8256067586552552935nteger @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [J3: nat] : ( times_3573771949741848930nteger @ ( B2 @ J3 ) @ ( power_8256067586552552935nteger @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [R5: nat] :
% 5.82/6.19 ( times_3573771949741848930nteger
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( A2 @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R5 ) )
% 5.82/6.19 @ ( power_8256067586552552935nteger @ X2 @ R5 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polynomial_product
% 5.82/6.19 thf(fact_8764_polynomial__product,axiom,
% 5.82/6.19 ! [M: nat,A2: nat > rat,N: nat,B2: nat > rat,X2: rat] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ M @ I2 )
% 5.82/6.19 => ( ( A2 @ I2 )
% 5.82/6.19 = zero_zero_rat ) )
% 5.82/6.19 => ( ! [J2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ J2 )
% 5.82/6.19 => ( ( B2 @ J2 )
% 5.82/6.19 = zero_zero_rat ) )
% 5.82/6.19 => ( ( times_times_rat
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [J3: nat] : ( times_times_rat @ ( B2 @ J3 ) @ ( power_power_rat @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [R5: nat] :
% 5.82/6.19 ( times_times_rat
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_rat @ ( A2 @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R5 ) )
% 5.82/6.19 @ ( power_power_rat @ X2 @ R5 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polynomial_product
% 5.82/6.19 thf(fact_8765_polynomial__product,axiom,
% 5.82/6.19 ! [M: nat,A2: nat > int,N: nat,B2: nat > int,X2: int] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ M @ I2 )
% 5.82/6.19 => ( ( A2 @ I2 )
% 5.82/6.19 = zero_zero_int ) )
% 5.82/6.19 => ( ! [J2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ J2 )
% 5.82/6.19 => ( ( B2 @ J2 )
% 5.82/6.19 = zero_zero_int ) )
% 5.82/6.19 => ( ( times_times_int
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( A2 @ I4 ) @ ( power_power_int @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [J3: nat] : ( times_times_int @ ( B2 @ J3 ) @ ( power_power_int @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [R5: nat] :
% 5.82/6.19 ( times_times_int
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_int @ ( A2 @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R5 ) )
% 5.82/6.19 @ ( power_power_int @ X2 @ R5 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polynomial_product
% 5.82/6.19 thf(fact_8766_polynomial__product,axiom,
% 5.82/6.19 ! [M: nat,A2: nat > real,N: nat,B2: nat > real,X2: real] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ M @ I2 )
% 5.82/6.19 => ( ( A2 @ I2 )
% 5.82/6.19 = zero_zero_real ) )
% 5.82/6.19 => ( ! [J2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ J2 )
% 5.82/6.19 => ( ( B2 @ J2 )
% 5.82/6.19 = zero_zero_real ) )
% 5.82/6.19 => ( ( times_times_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( A2 @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [J3: nat] : ( times_times_real @ ( B2 @ J3 ) @ ( power_power_real @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [R5: nat] :
% 5.82/6.19 ( times_times_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( A2 @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R5 ) )
% 5.82/6.19 @ ( power_power_real @ X2 @ R5 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polynomial_product
% 5.82/6.19 thf(fact_8767_prod_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > real,N: nat] :
% 5.82/6.19 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups129246275422532515t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.in_pairs_0
% 5.82/6.19 thf(fact_8768_prod_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > rat,N: nat] :
% 5.82/6.19 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups73079841787564623at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.in_pairs_0
% 5.82/6.19 thf(fact_8769_prod_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > int,N: nat] :
% 5.82/6.19 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.in_pairs_0
% 5.82/6.19 thf(fact_8770_prod_Oin__pairs__0,axiom,
% 5.82/6.19 ! [G: nat > nat,N: nat] :
% 5.82/6.19 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.82/6.19 = ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.in_pairs_0
% 5.82/6.19 thf(fact_8771_polyfun__eq__const,axiom,
% 5.82/6.19 ! [C2: nat > complex,N: nat,K: complex] :
% 5.82/6.19 ( ( ! [X3: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ X3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = K ) )
% 5.82/6.19 = ( ( ( C2 @ zero_zero_nat )
% 5.82/6.19 = K )
% 5.82/6.19 & ! [X3: nat] :
% 5.82/6.19 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.82/6.19 => ( ( C2 @ X3 )
% 5.82/6.19 = zero_zero_complex ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_eq_const
% 5.82/6.19 thf(fact_8772_polyfun__eq__const,axiom,
% 5.82/6.19 ! [C2: nat > real,N: nat,K: real] :
% 5.82/6.19 ( ( ! [X3: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ X3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = K ) )
% 5.82/6.19 = ( ( ( C2 @ zero_zero_nat )
% 5.82/6.19 = K )
% 5.82/6.19 & ! [X3: nat] :
% 5.82/6.19 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.82/6.19 => ( ( C2 @ X3 )
% 5.82/6.19 = zero_zero_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_eq_const
% 5.82/6.19 thf(fact_8773_polynomial__product__nat,axiom,
% 5.82/6.19 ! [M: nat,A2: nat > nat,N: nat,B2: nat > nat,X2: nat] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ M @ I2 )
% 5.82/6.19 => ( ( A2 @ I2 )
% 5.82/6.19 = zero_zero_nat ) )
% 5.82/6.19 => ( ! [J2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ J2 )
% 5.82/6.19 => ( ( B2 @ J2 )
% 5.82/6.19 = zero_zero_nat ) )
% 5.82/6.19 => ( ( times_times_nat
% 5.82/6.19 @ ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_nat @ ( A2 @ I4 ) @ ( power_power_nat @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 @ ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( times_times_nat @ ( B2 @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [R5: nat] :
% 5.82/6.19 ( times_times_nat
% 5.82/6.19 @ ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_nat @ ( A2 @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R5 ) )
% 5.82/6.19 @ ( power_power_nat @ X2 @ R5 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polynomial_product_nat
% 5.82/6.19 thf(fact_8774_floor__add,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.82/6.19 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) )
% 5.82/6.19 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.82/6.19 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % floor_add
% 5.82/6.19 thf(fact_8775_floor__add,axiom,
% 5.82/6.19 ! [X2: rat,Y3: rat] :
% 5.82/6.19 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.82/6.19 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) )
% 5.82/6.19 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.82/6.19 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % floor_add
% 5.82/6.19 thf(fact_8776_sum_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.zero_middle
% 5.82/6.19 thf(fact_8777_sum_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.zero_middle
% 5.82/6.19 thf(fact_8778_sum_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.zero_middle
% 5.82/6.19 thf(fact_8779_sum_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.zero_middle
% 5.82/6.19 thf(fact_8780_sum_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum.zero_middle
% 5.82/6.19 thf(fact_8781_prod_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > assn,H2: nat > assn] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups6906906614972039071t_assn
% 5.82/6.19 @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_assn @ ( J3 = K ) @ one_one_assn @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups6906906614972039071t_assn
% 5.82/6.19 @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.zero_middle
% 5.82/6.19 thf(fact_8782_prod_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups129246275422532515t_real
% 5.82/6.19 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ one_one_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups129246275422532515t_real
% 5.82/6.19 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.zero_middle
% 5.82/6.19 thf(fact_8783_prod_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups73079841787564623at_rat
% 5.82/6.19 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups73079841787564623at_rat
% 5.82/6.19 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.zero_middle
% 5.82/6.19 thf(fact_8784_prod_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups705719431365010083at_int
% 5.82/6.19 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.zero_middle
% 5.82/6.19 thf(fact_8785_prod_Ozero__middle,axiom,
% 5.82/6.19 ! [P6: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ P6 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K @ P6 )
% 5.82/6.19 => ( ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ P6 ) )
% 5.82/6.19 = ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P6 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod.zero_middle
% 5.82/6.19 thf(fact_8786_sum__gp0,axiom,
% 5.82/6.19 ! [X2: complex,N: nat] :
% 5.82/6.19 ( ( ( X2 = one_one_complex )
% 5.82/6.19 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.82/6.19 & ( ( X2 != one_one_complex )
% 5.82/6.19 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp0
% 5.82/6.19 thf(fact_8787_sum__gp0,axiom,
% 5.82/6.19 ! [X2: rat,N: nat] :
% 5.82/6.19 ( ( ( X2 = one_one_rat )
% 5.82/6.19 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.82/6.19 & ( ( X2 != one_one_rat )
% 5.82/6.19 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp0
% 5.82/6.19 thf(fact_8788_sum__gp0,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( ( X2 = one_one_real )
% 5.82/6.19 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.82/6.19 & ( ( X2 != one_one_real )
% 5.82/6.19 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_gp0
% 5.82/6.19 thf(fact_8789_gbinomial__sum__nat__pow2,axiom,
% 5.82/6.19 ! [M: nat] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_sum_nat_pow2
% 5.82/6.19 thf(fact_8790_gbinomial__sum__nat__pow2,axiom,
% 5.82/6.19 ! [M: nat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_sum_nat_pow2
% 5.82/6.19 thf(fact_8791_gbinomial__sum__nat__pow2,axiom,
% 5.82/6.19 ! [M: nat] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_sum_nat_pow2
% 5.82/6.19 thf(fact_8792_gbinomial__partial__sum__poly__xpos,axiom,
% 5.82/6.19 ! [M: nat,A2: complex,X2: complex,Y3: complex] :
% 5.82/6.19 ( ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A2 ) @ K3 ) @ ( power_power_complex @ X2 @ K3 ) ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A2 ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X2 @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X2 @ Y3 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_partial_sum_poly_xpos
% 5.82/6.19 thf(fact_8793_gbinomial__partial__sum__poly__xpos,axiom,
% 5.82/6.19 ! [M: nat,A2: rat,X2: rat,Y3: rat] :
% 5.82/6.19 ( ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A2 ) @ K3 ) @ ( power_power_rat @ X2 @ K3 ) ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A2 ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X2 @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_partial_sum_poly_xpos
% 5.82/6.19 thf(fact_8794_gbinomial__partial__sum__poly__xpos,axiom,
% 5.82/6.19 ! [M: nat,A2: real,X2: real,Y3: real] :
% 5.82/6.19 ( ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A2 ) @ K3 ) @ ( power_power_real @ X2 @ K3 ) ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A2 ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X2 @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_partial_sum_poly_xpos
% 5.82/6.19 thf(fact_8795_polyfun__diff__alt,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > complex,X2: complex,Y3: complex] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_complex
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( A2 @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( A2 @ I4 ) @ ( power_power_complex @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y3 )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A2 @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y3 @ K3 ) ) @ ( power_power_complex @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff_alt
% 5.82/6.19 thf(fact_8796_polyfun__diff__alt,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > code_integer,X2: code_integer,Y3: code_integer] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_8373710615458151222nteger
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( power_8256067586552552935nteger @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( power_8256067586552552935nteger @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X2 @ Y3 )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( A2 @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_8256067586552552935nteger @ Y3 @ K3 ) ) @ ( power_8256067586552552935nteger @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff_alt
% 5.82/6.19 thf(fact_8797_polyfun__diff__alt,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > rat,X2: rat,Y3: rat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_rat
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( power_power_rat @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y3 )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A2 @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y3 @ K3 ) ) @ ( power_power_rat @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff_alt
% 5.82/6.19 thf(fact_8798_polyfun__diff__alt,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > int,X2: int,Y3: int] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_int
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( A2 @ I4 ) @ ( power_power_int @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( A2 @ I4 ) @ ( power_power_int @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_int @ ( minus_minus_int @ X2 @ Y3 )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A2 @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y3 @ K3 ) ) @ ( power_power_int @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff_alt
% 5.82/6.19 thf(fact_8799_polyfun__diff__alt,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > real,X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( A2 @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( A2 @ I4 ) @ ( power_power_real @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_real @ ( minus_minus_real @ X2 @ Y3 )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A2 @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y3 @ K3 ) ) @ ( power_power_real @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff_alt
% 5.82/6.19 thf(fact_8800_polyfun__extremal__lemma,axiom,
% 5.82/6.19 ! [E: real,C2: nat > complex,N: nat] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ E )
% 5.82/6.19 => ? [M9: real] :
% 5.82/6.19 ! [Z5: complex] :
% 5.82/6.19 ( ( ord_less_eq_real @ M9 @ ( real_V1022390504157884413omplex @ Z5 ) )
% 5.82/6.19 => ( ord_less_eq_real
% 5.82/6.19 @ ( real_V1022390504157884413omplex
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( C2 @ I4 ) @ ( power_power_complex @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_extremal_lemma
% 5.82/6.19 thf(fact_8801_polyfun__extremal__lemma,axiom,
% 5.82/6.19 ! [E: real,C2: nat > real,N: nat] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ E )
% 5.82/6.19 => ? [M9: real] :
% 5.82/6.19 ! [Z5: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ M9 @ ( real_V7735802525324610683m_real @ Z5 ) )
% 5.82/6.19 => ( ord_less_eq_real
% 5.82/6.19 @ ( real_V7735802525324610683m_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( C2 @ I4 ) @ ( power_power_real @ Z5 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_extremal_lemma
% 5.82/6.19 thf(fact_8802_polyfun__diff,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > complex,X2: complex,Y3: complex] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_complex
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( A2 @ I4 ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( A2 @ I4 ) @ ( power_power_complex @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y3 )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( times_times_complex
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_complex @ ( A2 @ I4 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( power_power_complex @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff
% 5.82/6.19 thf(fact_8803_polyfun__diff,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > code_integer,X2: code_integer,Y3: code_integer] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_8373710615458151222nteger
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( power_8256067586552552935nteger @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( power_8256067586552552935nteger @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X2 @ Y3 )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( times_3573771949741848930nteger
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( power_8256067586552552935nteger @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( power_8256067586552552935nteger @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff
% 5.82/6.19 thf(fact_8804_polyfun__diff,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > rat,X2: rat,Y3: rat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_rat
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( power_power_rat @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y3 )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( times_times_rat
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( power_power_rat @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff
% 5.82/6.19 thf(fact_8805_polyfun__diff,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > int,X2: int,Y3: int] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_int
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( A2 @ I4 ) @ ( power_power_int @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( A2 @ I4 ) @ ( power_power_int @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_int @ ( minus_minus_int @ X2 @ Y3 )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( times_times_int
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_int @ ( A2 @ I4 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( power_power_int @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff
% 5.82/6.19 thf(fact_8806_polyfun__diff,axiom,
% 5.82/6.19 ! [N: nat,A2: nat > real,X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.82/6.19 => ( ( minus_minus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( A2 @ I4 ) @ ( power_power_real @ X2 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( A2 @ I4 ) @ ( power_power_real @ Y3 @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( times_times_real @ ( minus_minus_real @ X2 @ Y3 )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [J3: nat] :
% 5.82/6.19 ( times_times_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( A2 @ I4 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ ( minus_minus_nat @ I4 @ J3 ) @ one_one_nat ) ) )
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.82/6.19 @ ( power_power_real @ X2 @ J3 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % polyfun_diff
% 5.82/6.19 thf(fact_8807_choose__odd__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] :
% 5.82/6.19 ( if_Code_integer
% 5.82/6.19 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) )
% 5.82/6.19 @ zero_z3403309356797280102nteger )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_odd_sum
% 5.82/6.19 thf(fact_8808_choose__odd__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] :
% 5.82/6.19 ( if_complex
% 5.82/6.19 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) )
% 5.82/6.19 @ zero_zero_complex )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_odd_sum
% 5.82/6.19 thf(fact_8809_choose__odd__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] :
% 5.82/6.19 ( if_rat
% 5.82/6.19 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) )
% 5.82/6.19 @ zero_zero_rat )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_odd_sum
% 5.82/6.19 thf(fact_8810_choose__odd__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] :
% 5.82/6.19 ( if_int
% 5.82/6.19 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) )
% 5.82/6.19 @ zero_zero_int )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_odd_sum
% 5.82/6.19 thf(fact_8811_choose__odd__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] :
% 5.82/6.19 ( if_real
% 5.82/6.19 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) )
% 5.82/6.19 @ zero_zero_real )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_odd_sum
% 5.82/6.19 thf(fact_8812_choose__even__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [I4: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I4 ) ) @ zero_z3403309356797280102nteger )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_even_sum
% 5.82/6.19 thf(fact_8813_choose__even__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [I4: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I4 ) ) @ zero_zero_complex )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_even_sum
% 5.82/6.19 thf(fact_8814_choose__even__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I4 ) ) @ zero_zero_rat )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_even_sum
% 5.82/6.19 thf(fact_8815_choose__even__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [I4: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I4 ) ) @ zero_zero_int )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_even_sum
% 5.82/6.19 thf(fact_8816_choose__even__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I4 ) ) @ zero_zero_real )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) )
% 5.82/6.19 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_even_sum
% 5.82/6.19 thf(fact_8817_central__binomial__lower__bound,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % central_binomial_lower_bound
% 5.82/6.19 thf(fact_8818_binomial__Suc__n,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( binomial @ ( suc @ N ) @ N )
% 5.82/6.19 = ( suc @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_Suc_n
% 5.82/6.19 thf(fact_8819_binomial__n__n,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( binomial @ N @ N )
% 5.82/6.19 = one_one_nat ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_n_n
% 5.82/6.19 thf(fact_8820_binomial__1,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.19 = N ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_1
% 5.82/6.19 thf(fact_8821_binomial__0__Suc,axiom,
% 5.82/6.19 ! [K: nat] :
% 5.82/6.19 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.82/6.19 = zero_zero_nat ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_0_Suc
% 5.82/6.19 thf(fact_8822_binomial__eq__0__iff,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( ( binomial @ N @ K )
% 5.82/6.19 = zero_zero_nat )
% 5.82/6.19 = ( ord_less_nat @ N @ K ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_eq_0_iff
% 5.82/6.19 thf(fact_8823_binomial__Suc__Suc,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.82/6.19 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_Suc_Suc
% 5.82/6.19 thf(fact_8824_binomial__n__0,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( binomial @ N @ zero_zero_nat )
% 5.82/6.19 = one_one_nat ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_n_0
% 5.82/6.19 thf(fact_8825_zero__less__binomial__iff,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % zero_less_binomial_iff
% 5.82/6.19 thf(fact_8826_choose__one,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( binomial @ N @ one_one_nat )
% 5.82/6.19 = N ) ).
% 5.82/6.19
% 5.82/6.19 % choose_one
% 5.82/6.19 thf(fact_8827_binomial__eq__0,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ K )
% 5.82/6.19 => ( ( binomial @ N @ K )
% 5.82/6.19 = zero_zero_nat ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_eq_0
% 5.82/6.19 thf(fact_8828_Suc__times__binomial,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.82/6.19 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Suc_times_binomial
% 5.82/6.19 thf(fact_8829_Suc__times__binomial__eq,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Suc_times_binomial_eq
% 5.82/6.19 thf(fact_8830_binomial__symmetric,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( binomial @ N @ K )
% 5.82/6.19 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_symmetric
% 5.82/6.19 thf(fact_8831_choose__mult__lemma,axiom,
% 5.82/6.19 ! [M: nat,R2: nat,K: nat] :
% 5.82/6.19 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.82/6.19 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_mult_lemma
% 5.82/6.19 thf(fact_8832_binomial__le__pow,axiom,
% 5.82/6.19 ! [R2: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ R2 @ N )
% 5.82/6.19 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_le_pow
% 5.82/6.19 thf(fact_8833_zero__less__binomial,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zero_less_binomial
% 5.82/6.19 thf(fact_8834_Suc__times__binomial__add,axiom,
% 5.82/6.19 ! [A2: nat,B2: nat] :
% 5.82/6.19 ( ( times_times_nat @ ( suc @ A2 ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A2 @ B2 ) ) @ ( suc @ A2 ) ) )
% 5.82/6.19 = ( times_times_nat @ ( suc @ B2 ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A2 @ B2 ) ) @ A2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Suc_times_binomial_add
% 5.82/6.19 thf(fact_8835_binomial__Suc__Suc__eq__times,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.82/6.19 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_Suc_Suc_eq_times
% 5.82/6.19 thf(fact_8836_choose__mult,axiom,
% 5.82/6.19 ! [K: nat,M: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ M )
% 5.82/6.19 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.82/6.19 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_mult
% 5.82/6.19 thf(fact_8837_binomial__absorb__comp,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_absorb_comp
% 5.82/6.19 thf(fact_8838_sum__choose__upper,axiom,
% 5.82/6.19 ! [M: nat,N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_choose_upper
% 5.82/6.19 thf(fact_8839_binomial__absorption,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.82/6.19 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_absorption
% 5.82/6.19 thf(fact_8840_sum__choose__lower,axiom,
% 5.82/6.19 ! [R2: nat,N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_choose_lower
% 5.82/6.19 thf(fact_8841_choose__rising__sum_I1_J,axiom,
% 5.82/6.19 ! [N: nat,M: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_rising_sum(1)
% 5.82/6.19 thf(fact_8842_choose__rising__sum_I2_J,axiom,
% 5.82/6.19 ! [N: nat,M: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_rising_sum(2)
% 5.82/6.19 thf(fact_8843_binomial__antimono,axiom,
% 5.82/6.19 ! [K: nat,K4: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ K4 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K4 @ N )
% 5.82/6.19 => ( ord_less_eq_nat @ ( binomial @ N @ K4 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_antimono
% 5.82/6.19 thf(fact_8844_binomial__maximum,axiom,
% 5.82/6.19 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_maximum
% 5.82/6.19 thf(fact_8845_binomial__ge__n__over__k__pow__k,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ge_n_over_k_pow_k
% 5.82/6.19 thf(fact_8846_binomial__ge__n__over__k__pow__k,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ge_n_over_k_pow_k
% 5.82/6.19 thf(fact_8847_binomial__maximum_H,axiom,
% 5.82/6.19 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_maximum'
% 5.82/6.19 thf(fact_8848_binomial__mono,axiom,
% 5.82/6.19 ! [K: nat,K4: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ K4 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) @ N )
% 5.82/6.19 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K4 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_mono
% 5.82/6.19 thf(fact_8849_binomial__le__pow2,axiom,
% 5.82/6.19 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_le_pow2
% 5.82/6.19 thf(fact_8850_choose__reduce__nat,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.19 => ( ( binomial @ N @ K )
% 5.82/6.19 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_reduce_nat
% 5.82/6.19 thf(fact_8851_times__binomial__minus1__eq,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.82/6.19 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % times_binomial_minus1_eq
% 5.82/6.19 thf(fact_8852_sum__choose__diagonal,axiom,
% 5.82/6.19 ! [M: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_choose_diagonal
% 5.82/6.19 thf(fact_8853_vandermonde,axiom,
% 5.82/6.19 ! [M: nat,N: nat,R2: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ R2 ) )
% 5.82/6.19 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % vandermonde
% 5.82/6.19 thf(fact_8854_binomial__less__binomial__Suc,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_less_binomial_Suc
% 5.82/6.19 thf(fact_8855_binomial__strict__antimono,axiom,
% 5.82/6.19 ! [K: nat,K4: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ K @ K4 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.82/6.19 => ( ( ord_less_eq_nat @ K4 @ N )
% 5.82/6.19 => ( ord_less_nat @ ( binomial @ N @ K4 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_strict_antimono
% 5.82/6.19 thf(fact_8856_binomial__strict__mono,axiom,
% 5.82/6.19 ! [K: nat,K4: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ K @ K4 )
% 5.82/6.19 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) @ N )
% 5.82/6.19 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K4 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_strict_mono
% 5.82/6.19 thf(fact_8857_central__binomial__odd,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.19 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % central_binomial_odd
% 5.82/6.19 thf(fact_8858_binomial__addition__formula,axiom,
% 5.82/6.19 ! [N: nat,K: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( binomial @ N @ ( suc @ K ) )
% 5.82/6.19 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_addition_formula
% 5.82/6.19 thf(fact_8859_choose__row__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_row_sum
% 5.82/6.19 thf(fact_8860_binomial,axiom,
% 5.82/6.19 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.19 ( ( power_power_nat @ ( plus_plus_nat @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A2 @ K3 ) ) @ ( power_power_nat @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial
% 5.82/6.19 thf(fact_8861_choose__two,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.19 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_two
% 5.82/6.19 thf(fact_8862_binomial__ring,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex,N: nat] :
% 5.82/6.19 ( ( power_power_complex @ ( plus_plus_complex @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups2073611262835488442omplex
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A2 @ K3 ) ) @ ( power_power_complex @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ring
% 5.82/6.19 thf(fact_8863_binomial__ring,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer,N: nat] :
% 5.82/6.19 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups7501900531339628137nteger
% 5.82/6.19 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N @ K3 ) ) @ ( power_8256067586552552935nteger @ A2 @ K3 ) ) @ ( power_8256067586552552935nteger @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ring
% 5.82/6.19 thf(fact_8864_binomial__ring,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.19 ( ( power_power_rat @ ( plus_plus_rat @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A2 @ K3 ) ) @ ( power_power_rat @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ring
% 5.82/6.19 thf(fact_8865_binomial__ring,axiom,
% 5.82/6.19 ! [A2: int,B2: int,N: nat] :
% 5.82/6.19 ( ( power_power_int @ ( plus_plus_int @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A2 @ K3 ) ) @ ( power_power_int @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ring
% 5.82/6.19 thf(fact_8866_binomial__ring,axiom,
% 5.82/6.19 ! [A2: nat,B2: nat,N: nat] :
% 5.82/6.19 ( ( power_power_nat @ ( plus_plus_nat @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A2 @ K3 ) ) @ ( power_power_nat @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ring
% 5.82/6.19 thf(fact_8867_binomial__ring,axiom,
% 5.82/6.19 ! [A2: real,B2: real,N: nat] :
% 5.82/6.19 ( ( power_power_real @ ( plus_plus_real @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A2 @ K3 ) ) @ ( power_power_real @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_ring
% 5.82/6.19 thf(fact_8868_binomial__altdef__of__nat,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( groups6464643781859351333omplex
% 5.82/6.19 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I4 ) ) @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ K @ I4 ) ) )
% 5.82/6.19 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_altdef_of_nat
% 5.82/6.19 thf(fact_8869_binomial__altdef__of__nat,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( groups73079841787564623at_rat
% 5.82/6.19 @ ^ [I4: nat] : ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K @ I4 ) ) )
% 5.82/6.19 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_altdef_of_nat
% 5.82/6.19 thf(fact_8870_binomial__altdef__of__nat,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( groups129246275422532515t_real
% 5.82/6.19 @ ^ [I4: nat] : ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ K @ I4 ) ) )
% 5.82/6.19 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_altdef_of_nat
% 5.82/6.19 thf(fact_8871_pochhammer__binomial__sum,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat,N: nat] :
% 5.82/6.19 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups2906978787729119204at_rat
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A2 @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pochhammer_binomial_sum
% 5.82/6.19 thf(fact_8872_pochhammer__binomial__sum,axiom,
% 5.82/6.19 ! [A2: int,B2: int,N: nat] :
% 5.82/6.19 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups3539618377306564664at_int
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pochhammer_binomial_sum
% 5.82/6.19 thf(fact_8873_pochhammer__binomial__sum,axiom,
% 5.82/6.19 ! [A2: real,B2: real,N: nat] :
% 5.82/6.19 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A2 @ B2 ) @ N )
% 5.82/6.19 = ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A2 @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pochhammer_binomial_sum
% 5.82/6.19 thf(fact_8874_choose__square__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_square_sum
% 5.82/6.19 thf(fact_8875_binomial__r__part__sum,axiom,
% 5.82/6.19 ! [M: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.82/6.19 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_r_part_sum
% 5.82/6.19 thf(fact_8876_choose__linear__sum,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( groups3542108847815614940at_nat
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 5.82/6.19 @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.19 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % choose_linear_sum
% 5.82/6.19 thf(fact_8877_upd__rule,axiom,
% 5.82/6.19 ! [I: nat,Xs: list_o,A2: array_o,X2: $o] :
% 5.82/6.19 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.82/6.19 => ( hoare_6478655245392655262rray_o @ ( snga_assn_o @ A2 @ Xs ) @ ( array_upd_o @ I @ X2 @ A2 )
% 5.82/6.19 @ ^ [R5: array_o] : ( times_times_assn @ ( snga_assn_o @ A2 @ ( list_update_o @ Xs @ I @ X2 ) ) @ ( pure_assn @ ( R5 = A2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % upd_rule
% 5.82/6.19 thf(fact_8878_upd__rule,axiom,
% 5.82/6.19 ! [I: nat,Xs: list_nat,A2: array_nat,X2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.82/6.19 => ( hoare_6807272225193264096ay_nat @ ( snga_assn_nat @ A2 @ Xs ) @ ( array_upd_nat @ I @ X2 @ A2 )
% 5.82/6.19 @ ^ [R5: array_nat] : ( times_times_assn @ ( snga_assn_nat @ A2 @ ( list_update_nat @ Xs @ I @ X2 ) ) @ ( pure_assn @ ( R5 = A2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % upd_rule
% 5.82/6.19 thf(fact_8879_upd__rule,axiom,
% 5.82/6.19 ! [I: nat,Xs: list_VEBT_VEBTi,A2: array_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 5.82/6.19 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 5.82/6.19 => ( hoare_3353465787467722821_VEBTi @ ( snga_assn_VEBT_VEBTi @ A2 @ Xs ) @ ( array_upd_VEBT_VEBTi @ I @ X2 @ A2 )
% 5.82/6.19 @ ^ [R5: array_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ A2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X2 ) ) @ ( pure_assn @ ( R5 = A2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % upd_rule
% 5.82/6.19 thf(fact_8880_gbinomial__code,axiom,
% 5.82/6.19 ( gbinomial_complex
% 5.82/6.19 = ( ^ [A5: complex,K3: nat] :
% 5.82/6.19 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.82/6.19 @ ( divide1717551699836669952omplex
% 5.82/6.19 @ ( set_fo1517530859248394432omplex
% 5.82/6.19 @ ^ [L3: nat] : ( times_times_complex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ L3 ) ) )
% 5.82/6.19 @ zero_zero_nat
% 5.82/6.19 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.82/6.19 @ one_one_complex )
% 5.82/6.19 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_code
% 5.82/6.19 thf(fact_8881_gbinomial__code,axiom,
% 5.82/6.19 ( gbinomial_rat
% 5.82/6.19 = ( ^ [A5: rat,K3: nat] :
% 5.82/6.19 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.82/6.19 @ ( divide_divide_rat
% 5.82/6.19 @ ( set_fo1949268297981939178at_rat
% 5.82/6.19 @ ^ [L3: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L3 ) ) )
% 5.82/6.19 @ zero_zero_nat
% 5.82/6.19 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.82/6.19 @ one_one_rat )
% 5.82/6.19 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_code
% 5.82/6.19 thf(fact_8882_gbinomial__code,axiom,
% 5.82/6.19 ( gbinomial_real
% 5.82/6.19 = ( ^ [A5: real,K3: nat] :
% 5.82/6.19 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.82/6.19 @ ( divide_divide_real
% 5.82/6.19 @ ( set_fo3111899725591712190t_real
% 5.82/6.19 @ ^ [L3: nat] : ( times_times_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ L3 ) ) )
% 5.82/6.19 @ zero_zero_nat
% 5.82/6.19 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.82/6.19 @ one_one_real )
% 5.82/6.19 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % gbinomial_code
% 5.82/6.19 thf(fact_8883_powr__int,axiom,
% 5.82/6.19 ! [X2: real,I: int] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.82/6.19 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.82/6.19 = ( power_power_real @ X2 @ ( nat2 @ I ) ) ) )
% 5.82/6.19 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.82/6.19 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % powr_int
% 5.82/6.19 thf(fact_8884_of__nat__id,axiom,
% 5.82/6.19 ( semiri1316708129612266289at_nat
% 5.82/6.19 = ( ^ [N4: nat] : N4 ) ) ).
% 5.82/6.19
% 5.82/6.19 % of_nat_id
% 5.82/6.19 thf(fact_8885_neg__le__iff__le,axiom,
% 5.82/6.19 ! [B2: real,A2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_real @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_iff_le
% 5.82/6.19 thf(fact_8886_neg__le__iff__le,axiom,
% 5.82/6.19 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.19 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.82/6.19 = ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_iff_le
% 5.82/6.19 thf(fact_8887_neg__le__iff__le,axiom,
% 5.82/6.19 ! [B2: rat,A2: rat] :
% 5.82/6.19 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_iff_le
% 5.82/6.19 thf(fact_8888_neg__le__iff__le,axiom,
% 5.82/6.19 ! [B2: int,A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_iff_le
% 5.82/6.19 thf(fact_8889_neg__less__iff__less,axiom,
% 5.82/6.19 ! [B2: int,A2: int] :
% 5.82/6.19 ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A2 ) )
% 5.82/6.19 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_iff_less
% 5.82/6.19 thf(fact_8890_neg__less__iff__less,axiom,
% 5.82/6.19 ! [B2: real,A2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A2 ) )
% 5.82/6.19 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_iff_less
% 5.82/6.19 thf(fact_8891_neg__less__iff__less,axiom,
% 5.82/6.19 ! [B2: code_integer,A2: code_integer] :
% 5.82/6.19 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.82/6.19 = ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_iff_less
% 5.82/6.19 thf(fact_8892_neg__less__iff__less,axiom,
% 5.82/6.19 ! [B2: rat,A2: rat] :
% 5.82/6.19 ( ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A2 ) )
% 5.82/6.19 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_iff_less
% 5.82/6.19 thf(fact_8893_neg__numeral__eq__iff,axiom,
% 5.82/6.19 ! [M: num,N: num] :
% 5.82/6.19 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.82/6.19 = ( M = N ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_numeral_eq_iff
% 5.82/6.19 thf(fact_8894_neg__numeral__eq__iff,axiom,
% 5.82/6.19 ! [M: num,N: num] :
% 5.82/6.19 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.82/6.19 = ( M = N ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_numeral_eq_iff
% 5.82/6.19 thf(fact_8895_neg__numeral__eq__iff,axiom,
% 5.82/6.19 ! [M: num,N: num] :
% 5.82/6.19 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.82/6.19 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.82/6.19 = ( M = N ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_numeral_eq_iff
% 5.82/6.19 thf(fact_8896_neg__numeral__eq__iff,axiom,
% 5.82/6.19 ! [M: num,N: num] :
% 5.82/6.19 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.82/6.19 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.82/6.19 = ( M = N ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_numeral_eq_iff
% 5.82/6.19 thf(fact_8897_neg__numeral__eq__iff,axiom,
% 5.82/6.19 ! [M: num,N: num] :
% 5.82/6.19 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.82/6.19 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.82/6.19 = ( M = N ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_numeral_eq_iff
% 5.82/6.19 thf(fact_8898_minus__add__distrib,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( uminus_uminus_int @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.19 = ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_distrib
% 5.82/6.19 thf(fact_8899_minus__add__distrib,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( uminus_uminus_real @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.19 = ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ ( uminus_uminus_real @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_distrib
% 5.82/6.19 thf(fact_8900_minus__add__distrib,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A2 @ B2 ) )
% 5.82/6.19 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( uminus1482373934393186551omplex @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_distrib
% 5.82/6.19 thf(fact_8901_minus__add__distrib,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) )
% 5.82/6.19 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_distrib
% 5.82/6.19 thf(fact_8902_minus__add__distrib,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.19 = ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( uminus_uminus_rat @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_distrib
% 5.82/6.19 thf(fact_8903_minus__add__cancel,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ ( plus_plus_int @ A2 @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_cancel
% 5.82/6.19 thf(fact_8904_minus__add__cancel,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ ( plus_plus_real @ A2 @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_cancel
% 5.82/6.19 thf(fact_8905_minus__add__cancel,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( plus_plus_complex @ A2 @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_cancel
% 5.82/6.19 thf(fact_8906_minus__add__cancel,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_cancel
% 5.82/6.19 thf(fact_8907_minus__add__cancel,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( plus_plus_rat @ A2 @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % minus_add_cancel
% 5.82/6.19 thf(fact_8908_add__minus__cancel,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( plus_plus_int @ A2 @ ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % add_minus_cancel
% 5.82/6.19 thf(fact_8909_add__minus__cancel,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( plus_plus_real @ A2 @ ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % add_minus_cancel
% 5.82/6.19 thf(fact_8910_add__minus__cancel,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( plus_plus_complex @ A2 @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % add_minus_cancel
% 5.82/6.19 thf(fact_8911_add__minus__cancel,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( plus_p5714425477246183910nteger @ A2 @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % add_minus_cancel
% 5.82/6.19 thf(fact_8912_add__minus__cancel,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( plus_plus_rat @ A2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ B2 ) )
% 5.82/6.19 = B2 ) ).
% 5.82/6.19
% 5.82/6.19 % add_minus_cancel
% 5.82/6.19 thf(fact_8913_mult__minus__left,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( times_times_int @ ( uminus_uminus_int @ A2 ) @ B2 )
% 5.82/6.19 = ( uminus_uminus_int @ ( times_times_int @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_left
% 5.82/6.19 thf(fact_8914_mult__minus__left,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( times_times_real @ ( uminus_uminus_real @ A2 ) @ B2 )
% 5.82/6.19 = ( uminus_uminus_real @ ( times_times_real @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_left
% 5.82/6.19 thf(fact_8915_mult__minus__left,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A2 ) @ B2 )
% 5.82/6.19 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_left
% 5.82/6.19 thf(fact_8916_mult__minus__left,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B2 )
% 5.82/6.19 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_left
% 5.82/6.19 thf(fact_8917_mult__minus__left,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( times_times_rat @ ( uminus_uminus_rat @ A2 ) @ B2 )
% 5.82/6.19 = ( uminus_uminus_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_left
% 5.82/6.19 thf(fact_8918_minus__mult__minus,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( times_times_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( times_times_int @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_mult_minus
% 5.82/6.19 thf(fact_8919_minus__mult__minus,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( times_times_real @ ( uminus_uminus_real @ A2 ) @ ( uminus_uminus_real @ B2 ) )
% 5.82/6.19 = ( times_times_real @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_mult_minus
% 5.82/6.19 thf(fact_8920_minus__mult__minus,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.82/6.19 = ( times_times_complex @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_mult_minus
% 5.82/6.19 thf(fact_8921_minus__mult__minus,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.82/6.19 = ( times_3573771949741848930nteger @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_mult_minus
% 5.82/6.19 thf(fact_8922_minus__mult__minus,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( times_times_rat @ ( uminus_uminus_rat @ A2 ) @ ( uminus_uminus_rat @ B2 ) )
% 5.82/6.19 = ( times_times_rat @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_mult_minus
% 5.82/6.19 thf(fact_8923_mult__minus__right,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( times_times_int @ A2 @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( times_times_int @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_right
% 5.82/6.19 thf(fact_8924_mult__minus__right,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( times_times_real @ A2 @ ( uminus_uminus_real @ B2 ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( times_times_real @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_right
% 5.82/6.19 thf(fact_8925_mult__minus__right,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( times_times_complex @ A2 @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.82/6.19 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_right
% 5.82/6.19 thf(fact_8926_mult__minus__right,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( times_3573771949741848930nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.82/6.19 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_right
% 5.82/6.19 thf(fact_8927_mult__minus__right,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( times_times_rat @ A2 @ ( uminus_uminus_rat @ B2 ) )
% 5.82/6.19 = ( uminus_uminus_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mult_minus_right
% 5.82/6.19 thf(fact_8928_minus__diff__eq,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( uminus_uminus_int @ ( minus_minus_int @ A2 @ B2 ) )
% 5.82/6.19 = ( minus_minus_int @ B2 @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_diff_eq
% 5.82/6.19 thf(fact_8929_minus__diff__eq,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( uminus_uminus_real @ ( minus_minus_real @ A2 @ B2 ) )
% 5.82/6.19 = ( minus_minus_real @ B2 @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_diff_eq
% 5.82/6.19 thf(fact_8930_minus__diff__eq,axiom,
% 5.82/6.19 ! [A2: complex,B2: complex] :
% 5.82/6.19 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A2 @ B2 ) )
% 5.82/6.19 = ( minus_minus_complex @ B2 @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_diff_eq
% 5.82/6.19 thf(fact_8931_minus__diff__eq,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) )
% 5.82/6.19 = ( minus_8373710615458151222nteger @ B2 @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_diff_eq
% 5.82/6.19 thf(fact_8932_minus__diff__eq,axiom,
% 5.82/6.19 ! [A2: rat,B2: rat] :
% 5.82/6.19 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 5.82/6.19 = ( minus_minus_rat @ B2 @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_diff_eq
% 5.82/6.19 thf(fact_8933_div__minus__minus,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( divide_divide_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( divide_divide_int @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % div_minus_minus
% 5.82/6.19 thf(fact_8934_div__minus__minus,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.82/6.19 = ( divide6298287555418463151nteger @ A2 @ B2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % div_minus_minus
% 5.82/6.19 thf(fact_8935_mod__minus__minus,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mod_minus_minus
% 5.82/6.19 thf(fact_8936_mod__minus__minus,axiom,
% 5.82/6.19 ! [A2: code_integer,B2: code_integer] :
% 5.82/6.19 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.82/6.19 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A2 @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % mod_minus_minus
% 5.82/6.19 thf(fact_8937_neg__less__eq__nonneg,axiom,
% 5.82/6.19 ! [A2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ A2 )
% 5.82/6.19 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_eq_nonneg
% 5.82/6.19 thf(fact_8938_neg__less__eq__nonneg,axiom,
% 5.82/6.19 ! [A2: code_integer] :
% 5.82/6.19 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 5.82/6.19 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_eq_nonneg
% 5.82/6.19 thf(fact_8939_neg__less__eq__nonneg,axiom,
% 5.82/6.19 ! [A2: rat] :
% 5.82/6.19 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 5.82/6.19 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_eq_nonneg
% 5.82/6.19 thf(fact_8940_neg__less__eq__nonneg,axiom,
% 5.82/6.19 ! [A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 5.82/6.19 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_eq_nonneg
% 5.82/6.19 thf(fact_8941_less__eq__neg__nonpos,axiom,
% 5.82/6.19 ! [A2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ A2 @ ( uminus_uminus_real @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % less_eq_neg_nonpos
% 5.82/6.19 thf(fact_8942_less__eq__neg__nonpos,axiom,
% 5.82/6.19 ! [A2: code_integer] :
% 5.82/6.19 ( ( ord_le3102999989581377725nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.82/6.19 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.82/6.19
% 5.82/6.19 % less_eq_neg_nonpos
% 5.82/6.19 thf(fact_8943_less__eq__neg__nonpos,axiom,
% 5.82/6.19 ! [A2: rat] :
% 5.82/6.19 ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.19
% 5.82/6.19 % less_eq_neg_nonpos
% 5.82/6.19 thf(fact_8944_less__eq__neg__nonpos,axiom,
% 5.82/6.19 ! [A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % less_eq_neg_nonpos
% 5.82/6.19 thf(fact_8945_neg__le__0__iff__le,axiom,
% 5.82/6.19 ! [A2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_0_iff_le
% 5.82/6.19 thf(fact_8946_neg__le__0__iff__le,axiom,
% 5.82/6.19 ! [A2: code_integer] :
% 5.82/6.19 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ zero_z3403309356797280102nteger )
% 5.82/6.19 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_0_iff_le
% 5.82/6.19 thf(fact_8947_neg__le__0__iff__le,axiom,
% 5.82/6.19 ! [A2: rat] :
% 5.82/6.19 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ zero_zero_rat )
% 5.82/6.19 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_0_iff_le
% 5.82/6.19 thf(fact_8948_neg__le__0__iff__le,axiom,
% 5.82/6.19 ! [A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ zero_zero_int )
% 5.82/6.19 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_le_0_iff_le
% 5.82/6.19 thf(fact_8949_neg__0__le__iff__le,axiom,
% 5.82/6.19 ! [A2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_le_iff_le
% 5.82/6.19 thf(fact_8950_neg__0__le__iff__le,axiom,
% 5.82/6.19 ! [A2: code_integer] :
% 5.82/6.19 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.82/6.19 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_le_iff_le
% 5.82/6.19 thf(fact_8951_neg__0__le__iff__le,axiom,
% 5.82/6.19 ! [A2: rat] :
% 5.82/6.19 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_le_iff_le
% 5.82/6.19 thf(fact_8952_neg__0__le__iff__le,axiom,
% 5.82/6.19 ! [A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A2 ) )
% 5.82/6.19 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_le_iff_le
% 5.82/6.19 thf(fact_8953_neg__less__0__iff__less,axiom,
% 5.82/6.19 ! [A2: int] :
% 5.82/6.19 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ zero_zero_int )
% 5.82/6.19 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_0_iff_less
% 5.82/6.19 thf(fact_8954_neg__less__0__iff__less,axiom,
% 5.82/6.19 ! [A2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ A2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_0_iff_less
% 5.82/6.19 thf(fact_8955_neg__less__0__iff__less,axiom,
% 5.82/6.19 ! [A2: code_integer] :
% 5.82/6.19 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ zero_z3403309356797280102nteger )
% 5.82/6.19 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_0_iff_less
% 5.82/6.19 thf(fact_8956_neg__less__0__iff__less,axiom,
% 5.82/6.19 ! [A2: rat] :
% 5.82/6.19 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ zero_zero_rat )
% 5.82/6.19 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_less_0_iff_less
% 5.82/6.19 thf(fact_8957_neg__0__less__iff__less,axiom,
% 5.82/6.19 ! [A2: int] :
% 5.82/6.19 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A2 ) )
% 5.82/6.19 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_less_iff_less
% 5.82/6.19 thf(fact_8958_neg__0__less__iff__less,axiom,
% 5.82/6.19 ! [A2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A2 ) )
% 5.82/6.19 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_less_iff_less
% 5.82/6.19 thf(fact_8959_neg__0__less__iff__less,axiom,
% 5.82/6.19 ! [A2: code_integer] :
% 5.82/6.19 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.82/6.19 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_less_iff_less
% 5.82/6.19 thf(fact_8960_neg__0__less__iff__less,axiom,
% 5.82/6.19 ! [A2: rat] :
% 5.82/6.19 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A2 ) )
% 5.82/6.19 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_0_less_iff_less
% 5.82/6.19 thf(fact_8961_negative__zle,axiom,
% 5.82/6.19 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.82/6.19
% 5.82/6.19 % negative_zle
% 5.82/6.19 thf(fact_8962_negative__zless,axiom,
% 5.82/6.19 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.82/6.19
% 5.82/6.19 % negative_zless
% 5.82/6.19 thf(fact_8963_int__div__minus__is__minus1,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.82/6.19 => ( ( ( divide_divide_int @ A2 @ B2 )
% 5.82/6.19 = ( uminus_uminus_int @ A2 ) )
% 5.82/6.19 = ( B2
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_div_minus_is_minus1
% 5.82/6.19 thf(fact_8964_fact__mono__nat,axiom,
% 5.82/6.19 ! [M: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_mono_nat
% 5.82/6.19 thf(fact_8965_fact__ge__self,axiom,
% 5.82/6.19 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_ge_self
% 5.82/6.19 thf(fact_8966_fact__less__mono__nat,axiom,
% 5.82/6.19 ! [M: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.82/6.19 => ( ( ord_less_nat @ M @ N )
% 5.82/6.19 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_less_mono_nat
% 5.82/6.19 thf(fact_8967_int__cases,axiom,
% 5.82/6.19 ! [Z: int] :
% 5.82/6.19 ( ! [N3: nat] :
% 5.82/6.19 ( Z
% 5.82/6.19 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.82/6.19 => ~ ! [N3: nat] :
% 5.82/6.19 ( Z
% 5.82/6.19 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_cases
% 5.82/6.19 thf(fact_8968_int__of__nat__induct,axiom,
% 5.82/6.19 ! [P: int > $o,Z: int] :
% 5.82/6.19 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.82/6.19 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.82/6.19 => ( P @ Z ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_of_nat_induct
% 5.82/6.19 thf(fact_8969_pos__zmult__eq__1__iff__lemma,axiom,
% 5.82/6.19 ! [M: int,N: int] :
% 5.82/6.19 ( ( ( times_times_int @ M @ N )
% 5.82/6.19 = one_one_int )
% 5.82/6.19 => ( ( M = one_one_int )
% 5.82/6.19 | ( M
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pos_zmult_eq_1_iff_lemma
% 5.82/6.19 thf(fact_8970_zmult__eq__1__iff,axiom,
% 5.82/6.19 ! [M: int,N: int] :
% 5.82/6.19 ( ( ( times_times_int @ M @ N )
% 5.82/6.19 = one_one_int )
% 5.82/6.19 = ( ( ( M = one_one_int )
% 5.82/6.19 & ( N = one_one_int ) )
% 5.82/6.19 | ( ( M
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.19 & ( N
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zmult_eq_1_iff
% 5.82/6.19 thf(fact_8971_minus__int__code_I2_J,axiom,
% 5.82/6.19 ! [L: int] :
% 5.82/6.19 ( ( minus_minus_int @ zero_zero_int @ L )
% 5.82/6.19 = ( uminus_uminus_int @ L ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_int_code(2)
% 5.82/6.19 thf(fact_8972_fact__ge__Suc__0__nat,axiom,
% 5.82/6.19 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_ge_Suc_0_nat
% 5.82/6.19 thf(fact_8973_prod__Suc__Suc__fact,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.82/6.19 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod_Suc_Suc_fact
% 5.82/6.19 thf(fact_8974_prod__Suc__fact,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.82/6.19 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % prod_Suc_fact
% 5.82/6.19 thf(fact_8975_dvd__fact,axiom,
% 5.82/6.19 ! [M: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.82/6.19 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % dvd_fact
% 5.82/6.19 thf(fact_8976_int__cases4,axiom,
% 5.82/6.19 ! [M: int] :
% 5.82/6.19 ( ! [N3: nat] :
% 5.82/6.19 ( M
% 5.82/6.19 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.82/6.19 => ~ ! [N3: nat] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.19 => ( M
% 5.82/6.19 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_cases4
% 5.82/6.19 thf(fact_8977_int__zle__neg,axiom,
% 5.82/6.19 ! [N: nat,M: nat] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.82/6.19 = ( ( N = zero_zero_nat )
% 5.82/6.19 & ( M = zero_zero_nat ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_zle_neg
% 5.82/6.19 thf(fact_8978_negative__zle__0,axiom,
% 5.82/6.19 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.82/6.19
% 5.82/6.19 % negative_zle_0
% 5.82/6.19 thf(fact_8979_nonpos__int__cases,axiom,
% 5.82/6.19 ! [K: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.82/6.19 => ~ ! [N3: nat] :
% 5.82/6.19 ( K
% 5.82/6.19 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nonpos_int_cases
% 5.82/6.19 thf(fact_8980_zmod__zminus2__eq__if,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 = zero_zero_int )
% 5.82/6.19 => ( ( modulo_modulo_int @ A2 @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = zero_zero_int ) )
% 5.82/6.19 & ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 != zero_zero_int )
% 5.82/6.19 => ( ( modulo_modulo_int @ A2 @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( minus_minus_int @ ( modulo_modulo_int @ A2 @ B2 ) @ B2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zmod_zminus2_eq_if
% 5.82/6.19 thf(fact_8981_zmod__zminus1__eq__if,axiom,
% 5.82/6.19 ! [A2: int,B2: int] :
% 5.82/6.19 ( ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 = zero_zero_int )
% 5.82/6.19 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A2 ) @ B2 )
% 5.82/6.19 = zero_zero_int ) )
% 5.82/6.19 & ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 != zero_zero_int )
% 5.82/6.19 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A2 ) @ B2 )
% 5.82/6.19 = ( minus_minus_int @ B2 @ ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zmod_zminus1_eq_if
% 5.82/6.19 thf(fact_8982_fact__diff__Suc,axiom,
% 5.82/6.19 ! [N: nat,M: nat] :
% 5.82/6.19 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.82/6.19 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.82/6.19 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_diff_Suc
% 5.82/6.19 thf(fact_8983_fact__div__fact__le__pow,axiom,
% 5.82/6.19 ! [R2: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ R2 @ N )
% 5.82/6.19 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_div_fact_le_pow
% 5.82/6.19 thf(fact_8984_binomial__fact__lemma,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.82/6.19 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_fact_lemma
% 5.82/6.19 thf(fact_8985_int__cases3,axiom,
% 5.82/6.19 ! [K: int] :
% 5.82/6.19 ( ( K != zero_zero_int )
% 5.82/6.19 => ( ! [N3: nat] :
% 5.82/6.19 ( ( K
% 5.82/6.19 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.82/6.19 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.82/6.19 => ~ ! [N3: nat] :
% 5.82/6.19 ( ( K
% 5.82/6.19 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.82/6.19 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_cases3
% 5.82/6.19 thf(fact_8986_fact__eq__fact__times,axiom,
% 5.82/6.19 ! [N: nat,M: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.19 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.82/6.19 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.82/6.19 @ ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [X3: nat] : X3
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_eq_fact_times
% 5.82/6.19 thf(fact_8987_not__zle__0__negative,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % not_zle_0_negative
% 5.82/6.19 thf(fact_8988_negD,axiom,
% 5.82/6.19 ! [X2: int] :
% 5.82/6.19 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.82/6.19 => ? [N3: nat] :
% 5.82/6.19 ( X2
% 5.82/6.19 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % negD
% 5.82/6.19 thf(fact_8989_negative__zless__0,axiom,
% 5.82/6.19 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.82/6.19
% 5.82/6.19 % negative_zless_0
% 5.82/6.19 thf(fact_8990_verit__less__mono__div__int2,axiom,
% 5.82/6.19 ! [A: int,B: int,N: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ A @ B )
% 5.82/6.19 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.82/6.19 => ( ord_less_eq_int @ ( divide_divide_int @ B @ N ) @ ( divide_divide_int @ A @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % verit_less_mono_div_int2
% 5.82/6.19 thf(fact_8991_div__eq__minus1,axiom,
% 5.82/6.19 ! [B2: int] :
% 5.82/6.19 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.19 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B2 )
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % div_eq_minus1
% 5.82/6.19 thf(fact_8992_binomial__altdef__nat,axiom,
% 5.82/6.19 ! [K: nat,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ K @ N )
% 5.82/6.19 => ( ( binomial @ N @ K )
% 5.82/6.19 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_altdef_nat
% 5.82/6.19 thf(fact_8993_fact__div__fact,axiom,
% 5.82/6.19 ! [N: nat,M: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ N @ M )
% 5.82/6.19 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.82/6.19 = ( groups708209901874060359at_nat
% 5.82/6.19 @ ^ [X3: nat] : X3
% 5.82/6.19 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % fact_div_fact
% 5.82/6.19 thf(fact_8994_neg__int__cases,axiom,
% 5.82/6.19 ! [K: int] :
% 5.82/6.19 ( ( ord_less_int @ K @ zero_zero_int )
% 5.82/6.19 => ~ ! [N3: nat] :
% 5.82/6.19 ( ( K
% 5.82/6.19 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.82/6.19 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % neg_int_cases
% 5.82/6.19 thf(fact_8995_nat__mult__distrib__neg,axiom,
% 5.82/6.19 ! [Z: int,Z6: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.82/6.19 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.82/6.19 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat_mult_distrib_neg
% 5.82/6.19 thf(fact_8996_minus__mod__int__eq,axiom,
% 5.82/6.19 ! [L: int,K: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.82/6.19 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.82/6.19 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_mod_int_eq
% 5.82/6.19 thf(fact_8997_zmod__minus1,axiom,
% 5.82/6.19 ! [B2: int] :
% 5.82/6.19 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.19 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B2 )
% 5.82/6.19 = ( minus_minus_int @ B2 @ one_one_int ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zmod_minus1
% 5.82/6.19 thf(fact_8998_zdiv__zminus1__eq__if,axiom,
% 5.82/6.19 ! [B2: int,A2: int] :
% 5.82/6.19 ( ( B2 != zero_zero_int )
% 5.82/6.19 => ( ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 = zero_zero_int )
% 5.82/6.19 => ( ( divide_divide_int @ ( uminus_uminus_int @ A2 ) @ B2 )
% 5.82/6.19 = ( uminus_uminus_int @ ( divide_divide_int @ A2 @ B2 ) ) ) )
% 5.82/6.19 & ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 != zero_zero_int )
% 5.82/6.19 => ( ( divide_divide_int @ ( uminus_uminus_int @ A2 ) @ B2 )
% 5.82/6.19 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A2 @ B2 ) ) @ one_one_int ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zdiv_zminus1_eq_if
% 5.82/6.19 thf(fact_8999_zdiv__zminus2__eq__if,axiom,
% 5.82/6.19 ! [B2: int,A2: int] :
% 5.82/6.19 ( ( B2 != zero_zero_int )
% 5.82/6.19 => ( ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 = zero_zero_int )
% 5.82/6.19 => ( ( divide_divide_int @ A2 @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( divide_divide_int @ A2 @ B2 ) ) ) )
% 5.82/6.19 & ( ( ( modulo_modulo_int @ A2 @ B2 )
% 5.82/6.19 != zero_zero_int )
% 5.82/6.19 => ( ( divide_divide_int @ A2 @ ( uminus_uminus_int @ B2 ) )
% 5.82/6.19 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A2 @ B2 ) ) @ one_one_int ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zdiv_zminus2_eq_if
% 5.82/6.19 thf(fact_9000_square__fact__le__2__fact,axiom,
% 5.82/6.19 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % square_fact_le_2_fact
% 5.82/6.19 thf(fact_9001_zminus1__lemma,axiom,
% 5.82/6.19 ! [A2: int,B2: int,Q3: int,R2: int] :
% 5.82/6.19 ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.19 => ( ( B2 != zero_zero_int )
% 5.82/6.19 => ( eucl_rel_int @ ( uminus_uminus_int @ A2 ) @ B2 @ ( 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 @ B2 @ R2 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zminus1_lemma
% 5.82/6.19 thf(fact_9002_minus__1__div__exp__eq__int,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_1_div_exp_eq_int
% 5.82/6.19 thf(fact_9003_div__pos__neg__trivial,axiom,
% 5.82/6.19 ! [K: int,L: int] :
% 5.82/6.19 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.19 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.82/6.19 => ( ( divide_divide_int @ K @ L )
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % div_pos_neg_trivial
% 5.82/6.19 thf(fact_9004_int__bit__induct,axiom,
% 5.82/6.19 ! [P: int > $o,K: int] :
% 5.82/6.19 ( ( P @ zero_zero_int )
% 5.82/6.19 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.19 => ( ! [K2: int] :
% 5.82/6.19 ( ( P @ K2 )
% 5.82/6.19 => ( ( K2 != zero_zero_int )
% 5.82/6.19 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.19 => ( ! [K2: int] :
% 5.82/6.19 ( ( P @ K2 )
% 5.82/6.19 => ( ( K2
% 5.82/6.19 != ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.19 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.19 => ( P @ K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % int_bit_induct
% 5.82/6.19 thf(fact_9005_m1mod2k,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.19 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % m1mod2k
% 5.82/6.19 thf(fact_9006_Maclaurin__lemma,axiom,
% 5.82/6.19 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.82/6.19 => ? [B9: real] :
% 5.82/6.19 ( ( F @ H2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_lemma
% 5.82/6.19 thf(fact_9007_sb__dec__lem_H,axiom,
% 5.82/6.19 ! [K: nat,A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) @ A2 )
% 5.82/6.19 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A2 @ ( 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 ) ) @ A2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sb_dec_lem'
% 5.82/6.19 thf(fact_9008_m1mod22k,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( 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 ) ) )
% 5.82/6.19 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % m1mod22k
% 5.82/6.19 thf(fact_9009_sb__inc__lem_H,axiom,
% 5.82/6.19 ! [A2: int,K: nat] :
% 5.82/6.19 ( ( ord_less_int @ A2 @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) )
% 5.82/6.19 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A2 @ ( 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 @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sb_inc_lem'
% 5.82/6.19 thf(fact_9010_sb__dec__lem,axiom,
% 5.82/6.19 ! [K: nat,A2: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A2 ) )
% 5.82/6.19 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A2 @ ( 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 ) ) @ A2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sb_dec_lem
% 5.82/6.19 thf(fact_9011_binomial__code,axiom,
% 5.82/6.19 ( binomial
% 5.82/6.19 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % binomial_code
% 5.82/6.19 thf(fact_9012_one__div__minus__numeral,axiom,
% 5.82/6.19 ! [N: num] :
% 5.82/6.19 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % one_div_minus_numeral
% 5.82/6.19 thf(fact_9013_minus__one__div__numeral,axiom,
% 5.82/6.19 ! [N: num] :
% 5.82/6.19 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_one_div_numeral
% 5.82/6.19 thf(fact_9014_real__add__minus__iff,axiom,
% 5.82/6.19 ! [X2: real,A2: real] :
% 5.82/6.19 ( ( ( plus_plus_real @ X2 @ ( uminus_uminus_real @ A2 ) )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 = ( X2 = A2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_add_minus_iff
% 5.82/6.19 thf(fact_9015_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.82/6.19 ! [B2: num] :
% 5.82/6.19 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B2 ) ) ) )
% 5.82/6.19 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % floor_minus_one_divide_eq_div_numeral
% 5.82/6.19 thf(fact_9016_real__minus__mult__self__le,axiom,
% 5.82/6.19 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_minus_mult_self_le
% 5.82/6.19 thf(fact_9017_minus__real__def,axiom,
% 5.82/6.19 ( minus_minus_real
% 5.82/6.19 = ( ^ [X3: real,Y: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % minus_real_def
% 5.82/6.19 thf(fact_9018_complex__mod__minus__le__complex__mod,axiom,
% 5.82/6.19 ! [X2: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_mod_minus_le_complex_mod
% 5.82/6.19 thf(fact_9019_real__add__less__0__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y3 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_real @ Y3 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_add_less_0_iff
% 5.82/6.19 thf(fact_9020_real__0__less__add__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_0_less_add_iff
% 5.82/6.19 thf(fact_9021_real__0__le__add__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_0_le_add_iff
% 5.82/6.19 thf(fact_9022_real__add__le__0__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( plus_plus_real @ X2 @ Y3 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_eq_real @ Y3 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_add_le_0_iff
% 5.82/6.19 thf(fact_9023_realpow__square__minus__le,axiom,
% 5.82/6.19 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % realpow_square_minus_le
% 5.82/6.19 thf(fact_9024_powr__neg__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % powr_neg_one
% 5.82/6.19 thf(fact_9025_Bernoulli__inequality,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Bernoulli_inequality
% 5.82/6.19 thf(fact_9026_log__minus__eq__powr,axiom,
% 5.82/6.19 ! [B2: real,X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.19 => ( ( B2 != one_one_real )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( minus_minus_real @ ( log @ B2 @ X2 ) @ Y3 )
% 5.82/6.19 = ( log @ B2 @ ( times_times_real @ X2 @ ( powr_real @ B2 @ ( uminus_uminus_real @ Y3 ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % log_minus_eq_powr
% 5.82/6.19 thf(fact_9027_powr__neg__numeral,axiom,
% 5.82/6.19 ! [X2: real,N: num] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % powr_neg_numeral
% 5.82/6.19 thf(fact_9028_cos__coeff__def,axiom,
% 5.82/6.19 ( cos_coeff
% 5.82/6.19 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) @ zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_coeff_def
% 5.82/6.19 thf(fact_9029_sin__coeff__def,axiom,
% 5.82/6.19 ( sin_coeff
% 5.82/6.19 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_coeff_def
% 5.82/6.19 thf(fact_9030_signed__take__bit__Suc__bit0,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.82/6.19 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_Suc_bit0
% 5.82/6.19 thf(fact_9031_signed__take__bit__Suc__minus__bit0,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.82/6.19 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_Suc_minus_bit0
% 5.82/6.19 thf(fact_9032_signed__take__bit__Suc__bit1,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.82/6.19 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_Suc_bit1
% 5.82/6.19 thf(fact_9033_signed__take__bit__Suc__minus__bit1,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.82/6.19 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_Suc_minus_bit1
% 5.82/6.19 thf(fact_9034_signed__take__bit__add,axiom,
% 5.82/6.19 ! [N: nat,K: int,L: int] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.82/6.19 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_add
% 5.82/6.19 thf(fact_9035_signed__take__bit__diff,axiom,
% 5.82/6.19 ! [N: nat,K: int,L: int] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.82/6.19 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_diff
% 5.82/6.19 thf(fact_9036_signed__take__bit__int__less__exp,axiom,
% 5.82/6.19 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_less_exp
% 5.82/6.19 thf(fact_9037_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.82/6.19 ! [K: int,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.82/6.19 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_greater_eq_self_iff
% 5.82/6.19 thf(fact_9038_signed__take__bit__int__less__self__iff,axiom,
% 5.82/6.19 ! [N: nat,K: int] :
% 5.82/6.19 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.82/6.19 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_less_self_iff
% 5.82/6.19 thf(fact_9039_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.82/6.19 ! [N: nat,K: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.82/6.19 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_less_eq_self_iff
% 5.82/6.19 thf(fact_9040_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.82/6.19 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_greater_eq_minus_exp
% 5.82/6.19 thf(fact_9041_signed__take__bit__int__greater__self__iff,axiom,
% 5.82/6.19 ! [K: int,N: nat] :
% 5.82/6.19 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.82/6.19 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_greater_self_iff
% 5.82/6.19 thf(fact_9042_signed__take__bit__int__less__eq,axiom,
% 5.82/6.19 ! [N: nat,K: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.82/6.19 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_less_eq
% 5.82/6.19 thf(fact_9043_signed__take__bit__int__eq__self,axiom,
% 5.82/6.19 ! [N: nat,K: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.82/6.19 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.19 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.82/6.19 = K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_eq_self
% 5.82/6.19 thf(fact_9044_signed__take__bit__int__eq__self__iff,axiom,
% 5.82/6.19 ! [N: nat,K: int] :
% 5.82/6.19 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.82/6.19 = K )
% 5.82/6.19 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.82/6.19 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_eq_self_iff
% 5.82/6.19 thf(fact_9045_sin__coeff__Suc,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( sin_coeff @ ( suc @ N ) )
% 5.82/6.19 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_coeff_Suc
% 5.82/6.19 thf(fact_9046_cos__coeff__Suc,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( cos_coeff @ ( suc @ N ) )
% 5.82/6.19 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_coeff_Suc
% 5.82/6.19 thf(fact_9047_signed__take__bit__int__greater__eq,axiom,
% 5.82/6.19 ! [K: int,N: nat] :
% 5.82/6.19 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.19 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_int_greater_eq
% 5.82/6.19 thf(fact_9048_sin__paired,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( sums_real
% 5.82/6.19 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.82/6.19 @ ( sin_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_paired
% 5.82/6.19 thf(fact_9049_signed__take__bit__numeral__minus__bit1,axiom,
% 5.82/6.19 ! [L: num,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.82/6.19 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_numeral_minus_bit1
% 5.82/6.19 thf(fact_9050_cos__paired,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( sums_real
% 5.82/6.19 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_real @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.82/6.19 @ ( cos_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_paired
% 5.82/6.19 thf(fact_9051_or__int__unfold,axiom,
% 5.82/6.19 ( bit_se1409905431419307370or_int
% 5.82/6.19 = ( ^ [K3: int,L3: int] :
% 5.82/6.19 ( if_int
% 5.82/6.19 @ ( ( K3
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.19 | ( L3
% 5.82/6.19 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.82/6.19 @ ( uminus_uminus_int @ one_one_int )
% 5.82/6.19 @ ( if_int @ ( K3 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( 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 @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_int_unfold
% 5.82/6.19 thf(fact_9052_pred__numeral__simps_I1_J,axiom,
% 5.82/6.19 ( ( pred_numeral @ one )
% 5.82/6.19 = zero_zero_nat ) ).
% 5.82/6.19
% 5.82/6.19 % pred_numeral_simps(1)
% 5.82/6.19 thf(fact_9053_eq__numeral__Suc,axiom,
% 5.82/6.19 ! [K: num,N: nat] :
% 5.82/6.19 ( ( ( numeral_numeral_nat @ K )
% 5.82/6.19 = ( suc @ N ) )
% 5.82/6.19 = ( ( pred_numeral @ K )
% 5.82/6.19 = N ) ) ).
% 5.82/6.19
% 5.82/6.19 % eq_numeral_Suc
% 5.82/6.19 thf(fact_9054_Suc__eq__numeral,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( ( suc @ N )
% 5.82/6.19 = ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( N
% 5.82/6.19 = ( pred_numeral @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Suc_eq_numeral
% 5.82/6.19 thf(fact_9055_or__nonnegative__int__iff,axiom,
% 5.82/6.19 ! [K: int,L: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.82/6.19 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.19 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_nonnegative_int_iff
% 5.82/6.19 thf(fact_9056_pred__numeral__simps_I3_J,axiom,
% 5.82/6.19 ! [K: num] :
% 5.82/6.19 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.82/6.19 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pred_numeral_simps(3)
% 5.82/6.19 thf(fact_9057_less__numeral__Suc,axiom,
% 5.82/6.19 ! [K: num,N: nat] :
% 5.82/6.19 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.82/6.19 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % less_numeral_Suc
% 5.82/6.19 thf(fact_9058_less__Suc__numeral,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % less_Suc_numeral
% 5.82/6.19 thf(fact_9059_le__numeral__Suc,axiom,
% 5.82/6.19 ! [K: num,N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.82/6.19 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % le_numeral_Suc
% 5.82/6.19 thf(fact_9060_le__Suc__numeral,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % le_Suc_numeral
% 5.82/6.19 thf(fact_9061_diff__numeral__Suc,axiom,
% 5.82/6.19 ! [K: num,N: nat] :
% 5.82/6.19 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.82/6.19 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % diff_numeral_Suc
% 5.82/6.19 thf(fact_9062_diff__Suc__numeral,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % diff_Suc_numeral
% 5.82/6.19 thf(fact_9063_max__numeral__Suc,axiom,
% 5.82/6.19 ! [K: num,N: nat] :
% 5.82/6.19 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.82/6.19 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % max_numeral_Suc
% 5.82/6.19 thf(fact_9064_max__Suc__numeral,axiom,
% 5.82/6.19 ! [N: nat,K: num] :
% 5.82/6.19 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % max_Suc_numeral
% 5.82/6.19 thf(fact_9065_or__minus__numerals_I6_J,axiom,
% 5.82/6.19 ! [N: num] :
% 5.82/6.19 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.82/6.19 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_minus_numerals(6)
% 5.82/6.19 thf(fact_9066_or__minus__numerals_I2_J,axiom,
% 5.82/6.19 ! [N: num] :
% 5.82/6.19 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.19 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_minus_numerals(2)
% 5.82/6.19 thf(fact_9067_signed__take__bit__numeral__bit0,axiom,
% 5.82/6.19 ! [L: num,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.82/6.19 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_numeral_bit0
% 5.82/6.19 thf(fact_9068_signed__take__bit__numeral__minus__bit0,axiom,
% 5.82/6.19 ! [L: num,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.82/6.19 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_numeral_minus_bit0
% 5.82/6.19 thf(fact_9069_signed__take__bit__numeral__bit1,axiom,
% 5.82/6.19 ! [L: num,K: num] :
% 5.82/6.19 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.82/6.19 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % signed_take_bit_numeral_bit1
% 5.82/6.19 thf(fact_9070_sin__x__le__x,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_x_le_x
% 5.82/6.19 thf(fact_9071_OR__lower,axiom,
% 5.82/6.19 ! [X2: int,Y3: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.19 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % OR_lower
% 5.82/6.19 thf(fact_9072_or__greater__eq,axiom,
% 5.82/6.19 ! [L: int,K: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.82/6.19 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_greater_eq
% 5.82/6.19 thf(fact_9073_sin__le__one,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( sin_real @ X2 ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % sin_le_one
% 5.82/6.19 thf(fact_9074_cos__le__one,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( cos_real @ X2 ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_le_one
% 5.82/6.19 thf(fact_9075_numeral__eq__Suc,axiom,
% 5.82/6.19 ( numeral_numeral_nat
% 5.82/6.19 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % numeral_eq_Suc
% 5.82/6.19 thf(fact_9076_sin__x__ge__neg__x,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ ( sin_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_x_ge_neg_x
% 5.82/6.19 thf(fact_9077_sin__ge__minus__one,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_ge_minus_one
% 5.82/6.19 thf(fact_9078_cos__ge__minus__one,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_ge_minus_one
% 5.82/6.19 thf(fact_9079_pred__numeral__def,axiom,
% 5.82/6.19 ( pred_numeral
% 5.82/6.19 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pred_numeral_def
% 5.82/6.19 thf(fact_9080_lessThan__nat__numeral,axiom,
% 5.82/6.19 ! [K: num] :
% 5.82/6.19 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % lessThan_nat_numeral
% 5.82/6.19 thf(fact_9081_atMost__nat__numeral,axiom,
% 5.82/6.19 ! [K: num] :
% 5.82/6.19 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % atMost_nat_numeral
% 5.82/6.19 thf(fact_9082_cos__two__neq__zero,axiom,
% 5.82/6.19 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 != zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_two_neq_zero
% 5.82/6.19 thf(fact_9083_sin__gt__zero__02,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_gt_zero_02
% 5.82/6.19 thf(fact_9084_cos__two__less__zero,axiom,
% 5.82/6.19 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.82/6.19
% 5.82/6.19 % cos_two_less_zero
% 5.82/6.19 thf(fact_9085_cos__is__zero,axiom,
% 5.82/6.19 ? [X4: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.82/6.19 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 & ( ( cos_real @ X4 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 & ! [Y5: real] :
% 5.82/6.19 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.82/6.19 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 & ( ( cos_real @ Y5 )
% 5.82/6.19 = zero_zero_real ) )
% 5.82/6.19 => ( Y5 = X4 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_is_zero
% 5.82/6.19 thf(fact_9086_cos__two__le__zero,axiom,
% 5.82/6.19 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.82/6.19
% 5.82/6.19 % cos_two_le_zero
% 5.82/6.19 thf(fact_9087_atLeastLessThan__nat__numeral,axiom,
% 5.82/6.19 ! [M: nat,K: num] :
% 5.82/6.19 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.82/6.19 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.82/6.19 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.82/6.19 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.82/6.19 = bot_bot_set_nat ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % atLeastLessThan_nat_numeral
% 5.82/6.19 thf(fact_9088_OR__upper,axiom,
% 5.82/6.19 ! [X2: int,N: nat,Y3: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.19 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.19 => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.19 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % OR_upper
% 5.82/6.19 thf(fact_9089_cos__double__less__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_double_less_one
% 5.82/6.19 thf(fact_9090_Maclaurin__cos__expansion2,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ T7 )
% 5.82/6.19 & ( ord_less_real @ T7 @ X2 )
% 5.82/6.19 & ( ( cos_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_cos_expansion2
% 5.82/6.19 thf(fact_9091_sin__pi__minus,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( minus_minus_real @ pi @ X2 ) )
% 5.82/6.19 = ( sin_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_pi_minus
% 5.82/6.19 thf(fact_9092_or__nat__numerals_I2_J,axiom,
% 5.82/6.19 ! [Y3: num] :
% 5.82/6.19 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.82/6.19 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_nat_numerals(2)
% 5.82/6.19 thf(fact_9093_or__nat__numerals_I4_J,axiom,
% 5.82/6.19 ! [X2: num] :
% 5.82/6.19 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.19 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_nat_numerals(4)
% 5.82/6.19 thf(fact_9094_cos__pi,axiom,
% 5.82/6.19 ( ( cos_real @ pi )
% 5.82/6.19 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_pi
% 5.82/6.19 thf(fact_9095_cos__periodic__pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_periodic_pi
% 5.82/6.19 thf(fact_9096_cos__periodic__pi2,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_periodic_pi2
% 5.82/6.19 thf(fact_9097_sin__periodic__pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_periodic_pi
% 5.82/6.19 thf(fact_9098_sin__periodic__pi2,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_periodic_pi2
% 5.82/6.19 thf(fact_9099_cos__pi__minus,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( minus_minus_real @ pi @ X2 ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_pi_minus
% 5.82/6.19 thf(fact_9100_cos__minus__pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( minus_minus_real @ X2 @ pi ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_minus_pi
% 5.82/6.19 thf(fact_9101_sin__minus__pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( minus_minus_real @ X2 @ pi ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_minus_pi
% 5.82/6.19 thf(fact_9102_or__nat__numerals_I3_J,axiom,
% 5.82/6.19 ! [X2: num] :
% 5.82/6.19 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.19 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_nat_numerals(3)
% 5.82/6.19 thf(fact_9103_or__nat__numerals_I1_J,axiom,
% 5.82/6.19 ! [Y3: num] :
% 5.82/6.19 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.82/6.19 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_nat_numerals(1)
% 5.82/6.19 thf(fact_9104_cos__pi__half,axiom,
% 5.82/6.19 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_pi_half
% 5.82/6.19 thf(fact_9105_sin__two__pi,axiom,
% 5.82/6.19 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 = zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % sin_two_pi
% 5.82/6.19 thf(fact_9106_cos__two__pi,axiom,
% 5.82/6.19 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_two_pi
% 5.82/6.19 thf(fact_9107_sin__pi__half,axiom,
% 5.82/6.19 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % sin_pi_half
% 5.82/6.19 thf(fact_9108_cos__periodic,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.82/6.19 = ( cos_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_periodic
% 5.82/6.19 thf(fact_9109_sin__periodic,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.82/6.19 = ( sin_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_periodic
% 5.82/6.19 thf(fact_9110_cos__2pi__minus,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.82/6.19 = ( cos_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_2pi_minus
% 5.82/6.19 thf(fact_9111_cos__npi,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.82/6.19 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_npi
% 5.82/6.19 thf(fact_9112_cos__npi2,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.82/6.19 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_npi2
% 5.82/6.19 thf(fact_9113_sin__2npi,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.82/6.19 = zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % sin_2npi
% 5.82/6.19 thf(fact_9114_cos__2npi,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_2npi
% 5.82/6.19 thf(fact_9115_sin__2pi__minus,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_2pi_minus
% 5.82/6.19 thf(fact_9116_sin__int__2pin,axiom,
% 5.82/6.19 ! [N: int] :
% 5.82/6.19 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.82/6.19 = zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % sin_int_2pin
% 5.82/6.19 thf(fact_9117_cos__int__2pin,axiom,
% 5.82/6.19 ! [N: int] :
% 5.82/6.19 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_int_2pin
% 5.82/6.19 thf(fact_9118_cos__3over2__pi,axiom,
% 5.82/6.19 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.82/6.19 = zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_3over2_pi
% 5.82/6.19 thf(fact_9119_sin__3over2__pi,axiom,
% 5.82/6.19 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.82/6.19 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_3over2_pi
% 5.82/6.19 thf(fact_9120_cos__npi__int,axiom,
% 5.82/6.19 ! [N: int] :
% 5.82/6.19 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.19 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.82/6.19 = one_one_real ) )
% 5.82/6.19 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.82/6.19 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.82/6.19 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_npi_int
% 5.82/6.19 thf(fact_9121_cos__pi__eq__zero,axiom,
% 5.82/6.19 ! [M: nat] :
% 5.82/6.19 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_pi_eq_zero
% 5.82/6.19 thf(fact_9122_sin__cos__npi,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_cos_npi
% 5.82/6.19 thf(fact_9123_pi__ge__zero,axiom,
% 5.82/6.19 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.82/6.19
% 5.82/6.19 % pi_ge_zero
% 5.82/6.19 thf(fact_9124_cos__monotone__0__pi__le,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.19 => ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_monotone_0_pi_le
% 5.82/6.19 thf(fact_9125_cos__mono__le__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_mono_le_eq
% 5.82/6.19 thf(fact_9126_cos__inj__pi,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.82/6.19 => ( ( ( cos_real @ X2 )
% 5.82/6.19 = ( cos_real @ Y3 ) )
% 5.82/6.19 => ( X2 = Y3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_inj_pi
% 5.82/6.19 thf(fact_9127_sin__ge__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.19 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_ge_zero
% 5.82/6.19 thf(fact_9128_pi__less__4,axiom,
% 5.82/6.19 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_less_4
% 5.82/6.19 thf(fact_9129_pi__ge__two,axiom,
% 5.82/6.19 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.82/6.19
% 5.82/6.19 % pi_ge_two
% 5.82/6.19 thf(fact_9130_pi__half__neq__two,axiom,
% 5.82/6.19 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_half_neq_two
% 5.82/6.19 thf(fact_9131_cos__monotone__0__pi,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.19 => ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_monotone_0_pi
% 5.82/6.19 thf(fact_9132_cos__mono__less__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.82/6.19 => ( ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_real @ Y3 @ X2 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_mono_less_eq
% 5.82/6.19 thf(fact_9133_cos__monotone__minus__pi__0_H,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.19 => ( ord_less_eq_real @ ( cos_real @ Y3 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_monotone_minus_pi_0'
% 5.82/6.19 thf(fact_9134_pi__half__neq__zero,axiom,
% 5.82/6.19 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 != zero_zero_real ) ).
% 5.82/6.19
% 5.82/6.19 % pi_half_neq_zero
% 5.82/6.19 thf(fact_9135_pi__half__less__two,axiom,
% 5.82/6.19 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_half_less_two
% 5.82/6.19 thf(fact_9136_pi__half__le__two,axiom,
% 5.82/6.19 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_half_le_two
% 5.82/6.19 thf(fact_9137_cos__monotone__minus__pi__0,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.19 => ( ord_less_real @ ( cos_real @ Y3 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_monotone_minus_pi_0
% 5.82/6.19 thf(fact_9138_cos__total,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.19 => ? [X4: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.82/6.19 & ( ord_less_eq_real @ X4 @ pi )
% 5.82/6.19 & ( ( cos_real @ X4 )
% 5.82/6.19 = Y3 )
% 5.82/6.19 & ! [Y5: real] :
% 5.82/6.19 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.82/6.19 & ( ord_less_eq_real @ Y5 @ pi )
% 5.82/6.19 & ( ( cos_real @ Y5 )
% 5.82/6.19 = Y3 ) )
% 5.82/6.19 => ( Y5 = X4 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_total
% 5.82/6.19 thf(fact_9139_sincos__principal__value,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ? [Y4: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 5.82/6.19 & ( ord_less_eq_real @ Y4 @ pi )
% 5.82/6.19 & ( ( sin_real @ Y4 )
% 5.82/6.19 = ( sin_real @ X2 ) )
% 5.82/6.19 & ( ( cos_real @ Y4 )
% 5.82/6.19 = ( cos_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sincos_principal_value
% 5.82/6.19 thf(fact_9140_pi__half__gt__zero,axiom,
% 5.82/6.19 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_half_gt_zero
% 5.82/6.19 thf(fact_9141_pi__half__ge__zero,axiom,
% 5.82/6.19 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_half_ge_zero
% 5.82/6.19 thf(fact_9142_m2pi__less__pi,axiom,
% 5.82/6.19 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.82/6.19
% 5.82/6.19 % m2pi_less_pi
% 5.82/6.19 thf(fact_9143_sin__pi__divide__n__ge__0,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( N != zero_zero_nat )
% 5.82/6.19 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_pi_divide_n_ge_0
% 5.82/6.19 thf(fact_9144_minus__pi__half__less__zero,axiom,
% 5.82/6.19 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.82/6.19
% 5.82/6.19 % minus_pi_half_less_zero
% 5.82/6.19 thf(fact_9145_cos__gt__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_gt_zero
% 5.82/6.19 thf(fact_9146_sin__gt__zero2,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_gt_zero2
% 5.82/6.19 thf(fact_9147_sin__lt__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ pi @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_lt_zero
% 5.82/6.19 thf(fact_9148_cos__60,axiom,
% 5.82/6.19 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_60
% 5.82/6.19 thf(fact_9149_sin__30,axiom,
% 5.82/6.19 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_30
% 5.82/6.19 thf(fact_9150_sin__monotone__2pi__le,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( sin_real @ Y3 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_monotone_2pi_le
% 5.82/6.19 thf(fact_9151_sin__mono__le__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_mono_le_eq
% 5.82/6.19 thf(fact_9152_sin__inj__pi,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ( sin_real @ X2 )
% 5.82/6.19 = ( sin_real @ Y3 ) )
% 5.82/6.19 => ( X2 = Y3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_inj_pi
% 5.82/6.19 thf(fact_9153_cos__one__2pi__int,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( cos_real @ X2 )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 = ( ? [X3: int] :
% 5.82/6.19 ( X2
% 5.82/6.19 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_one_2pi_int
% 5.82/6.19 thf(fact_9154_sin__le__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ pi @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_le_zero
% 5.82/6.19 thf(fact_9155_cos__gt__zero__pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_gt_zero_pi
% 5.82/6.19 thf(fact_9156_sin__less__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.19 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_less_zero
% 5.82/6.19 thf(fact_9157_cos__ge__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_ge_zero
% 5.82/6.19 thf(fact_9158_sin__monotone__2pi,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ ( sin_real @ Y3 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_monotone_2pi
% 5.82/6.19 thf(fact_9159_sin__mono__less__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_mono_less_eq
% 5.82/6.19 thf(fact_9160_sin__total,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.19 => ? [X4: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.82/6.19 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( sin_real @ X4 )
% 5.82/6.19 = Y3 )
% 5.82/6.19 & ! [Y5: real] :
% 5.82/6.19 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.82/6.19 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( sin_real @ Y5 )
% 5.82/6.19 = Y3 ) )
% 5.82/6.19 => ( Y5 = X4 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_total
% 5.82/6.19 thf(fact_9161_or__nat__unfold,axiom,
% 5.82/6.19 ( bit_se1412395901928357646or_nat
% 5.82/6.19 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % or_nat_unfold
% 5.82/6.19 thf(fact_9162_cos__one__2pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( cos_real @ X2 )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 = ( ? [X3: nat] :
% 5.82/6.19 ( X2
% 5.82/6.19 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.82/6.19 | ? [X3: nat] :
% 5.82/6.19 ( X2
% 5.82/6.19 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_one_2pi
% 5.82/6.19 thf(fact_9163_sin__pi__divide__n__gt__0,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_pi_divide_n_gt_0
% 5.82/6.19 thf(fact_9164_sincos__total__pi,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.19 & ( ord_less_eq_real @ T7 @ pi )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( cos_real @ T7 ) )
% 5.82/6.19 & ( Y3
% 5.82/6.19 = ( sin_real @ T7 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sincos_total_pi
% 5.82/6.19 thf(fact_9165_sin__expansion__lemma,axiom,
% 5.82/6.19 ! [X2: real,M: nat] :
% 5.82/6.19 ( ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_expansion_lemma
% 5.82/6.19 thf(fact_9166_cos__zero__iff__int,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( cos_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 = ( ? [I4: int] :
% 5.82/6.19 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_zero_iff_int
% 5.82/6.19 thf(fact_9167_sin__zero__iff__int,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( sin_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 = ( ? [I4: int] :
% 5.82/6.19 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_zero_iff_int
% 5.82/6.19 thf(fact_9168_cos__zero__lemma,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ( cos_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 => ? [N3: nat] :
% 5.82/6.19 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_zero_lemma
% 5.82/6.19 thf(fact_9169_sin__zero__lemma,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ( sin_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 => ? [N3: nat] :
% 5.82/6.19 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_zero_lemma
% 5.82/6.19 thf(fact_9170_cos__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( cos_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 = ( ? [N4: nat] :
% 5.82/6.19 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.19 | ? [N4: nat] :
% 5.82/6.19 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_zero_iff
% 5.82/6.19 thf(fact_9171_sin__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( sin_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 = ( ? [N4: nat] :
% 5.82/6.19 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.19 | ? [N4: nat] :
% 5.82/6.19 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_zero_iff
% 5.82/6.19 thf(fact_9172_cos__expansion__lemma,axiom,
% 5.82/6.19 ! [X2: real,M: nat] :
% 5.82/6.19 ( ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_expansion_lemma
% 5.82/6.19 thf(fact_9173_sincos__total__pi__half,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.19 & ( ord_less_eq_real @ T7 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( cos_real @ T7 ) )
% 5.82/6.19 & ( Y3
% 5.82/6.19 = ( sin_real @ T7 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sincos_total_pi_half
% 5.82/6.19 thf(fact_9174_sincos__total__2pi__le,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.19 & ( ord_less_eq_real @ T7 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 & ( X2
% 5.82/6.19 = ( cos_real @ T7 ) )
% 5.82/6.19 & ( Y3
% 5.82/6.19 = ( sin_real @ T7 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sincos_total_2pi_le
% 5.82/6.19 thf(fact_9175_sincos__total__2pi,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 => ~ ! [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.19 => ( ( ord_less_real @ T7 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 => ( ( X2
% 5.82/6.19 = ( cos_real @ T7 ) )
% 5.82/6.19 => ( Y3
% 5.82/6.19 != ( sin_real @ T7 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sincos_total_2pi
% 5.82/6.19 thf(fact_9176_Maclaurin__sin__expansion,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ? [T7: real] :
% 5.82/6.19 ( ( sin_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_sin_expansion
% 5.82/6.19 thf(fact_9177_Maclaurin__sin__expansion4,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ T7 )
% 5.82/6.19 & ( ord_less_eq_real @ T7 @ X2 )
% 5.82/6.19 & ( ( sin_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_sin_expansion4
% 5.82/6.19 thf(fact_9178_Maclaurin__sin__expansion3,axiom,
% 5.82/6.19 ! [N: nat,X2: real] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ T7 )
% 5.82/6.19 & ( ord_less_real @ T7 @ X2 )
% 5.82/6.19 & ( ( sin_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_sin_expansion3
% 5.82/6.19 thf(fact_9179_Maclaurin__minus__cos__expansion,axiom,
% 5.82/6.19 ! [N: nat,X2: real] :
% 5.82/6.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_real @ X2 @ T7 )
% 5.82/6.19 & ( ord_less_real @ T7 @ zero_zero_real )
% 5.82/6.19 & ( ( cos_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_minus_cos_expansion
% 5.82/6.19 thf(fact_9180_Maclaurin__cos__expansion,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ? [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.19 & ( ( cos_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_cos_expansion
% 5.82/6.19 thf(fact_9181_Maclaurin__sin__expansion2,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ? [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.19 & ( ( sin_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T7 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_sin_expansion2
% 5.82/6.19 thf(fact_9182_pi__series,axiom,
% 5.82/6.19 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( suminf_real
% 5.82/6.19 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % pi_series
% 5.82/6.19 thf(fact_9183_tan__periodic__pi,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( tan_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.82/6.19 = ( tan_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_periodic_pi
% 5.82/6.19 thf(fact_9184_tan__periodic__n,axiom,
% 5.82/6.19 ! [X2: real,N: num] :
% 5.82/6.19 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.82/6.19 = ( tan_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_periodic_n
% 5.82/6.19 thf(fact_9185_tan__periodic__nat,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.82/6.19 = ( tan_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_periodic_nat
% 5.82/6.19 thf(fact_9186_tan__periodic__int,axiom,
% 5.82/6.19 ! [X2: real,I: int] :
% 5.82/6.19 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.82/6.19 = ( tan_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_periodic_int
% 5.82/6.19 thf(fact_9187_tan__periodic,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.82/6.19 = ( tan_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_periodic
% 5.82/6.19 thf(fact_9188_square__powr__half,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( powr_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( abs_abs_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % square_powr_half
% 5.82/6.19 thf(fact_9189_abs__sin__x__le__abs__x,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ ( abs_abs_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % abs_sin_x_le_abs_x
% 5.82/6.19 thf(fact_9190_lemma__interval__lt,axiom,
% 5.82/6.19 ! [A2: real,X2: real,B2: real] :
% 5.82/6.19 ( ( ord_less_real @ A2 @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ B2 )
% 5.82/6.19 => ? [D4: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.19 & ! [Y5: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y5 ) ) @ D4 )
% 5.82/6.19 => ( ( ord_less_real @ A2 @ Y5 )
% 5.82/6.19 & ( ord_less_real @ Y5 @ B2 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % lemma_interval_lt
% 5.82/6.19 thf(fact_9191_abs__cos__le__one,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X2 ) ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % abs_cos_le_one
% 5.82/6.19 thf(fact_9192_abs__sin__le__one,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % abs_sin_le_one
% 5.82/6.19 thf(fact_9193_sin__bound__lemma,axiom,
% 5.82/6.19 ! [X2: real,Y3: real,U: real,V: real] :
% 5.82/6.19 ( ( X2 = Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.82/6.19 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y3 ) ) @ V ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_bound_lemma
% 5.82/6.19 thf(fact_9194_tan__bound__pi2,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_bound_pi2
% 5.82/6.19 thf(fact_9195_tan__total__pi4,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ? [Z2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.82/6.19 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 & ( ( tan_real @ Z2 )
% 5.82/6.19 = X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_total_pi4
% 5.82/6.19 thf(fact_9196_lemma__interval,axiom,
% 5.82/6.19 ! [A2: real,X2: real,B2: real] :
% 5.82/6.19 ( ( ord_less_real @ A2 @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ B2 )
% 5.82/6.19 => ? [D4: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.19 & ! [Y5: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y5 ) ) @ D4 )
% 5.82/6.19 => ( ( ord_less_eq_real @ A2 @ Y5 )
% 5.82/6.19 & ( ord_less_eq_real @ Y5 @ B2 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % lemma_interval
% 5.82/6.19 thf(fact_9197_sin__zero__abs__cos__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( sin_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 => ( ( abs_abs_real @ ( cos_real @ X2 ) )
% 5.82/6.19 = one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_zero_abs_cos_one
% 5.82/6.19 thf(fact_9198_tan__45,axiom,
% 5.82/6.19 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % tan_45
% 5.82/6.19 thf(fact_9199_sin__cos__le1,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) ) ) ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % sin_cos_le1
% 5.82/6.19 thf(fact_9200_lemma__tan__total,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ? [X4: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.82/6.19 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ord_less_real @ Y3 @ ( tan_real @ X4 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % lemma_tan_total
% 5.82/6.19 thf(fact_9201_tan__gt__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_gt_zero
% 5.82/6.19 thf(fact_9202_tan__total,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ? [X4: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.82/6.19 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( tan_real @ X4 )
% 5.82/6.19 = Y3 )
% 5.82/6.19 & ! [Y5: real] :
% 5.82/6.19 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.82/6.19 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( tan_real @ Y5 )
% 5.82/6.19 = Y3 ) )
% 5.82/6.19 => ( Y5 = X4 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_total
% 5.82/6.19 thf(fact_9203_tan__monotone,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_monotone
% 5.82/6.19 thf(fact_9204_tan__monotone_H,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ X2 )
% 5.82/6.19 = ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_monotone'
% 5.82/6.19 thf(fact_9205_tan__mono__lt__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_mono_lt_eq
% 5.82/6.19 thf(fact_9206_lemma__tan__total1,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ? [X4: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.82/6.19 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( tan_real @ X4 )
% 5.82/6.19 = Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % lemma_tan_total1
% 5.82/6.19 thf(fact_9207_tan__minus__45,axiom,
% 5.82/6.19 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.19 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_minus_45
% 5.82/6.19 thf(fact_9208_tan__inverse,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y3 ) )
% 5.82/6.19 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_inverse
% 5.82/6.19 thf(fact_9209_tan__total__pos,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ? [X4: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.82/6.19 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( tan_real @ X4 )
% 5.82/6.19 = Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_total_pos
% 5.82/6.19 thf(fact_9210_tan__pos__pi2__le,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_pos_pi2_le
% 5.82/6.19 thf(fact_9211_tan__less__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.19 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_less_zero
% 5.82/6.19 thf(fact_9212_tan__mono__le,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_mono_le
% 5.82/6.19 thf(fact_9213_tan__mono__le__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_mono_le_eq
% 5.82/6.19 thf(fact_9214_monoseq__arctan__series,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ( topolo6980174941875973593q_real
% 5.82/6.19 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % monoseq_arctan_series
% 5.82/6.19 thf(fact_9215_arctan__series,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ( ( arctan @ X2 )
% 5.82/6.19 = ( suminf_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_series
% 5.82/6.19 thf(fact_9216_ln__series,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.19 => ( ( ln_ln_real @ X2 )
% 5.82/6.19 = ( suminf_real
% 5.82/6.19 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_series
% 5.82/6.19 thf(fact_9217_summable__arctan__series,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ( summable_real
% 5.82/6.19 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % summable_arctan_series
% 5.82/6.19 thf(fact_9218_zdvd1__eq,axiom,
% 5.82/6.19 ! [X2: int] :
% 5.82/6.19 ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.82/6.19 = ( ( abs_abs_int @ X2 )
% 5.82/6.19 = one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % zdvd1_eq
% 5.82/6.19 thf(fact_9219_zabs__less__one__iff,axiom,
% 5.82/6.19 ! [Z: int] :
% 5.82/6.19 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.82/6.19 = ( Z = zero_zero_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % zabs_less_one_iff
% 5.82/6.19 thf(fact_9220_arctan__le__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_le_zero_iff
% 5.82/6.19 thf(fact_9221_zero__le__arctan__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.82/6.19 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % zero_le_arctan_iff
% 5.82/6.19 thf(fact_9222_ln__le__cancel__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_le_cancel_iff
% 5.82/6.19 thf(fact_9223_ln__eq__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ( ln_ln_real @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 = ( X2 = one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_eq_zero_iff
% 5.82/6.19 thf(fact_9224_ln__gt__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.19 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_gt_zero_iff
% 5.82/6.19 thf(fact_9225_ln__less__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_less_zero_iff
% 5.82/6.19 thf(fact_9226_ln__ge__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.19 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_ge_zero_iff
% 5.82/6.19 thf(fact_9227_ln__le__zero__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_le_zero_iff
% 5.82/6.19 thf(fact_9228_summable__rabs__cancel,axiom,
% 5.82/6.19 ! [F: nat > real] :
% 5.82/6.19 ( ( summable_real
% 5.82/6.19 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) )
% 5.82/6.19 => ( summable_real @ F ) ) ).
% 5.82/6.19
% 5.82/6.19 % summable_rabs_cancel
% 5.82/6.19 thf(fact_9229_arctan__monotone_H,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_monotone'
% 5.82/6.19 thf(fact_9230_arctan__le__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_le_iff
% 5.82/6.19 thf(fact_9231_abs__zmult__eq__1,axiom,
% 5.82/6.19 ! [M: int,N: int] :
% 5.82/6.19 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.82/6.19 = one_one_int )
% 5.82/6.19 => ( ( abs_abs_int @ M )
% 5.82/6.19 = one_one_int ) ) ).
% 5.82/6.19
% 5.82/6.19 % abs_zmult_eq_1
% 5.82/6.19 thf(fact_9232_infinite__int__iff__unbounded__le,axiom,
% 5.82/6.19 ! [S: set_int] :
% 5.82/6.19 ( ( ~ ( finite_finite_int @ S ) )
% 5.82/6.19 = ( ! [M6: int] :
% 5.82/6.19 ? [N4: int] :
% 5.82/6.19 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N4 ) )
% 5.82/6.19 & ( member_int @ N4 @ S ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % infinite_int_iff_unbounded_le
% 5.82/6.19 thf(fact_9233_ln__bound,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_bound
% 5.82/6.19 thf(fact_9234_ln__gt__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.19 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_gt_zero
% 5.82/6.19 thf(fact_9235_ln__less__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.19 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_less_zero
% 5.82/6.19 thf(fact_9236_ln__gt__zero__imp__gt__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_gt_zero_imp_gt_one
% 5.82/6.19 thf(fact_9237_ln__ge__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_ge_zero
% 5.82/6.19 thf(fact_9238_abs__mod__less,axiom,
% 5.82/6.19 ! [L: int,K: int] :
% 5.82/6.19 ( ( L != zero_zero_int )
% 5.82/6.19 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % abs_mod_less
% 5.82/6.19 thf(fact_9239_nat__abs__mult__distrib,axiom,
% 5.82/6.19 ! [W: int,Z: int] :
% 5.82/6.19 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.82/6.19 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat_abs_mult_distrib
% 5.82/6.19 thf(fact_9240_dvd__imp__le__int,axiom,
% 5.82/6.19 ! [I: int,D2: int] :
% 5.82/6.19 ( ( I != zero_zero_int )
% 5.82/6.19 => ( ( dvd_dvd_int @ D2 @ I )
% 5.82/6.19 => ( ord_less_eq_int @ ( abs_abs_int @ D2 ) @ ( abs_abs_int @ I ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % dvd_imp_le_int
% 5.82/6.19 thf(fact_9241_summable__rabs__comparison__test,axiom,
% 5.82/6.19 ! [F: nat > real,G: nat > real] :
% 5.82/6.19 ( ? [N10: nat] :
% 5.82/6.19 ! [N3: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ N10 @ N3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.82/6.19 => ( ( summable_real @ G )
% 5.82/6.19 => ( summable_real
% 5.82/6.19 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % summable_rabs_comparison_test
% 5.82/6.19 thf(fact_9242_summable__rabs,axiom,
% 5.82/6.19 ! [F: nat > real] :
% 5.82/6.19 ( ( summable_real
% 5.82/6.19 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.82/6.19 @ ( suminf_real
% 5.82/6.19 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % summable_rabs
% 5.82/6.19 thf(fact_9243_ln__ge__zero__imp__ge__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_ge_zero_imp_ge_one
% 5.82/6.19 thf(fact_9244_ln__add__one__self__le__self,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_add_one_self_le_self
% 5.82/6.19 thf(fact_9245_ln__mult,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_mult
% 5.82/6.19 thf(fact_9246_ln__eq__minus__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ( ln_ln_real @ X2 )
% 5.82/6.19 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.82/6.19 => ( X2 = one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_eq_minus_one
% 5.82/6.19 thf(fact_9247_ln__div,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ln_ln_real @ ( divide_divide_real @ X2 @ Y3 ) )
% 5.82/6.19 = ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_div
% 5.82/6.19 thf(fact_9248_nat__abs__triangle__ineq,axiom,
% 5.82/6.19 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat_abs_triangle_ineq
% 5.82/6.19 thf(fact_9249_zdvd__mult__cancel1,axiom,
% 5.82/6.19 ! [M: int,N: int] :
% 5.82/6.19 ( ( M != zero_zero_int )
% 5.82/6.19 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.82/6.19 = ( ( abs_abs_int @ N )
% 5.82/6.19 = one_one_int ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % zdvd_mult_cancel1
% 5.82/6.19 thf(fact_9250_div__abs__eq__div__nat,axiom,
% 5.82/6.19 ! [K: int,L: int] :
% 5.82/6.19 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.82/6.19 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % div_abs_eq_div_nat
% 5.82/6.19 thf(fact_9251_ln__2__less__1,axiom,
% 5.82/6.19 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.82/6.19
% 5.82/6.19 % ln_2_less_1
% 5.82/6.19 thf(fact_9252_ln__le__minus__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_le_minus_one
% 5.82/6.19 thf(fact_9253_ln__diff__le,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X2 @ Y3 ) @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_diff_le
% 5.82/6.19 thf(fact_9254_ln__add__one__self__le__self2,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_add_one_self_le_self2
% 5.82/6.19 thf(fact_9255_even__add__abs__iff,axiom,
% 5.82/6.19 ! [K: int,L: int] :
% 5.82/6.19 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.82/6.19 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % even_add_abs_iff
% 5.82/6.19 thf(fact_9256_even__abs__add__iff,axiom,
% 5.82/6.19 ! [K: int,L: int] :
% 5.82/6.19 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.82/6.19 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % even_abs_add_iff
% 5.82/6.19 thf(fact_9257_nat__abs__int__diff,axiom,
% 5.82/6.19 ! [A2: nat,B2: nat] :
% 5.82/6.19 ( ( ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.19 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) )
% 5.82/6.19 = ( minus_minus_nat @ B2 @ A2 ) ) )
% 5.82/6.19 & ( ~ ( ord_less_eq_nat @ A2 @ B2 )
% 5.82/6.19 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) )
% 5.82/6.19 = ( minus_minus_nat @ A2 @ B2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat_abs_int_diff
% 5.82/6.19 thf(fact_9258_ln__one__minus__pos__upper__bound,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.19 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_one_minus_pos_upper_bound
% 5.82/6.19 thf(fact_9259_ln__powr__bound,axiom,
% 5.82/6.19 ! [X2: real,A2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A2 ) @ A2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_powr_bound
% 5.82/6.19 thf(fact_9260_ln__powr__bound2,axiom,
% 5.82/6.19 ! [X2: real,A2: real] :
% 5.82/6.19 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.19 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A2 ) @ ( times_times_real @ ( powr_real @ A2 @ A2 ) @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_powr_bound2
% 5.82/6.19 thf(fact_9261_log__eq__div__ln__mult__log,axiom,
% 5.82/6.19 ! [A2: real,B2: real,X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.19 => ( ( A2 != one_one_real )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.19 => ( ( B2 != one_one_real )
% 5.82/6.19 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( log @ A2 @ X2 )
% 5.82/6.19 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B2 ) @ ( ln_ln_real @ A2 ) ) @ ( log @ B2 @ X2 ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % log_eq_div_ln_mult_log
% 5.82/6.19 thf(fact_9262_monoseq__realpow,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.19 => ( topolo6980174941875973593q_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % monoseq_realpow
% 5.82/6.19 thf(fact_9263_summable__power__series,axiom,
% 5.82/6.19 ! [F: nat > real,Z: real] :
% 5.82/6.19 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 5.82/6.19 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.82/6.19 => ( ( ord_less_real @ Z @ one_one_real )
% 5.82/6.19 => ( summable_real
% 5.82/6.19 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % summable_power_series
% 5.82/6.19 thf(fact_9264_nat__intermed__int__val,axiom,
% 5.82/6.19 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ( ord_less_eq_nat @ M @ I2 )
% 5.82/6.19 & ( ord_less_nat @ I2 @ N ) )
% 5.82/6.19 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.82/6.19 => ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.19 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.82/6.19 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.82/6.19 => ? [I2: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ M @ I2 )
% 5.82/6.19 & ( ord_less_eq_nat @ I2 @ N )
% 5.82/6.19 & ( ( F @ I2 )
% 5.82/6.19 = K ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat_intermed_int_val
% 5.82/6.19 thf(fact_9265_decr__lemma,axiom,
% 5.82/6.19 ! [D2: int,X2: int,Z: int] :
% 5.82/6.19 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.19 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 5.82/6.19
% 5.82/6.19 % decr_lemma
% 5.82/6.19 thf(fact_9266_incr__lemma,axiom,
% 5.82/6.19 ! [D2: int,Z: int,X2: int] :
% 5.82/6.19 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.82/6.19 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % incr_lemma
% 5.82/6.19 thf(fact_9267_arctan__ubound,axiom,
% 5.82/6.19 ! [Y3: real] : ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_ubound
% 5.82/6.19 thf(fact_9268_arctan__one,axiom,
% 5.82/6.19 ( ( arctan @ one_one_real )
% 5.82/6.19 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_one
% 5.82/6.19 thf(fact_9269_nat__ivt__aux,axiom,
% 5.82/6.19 ! [N: nat,F: nat > int,K: int] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ I2 @ N )
% 5.82/6.19 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.82/6.19 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.82/6.19 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.82/6.19 => ? [I2: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ I2 @ N )
% 5.82/6.19 & ( ( F @ I2 )
% 5.82/6.19 = K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat_ivt_aux
% 5.82/6.19 thf(fact_9270_arctan__lbound,axiom,
% 5.82/6.19 ! [Y3: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_lbound
% 5.82/6.19 thf(fact_9271_arctan__bounded,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 5.82/6.19 & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_bounded
% 5.82/6.19 thf(fact_9272_arctan,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 5.82/6.19 & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 & ( ( tan_real @ ( arctan @ Y3 ) )
% 5.82/6.19 = Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan
% 5.82/6.19 thf(fact_9273_arctan__tan,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.82/6.19 = X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_tan
% 5.82/6.19 thf(fact_9274_arctan__unique,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ( tan_real @ X2 )
% 5.82/6.19 = Y3 )
% 5.82/6.19 => ( ( arctan @ Y3 )
% 5.82/6.19 = X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_unique
% 5.82/6.19 thf(fact_9275_nat0__intermed__int__val,axiom,
% 5.82/6.19 ! [N: nat,F: nat > int,K: int] :
% 5.82/6.19 ( ! [I2: nat] :
% 5.82/6.19 ( ( ord_less_nat @ I2 @ N )
% 5.82/6.19 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.82/6.19 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.82/6.19 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.82/6.19 => ? [I2: nat] :
% 5.82/6.19 ( ( ord_less_eq_nat @ I2 @ N )
% 5.82/6.19 & ( ( F @ I2 )
% 5.82/6.19 = K ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % nat0_intermed_int_val
% 5.82/6.19 thf(fact_9276_ln__one__plus__pos__lower__bound,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.19 => ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_one_plus_pos_lower_bound
% 5.82/6.19 thf(fact_9277_arctan__add,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.19 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) )
% 5.82/6.19 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_add
% 5.82/6.19 thf(fact_9278_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.19 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.82/6.19 thf(fact_9279_machin__Euler,axiom,
% 5.82/6.19 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % machin_Euler
% 5.82/6.19 thf(fact_9280_machin,axiom,
% 5.82/6.19 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % machin
% 5.82/6.19 thf(fact_9281_sum__pos__lt__pair,axiom,
% 5.82/6.19 ! [F: nat > real,K: nat] :
% 5.82/6.19 ( ( summable_real @ F )
% 5.82/6.19 => ( ! [D4: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D4 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D4 ) @ one_one_nat ) ) ) ) )
% 5.82/6.19 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sum_pos_lt_pair
% 5.82/6.19 thf(fact_9282_ln__one__minus__pos__lower__bound,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_one_minus_pos_lower_bound
% 5.82/6.19 thf(fact_9283_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % abs_ln_one_plus_x_minus_x_bound
% 5.82/6.19 thf(fact_9284_arctan__double,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.82/6.19 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_double
% 5.82/6.19 thf(fact_9285_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.19 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.82/6.19 thf(fact_9286_tanh__ln__real,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.19 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tanh_ln_real
% 5.82/6.19 thf(fact_9287_sin__tan,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( sin_real @ X2 )
% 5.82/6.19 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_tan
% 5.82/6.19 thf(fact_9288_real__sqrt__le__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_le_iff
% 5.82/6.19 thf(fact_9289_real__sqrt__eq__1__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( sqrt @ X2 )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 = ( X2 = one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_eq_1_iff
% 5.82/6.19 thf(fact_9290_real__sqrt__one,axiom,
% 5.82/6.19 ( ( sqrt @ one_one_real )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_one
% 5.82/6.19 thf(fact_9291_tanh__real__le__iff,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tanh_real_le_iff
% 5.82/6.19 thf(fact_9292_real__sqrt__ge__0__iff,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_ge_0_iff
% 5.82/6.19 thf(fact_9293_real__sqrt__le__0__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_le_0_iff
% 5.82/6.19 thf(fact_9294_real__sqrt__gt__1__iff,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y3 ) )
% 5.82/6.19 = ( ord_less_real @ one_one_real @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_gt_1_iff
% 5.82/6.19 thf(fact_9295_real__sqrt__lt__1__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.82/6.19 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_lt_1_iff
% 5.82/6.19 thf(fact_9296_real__sqrt__le__1__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_le_1_iff
% 5.82/6.19 thf(fact_9297_real__sqrt__ge__1__iff,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y3 ) )
% 5.82/6.19 = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_ge_1_iff
% 5.82/6.19 thf(fact_9298_tanh__real__nonpos__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.82/6.19 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % tanh_real_nonpos_iff
% 5.82/6.19 thf(fact_9299_tanh__real__nonneg__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.82/6.19 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tanh_real_nonneg_iff
% 5.82/6.19 thf(fact_9300_real__sqrt__four,axiom,
% 5.82/6.19 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_four
% 5.82/6.19 thf(fact_9301_artanh__minus__real,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.19 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.82/6.19 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % artanh_minus_real
% 5.82/6.19 thf(fact_9302_real__sqrt__abs,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sqrt @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( abs_abs_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_abs
% 5.82/6.19 thf(fact_9303_real__sqrt__pow2__iff,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.19 = X2 )
% 5.82/6.19 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_pow2_iff
% 5.82/6.19 thf(fact_9304_real__sqrt__pow2,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.19 = X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_pow2
% 5.82/6.19 thf(fact_9305_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real,Xa: real,Ya: real] :
% 5.82/6.19 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.19 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_mult_squared_eq
% 5.82/6.19 thf(fact_9306_real__sqrt__le__mono,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_le_mono
% 5.82/6.19 thf(fact_9307_real__sqrt__ge__zero,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_ge_zero
% 5.82/6.19 thf(fact_9308_real__sqrt__eq__zero__cancel,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ( sqrt @ X2 )
% 5.82/6.19 = zero_zero_real )
% 5.82/6.19 => ( X2 = zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_eq_zero_cancel
% 5.82/6.19 thf(fact_9309_real__sqrt__ge__one,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.19 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_ge_one
% 5.82/6.19 thf(fact_9310_tanh__real__lt__1,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % tanh_real_lt_1
% 5.82/6.19 thf(fact_9311_real__div__sqrt,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( divide_divide_real @ X2 @ ( sqrt @ X2 ) )
% 5.82/6.19 = ( sqrt @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_div_sqrt
% 5.82/6.19 thf(fact_9312_sqrt__add__le__add__sqrt,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_add_le_add_sqrt
% 5.82/6.19 thf(fact_9313_le__real__sqrt__sumsq,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % le_real_sqrt_sumsq
% 5.82/6.19 thf(fact_9314_tanh__real__gt__neg1,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.82/6.19
% 5.82/6.19 % tanh_real_gt_neg1
% 5.82/6.19 thf(fact_9315_sqrt2__less__2,axiom,
% 5.82/6.19 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt2_less_2
% 5.82/6.19 thf(fact_9316_real__less__rsqrt,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 5.82/6.19 => ( ord_less_real @ X2 @ ( sqrt @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_less_rsqrt
% 5.82/6.19 thf(fact_9317_real__le__rsqrt,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_le_rsqrt
% 5.82/6.19 thf(fact_9318_sqrt__le__D,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_le_D
% 5.82/6.19 thf(fact_9319_real__sqrt__unique,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] :
% 5.82/6.19 ( ( ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.19 = X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( sqrt @ X2 )
% 5.82/6.19 = Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_unique
% 5.82/6.19 thf(fact_9320_real__le__lsqrt,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_le_lsqrt
% 5.82/6.19 thf(fact_9321_lemma__real__divide__sqrt__less,axiom,
% 5.82/6.19 ! [U: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ U )
% 5.82/6.19 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.82/6.19
% 5.82/6.19 % lemma_real_divide_sqrt_less
% 5.82/6.19 thf(fact_9322_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = Y3 )
% 5.82/6.19 => ( X2 = zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_eq_cancel2
% 5.82/6.19 thf(fact_9323_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = X2 )
% 5.82/6.19 => ( Y3 = zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_eq_cancel
% 5.82/6.19 thf(fact_9324_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.82/6.19 ! [A2: real,C2: real,B2: real,D2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A2 @ C2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B2 @ D2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_triangle_ineq
% 5.82/6.19 thf(fact_9325_real__sqrt__sum__squares__ge2,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] : ( ord_less_eq_real @ Y3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_ge2
% 5.82/6.19 thf(fact_9326_real__sqrt__sum__squares__ge1,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_ge1
% 5.82/6.19 thf(fact_9327_sqrt__ge__absD,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y3 ) )
% 5.82/6.19 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_ge_absD
% 5.82/6.19 thf(fact_9328_cos__45,axiom,
% 5.82/6.19 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_45
% 5.82/6.19 thf(fact_9329_sin__45,axiom,
% 5.82/6.19 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_45
% 5.82/6.19 thf(fact_9330_tan__60,axiom,
% 5.82/6.19 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.82/6.19 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_60
% 5.82/6.19 thf(fact_9331_real__less__lsqrt,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ord_less_real @ ( sqrt @ X2 ) @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_less_lsqrt
% 5.82/6.19 thf(fact_9332_sqrt__sum__squares__le__sum,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_sum_squares_le_sum
% 5.82/6.19 thf(fact_9333_sqrt__even__pow2,axiom,
% 5.82/6.19 ! [N: nat] :
% 5.82/6.19 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.19 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.19 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_even_pow2
% 5.82/6.19 thf(fact_9334_sqrt__sum__squares__le__sum__abs,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y3 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_sum_squares_le_sum_abs
% 5.82/6.19 thf(fact_9335_real__sqrt__ge__abs2,axiom,
% 5.82/6.19 ! [Y3: real,X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_ge_abs2
% 5.82/6.19 thf(fact_9336_real__sqrt__ge__abs1,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_ge_abs1
% 5.82/6.19 thf(fact_9337_ln__sqrt,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.82/6.19 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % ln_sqrt
% 5.82/6.19 thf(fact_9338_cos__30,axiom,
% 5.82/6.19 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_30
% 5.82/6.19 thf(fact_9339_sin__60,axiom,
% 5.82/6.19 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_60
% 5.82/6.19 thf(fact_9340_real__sqrt__power__even,axiom,
% 5.82/6.19 ! [N: nat,X2: real] :
% 5.82/6.19 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( power_power_real @ ( sqrt @ X2 ) @ N )
% 5.82/6.19 = ( power_power_real @ X2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_power_even
% 5.82/6.19 thf(fact_9341_arsinh__real__aux,axiom,
% 5.82/6.19 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arsinh_real_aux
% 5.82/6.19 thf(fact_9342_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.82/6.19 ! [X2: real,Y3: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_mult_ge_zero
% 5.82/6.19 thf(fact_9343_arith__geo__mean__sqrt,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y3 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arith_geo_mean_sqrt
% 5.82/6.19 thf(fact_9344_powr__half__sqrt,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 = ( sqrt @ X2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % powr_half_sqrt
% 5.82/6.19 thf(fact_9345_tan__30,axiom,
% 5.82/6.19 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % tan_30
% 5.82/6.19 thf(fact_9346_cos__x__y__le__one,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % cos_x_y_le_one
% 5.82/6.19 thf(fact_9347_real__sqrt__sum__squares__less,axiom,
% 5.82/6.19 ! [X2: real,U: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.19 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % real_sqrt_sum_squares_less
% 5.82/6.19 thf(fact_9348_arcosh__real__def,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.19 => ( ( arcosh_real @ X2 )
% 5.82/6.19 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arcosh_real_def
% 5.82/6.19 thf(fact_9349_cos__arctan,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( cos_real @ ( arctan @ X2 ) )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_arctan
% 5.82/6.19 thf(fact_9350_sin__arctan,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( sin_real @ ( arctan @ X2 ) )
% 5.82/6.19 = ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_arctan
% 5.82/6.19 thf(fact_9351_sqrt__sum__squares__half__less,axiom,
% 5.82/6.19 ! [X2: real,U: real,Y3: real] :
% 5.82/6.19 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.19 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sqrt_sum_squares_half_less
% 5.82/6.19 thf(fact_9352_sin__cos__sqrt,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.82/6.19 => ( ( sin_real @ X2 )
% 5.82/6.19 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % sin_cos_sqrt
% 5.82/6.19 thf(fact_9353_arctan__half,axiom,
% 5.82/6.19 ( arctan
% 5.82/6.19 = ( ^ [X3: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X3 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arctan_half
% 5.82/6.19 thf(fact_9354_cos__tan,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.19 => ( ( cos_real @ X2 )
% 5.82/6.19 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_tan
% 5.82/6.19 thf(fact_9355_arsinh__real__def,axiom,
% 5.82/6.19 ( arsinh_real
% 5.82/6.19 = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % arsinh_real_def
% 5.82/6.19 thf(fact_9356_complex__unimodular__polar,axiom,
% 5.82/6.19 ! [Z: complex] :
% 5.82/6.19 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.82/6.19 = one_one_real )
% 5.82/6.19 => ~ ! [T7: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.19 => ( ( ord_less_real @ T7 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.19 => ( Z
% 5.82/6.19 != ( complex2 @ ( cos_real @ T7 ) @ ( sin_real @ T7 ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_unimodular_polar
% 5.82/6.19 thf(fact_9357_summable__complex__of__real,axiom,
% 5.82/6.19 ! [F: nat > real] :
% 5.82/6.19 ( ( summable_complex
% 5.82/6.19 @ ^ [N4: nat] : ( real_V4546457046886955230omplex @ ( F @ N4 ) ) )
% 5.82/6.19 = ( summable_real @ F ) ) ).
% 5.82/6.19
% 5.82/6.19 % summable_complex_of_real
% 5.82/6.19 thf(fact_9358_norm__cos__sin,axiom,
% 5.82/6.19 ! [T: real] :
% 5.82/6.19 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.82/6.19 = one_one_real ) ).
% 5.82/6.19
% 5.82/6.19 % norm_cos_sin
% 5.82/6.19 thf(fact_9359_complex__diff,axiom,
% 5.82/6.19 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.19 ( ( minus_minus_complex @ ( complex2 @ A2 @ B2 ) @ ( complex2 @ C2 @ D2 ) )
% 5.82/6.19 = ( complex2 @ ( minus_minus_real @ A2 @ C2 ) @ ( minus_minus_real @ B2 @ D2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_diff
% 5.82/6.19 thf(fact_9360_complex__of__real__add__Complex,axiom,
% 5.82/6.19 ! [R2: real,X2: real,Y3: real] :
% 5.82/6.19 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X2 @ Y3 ) )
% 5.82/6.19 = ( complex2 @ ( plus_plus_real @ R2 @ X2 ) @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_of_real_add_Complex
% 5.82/6.19 thf(fact_9361_Complex__add__complex__of__real,axiom,
% 5.82/6.19 ! [X2: real,Y3: real,R2: real] :
% 5.82/6.19 ( ( plus_plus_complex @ ( complex2 @ X2 @ Y3 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.82/6.19 = ( complex2 @ ( plus_plus_real @ X2 @ R2 ) @ Y3 ) ) ).
% 5.82/6.19
% 5.82/6.19 % Complex_add_complex_of_real
% 5.82/6.19 thf(fact_9362_complex__add,axiom,
% 5.82/6.19 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.19 ( ( plus_plus_complex @ ( complex2 @ A2 @ B2 ) @ ( complex2 @ C2 @ D2 ) )
% 5.82/6.19 = ( complex2 @ ( plus_plus_real @ A2 @ C2 ) @ ( plus_plus_real @ B2 @ D2 ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_add
% 5.82/6.19 thf(fact_9363_complex__mult,axiom,
% 5.82/6.19 ! [A2: real,B2: real,C2: real,D2: real] :
% 5.82/6.19 ( ( times_times_complex @ ( complex2 @ A2 @ B2 ) @ ( complex2 @ C2 @ D2 ) )
% 5.82/6.19 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A2 @ C2 ) @ ( times_times_real @ B2 @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ A2 @ D2 ) @ ( times_times_real @ B2 @ C2 ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_mult
% 5.82/6.19 thf(fact_9364_Complex__eq__1,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( ( complex2 @ A2 @ B2 )
% 5.82/6.19 = one_one_complex )
% 5.82/6.19 = ( ( A2 = one_one_real )
% 5.82/6.19 & ( B2 = zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Complex_eq_1
% 5.82/6.19 thf(fact_9365_one__complex_Ocode,axiom,
% 5.82/6.19 ( one_one_complex
% 5.82/6.19 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.82/6.19
% 5.82/6.19 % one_complex.code
% 5.82/6.19 thf(fact_9366_Complex__eq__neg__1,axiom,
% 5.82/6.19 ! [A2: real,B2: real] :
% 5.82/6.19 ( ( ( complex2 @ A2 @ B2 )
% 5.82/6.19 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.82/6.19 = ( ( A2
% 5.82/6.19 = ( uminus_uminus_real @ one_one_real ) )
% 5.82/6.19 & ( B2 = zero_zero_real ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Complex_eq_neg_1
% 5.82/6.19 thf(fact_9367_complex__norm,axiom,
% 5.82/6.19 ! [X2: real,Y3: real] :
% 5.82/6.19 ( ( real_V1022390504157884413omplex @ ( complex2 @ X2 @ Y3 ) )
% 5.82/6.19 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % complex_norm
% 5.82/6.19 thf(fact_9368_Maclaurin__exp__lt,axiom,
% 5.82/6.19 ! [X2: real,N: nat] :
% 5.82/6.19 ( ( X2 != zero_zero_real )
% 5.82/6.19 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.19 => ? [T7: real] :
% 5.82/6.19 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T7 ) )
% 5.82/6.19 & ( ord_less_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.19 & ( ( exp_real @ X2 )
% 5.82/6.19 = ( plus_plus_real
% 5.82/6.19 @ ( groups6591440286371151544t_real
% 5.82/6.19 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.82/6.19 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.19 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % Maclaurin_exp_lt
% 5.82/6.19 thf(fact_9369_cos__arcsin,axiom,
% 5.82/6.19 ! [X2: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.19 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.19 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.82/6.19 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.19
% 5.82/6.19 % cos_arcsin
% 5.82/6.19 thf(fact_9370_sin__arccos__abs,axiom,
% 5.82/6.19 ! [Y3: real] :
% 5.82/6.19 ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.19 => ( ( sin_real @ ( arccos @ Y3 ) )
% 5.82/6.20 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sin_arccos_abs
% 5.82/6.20 thf(fact_9371_exp__le__cancel__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( exp_real @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_le_cancel_iff
% 5.82/6.20 thf(fact_9372_exp__eq__one__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ( exp_real @ X2 )
% 5.82/6.20 = one_one_real )
% 5.82/6.20 = ( X2 = zero_zero_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_eq_one_iff
% 5.82/6.20 thf(fact_9373_arccos__1,axiom,
% 5.82/6.20 ( ( arccos @ one_one_real )
% 5.82/6.20 = zero_zero_real ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_1
% 5.82/6.20 thf(fact_9374_one__less__exp__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.82/6.20 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % one_less_exp_iff
% 5.82/6.20 thf(fact_9375_exp__less__one__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.82/6.20 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_less_one_iff
% 5.82/6.20 thf(fact_9376_one__le__exp__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.82/6.20 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % one_le_exp_iff
% 5.82/6.20 thf(fact_9377_exp__le__one__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_le_one_iff
% 5.82/6.20 thf(fact_9378_arccos__minus__1,axiom,
% 5.82/6.20 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.82/6.20 = pi ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_minus_1
% 5.82/6.20 thf(fact_9379_cos__arccos,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( cos_real @ ( arccos @ Y3 ) )
% 5.82/6.20 = Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cos_arccos
% 5.82/6.20 thf(fact_9380_sin__arcsin,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.82/6.20 = Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sin_arcsin
% 5.82/6.20 thf(fact_9381_arccos__0,axiom,
% 5.82/6.20 ( ( arccos @ zero_zero_real )
% 5.82/6.20 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_0
% 5.82/6.20 thf(fact_9382_arcsin__1,axiom,
% 5.82/6.20 ( ( arcsin @ one_one_real )
% 5.82/6.20 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_1
% 5.82/6.20 thf(fact_9383_arcsin__minus__1,axiom,
% 5.82/6.20 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.82/6.20 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_minus_1
% 5.82/6.20 thf(fact_9384_not__exp__le__zero,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ~ ( ord_less_eq_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.82/6.20
% 5.82/6.20 % not_exp_le_zero
% 5.82/6.20 thf(fact_9385_exp__ge__zero,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_ge_zero
% 5.82/6.20 thf(fact_9386_exp__gt__one,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_gt_one
% 5.82/6.20 thf(fact_9387_exp__ge__add__one__self,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_ge_add_one_self
% 5.82/6.20 thf(fact_9388_log__ln,axiom,
% 5.82/6.20 ( ln_ln_real
% 5.82/6.20 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % log_ln
% 5.82/6.20 thf(fact_9389_arccos__le__arccos,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_le_arccos
% 5.82/6.20 thf(fact_9390_arccos__eq__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 & ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real ) )
% 5.82/6.20 => ( ( ( arccos @ X2 )
% 5.82/6.20 = ( arccos @ Y3 ) )
% 5.82/6.20 = ( X2 = Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_eq_iff
% 5.82/6.20 thf(fact_9391_arccos__le__mono,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( arccos @ X2 ) @ ( arccos @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_le_mono
% 5.82/6.20 thf(fact_9392_arcsin__le__arcsin,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_le_arcsin
% 5.82/6.20 thf(fact_9393_arcsin__minus,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( arcsin @ ( uminus_uminus_real @ X2 ) )
% 5.82/6.20 = ( uminus_uminus_real @ ( arcsin @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_minus
% 5.82/6.20 thf(fact_9394_arcsin__eq__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.20 => ( ( ( arcsin @ X2 )
% 5.82/6.20 = ( arcsin @ Y3 ) )
% 5.82/6.20 = ( X2 = Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_eq_iff
% 5.82/6.20 thf(fact_9395_arcsin__le__mono,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_le_mono
% 5.82/6.20 thf(fact_9396_exp__ge__add__one__self__aux,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_ge_add_one_self_aux
% 5.82/6.20 thf(fact_9397_lemma__exp__total,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ one_one_real @ Y3 )
% 5.82/6.20 => ? [X4: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.82/6.20 & ( ord_less_eq_real @ X4 @ ( minus_minus_real @ Y3 @ one_one_real ) )
% 5.82/6.20 & ( ( exp_real @ X4 )
% 5.82/6.20 = Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % lemma_exp_total
% 5.82/6.20 thf(fact_9398_ln__ge__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ ( ln_ln_real @ X2 ) )
% 5.82/6.20 = ( ord_less_eq_real @ ( exp_real @ Y3 ) @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % ln_ge_iff
% 5.82/6.20 thf(fact_9399_ln__x__over__x__mono,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.20 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y3 ) @ Y3 ) @ ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % ln_x_over_x_mono
% 5.82/6.20 thf(fact_9400_arccos__lbound,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_lbound
% 5.82/6.20 thf(fact_9401_arccos__less__arccos,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_real @ ( arccos @ Y3 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_less_arccos
% 5.82/6.20 thf(fact_9402_arccos__less__mono,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ Y3 @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_less_mono
% 5.82/6.20 thf(fact_9403_exp__le,axiom,
% 5.82/6.20 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_le
% 5.82/6.20 thf(fact_9404_arccos__ubound,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_ubound
% 5.82/6.20 thf(fact_9405_arccos__cos,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.20 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.82/6.20 = X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_cos
% 5.82/6.20 thf(fact_9406_arcsin__less__arcsin,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_less_arcsin
% 5.82/6.20 thf(fact_9407_arcsin__less__mono,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.20 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_less_mono
% 5.82/6.20 thf(fact_9408_cos__arccos__abs,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.82/6.20 => ( ( cos_real @ ( arccos @ Y3 ) )
% 5.82/6.20 = Y3 ) ) ).
% 5.82/6.20
% 5.82/6.20 % cos_arccos_abs
% 5.82/6.20 thf(fact_9409_arccos__cos__eq__abs,axiom,
% 5.82/6.20 ! [Theta: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.82/6.20 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.82/6.20 = ( abs_abs_real @ Theta ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_cos_eq_abs
% 5.82/6.20 thf(fact_9410_exp__half__le2,axiom,
% 5.82/6.20 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_half_le2
% 5.82/6.20 thf(fact_9411_arccos__lt__bounded,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.82/6.20 & ( ord_less_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_lt_bounded
% 5.82/6.20 thf(fact_9412_arccos__bounded,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_bounded
% 5.82/6.20 thf(fact_9413_sin__arccos__nonzero,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.82/6.20 != zero_zero_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sin_arccos_nonzero
% 5.82/6.20 thf(fact_9414_arccos__cos2,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.82/6.20 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.82/6.20 = ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_cos2
% 5.82/6.20 thf(fact_9415_arccos__minus,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.82/6.20 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_minus
% 5.82/6.20 thf(fact_9416_cos__arcsin__nonzero,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.82/6.20 != zero_zero_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cos_arcsin_nonzero
% 5.82/6.20 thf(fact_9417_arccos,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi )
% 5.82/6.20 & ( ( cos_real @ ( arccos @ Y3 ) )
% 5.82/6.20 = Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos
% 5.82/6.20 thf(fact_9418_arccos__minus__abs,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.82/6.20 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_minus_abs
% 5.82/6.20 thf(fact_9419_exp__bound,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_bound
% 5.82/6.20 thf(fact_9420_real__exp__bound__lemma,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_exp_bound_lemma
% 5.82/6.20 thf(fact_9421_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 )
% 5.82/6.20 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_ge_one_plus_x_over_n_power_n
% 5.82/6.20 thf(fact_9422_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.82/6.20 ! [X2: real,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.82/6.20 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_ge_one_minus_x_over_n_power_n
% 5.82/6.20 thf(fact_9423_arccos__le__pi2,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_le_pi2
% 5.82/6.20 thf(fact_9424_arcsin__lt__bounded,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.82/6.20 & ( ord_less_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_lt_bounded
% 5.82/6.20 thf(fact_9425_arcsin__bounded,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_bounded
% 5.82/6.20 thf(fact_9426_arcsin__ubound,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_ubound
% 5.82/6.20 thf(fact_9427_arcsin__lbound,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_lbound
% 5.82/6.20 thf(fact_9428_Maclaurin__exp__le,axiom,
% 5.82/6.20 ! [X2: real,N: nat] :
% 5.82/6.20 ? [T7: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.20 & ( ( exp_real @ X2 )
% 5.82/6.20 = ( plus_plus_real
% 5.82/6.20 @ ( groups6591440286371151544t_real
% 5.82/6.20 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.82/6.20 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.20 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Maclaurin_exp_le
% 5.82/6.20 thf(fact_9429_exp__lower__Taylor__quadratic,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( divide_divide_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_lower_Taylor_quadratic
% 5.82/6.20 thf(fact_9430_arcsin__sin,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.82/6.20 = X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_sin
% 5.82/6.20 thf(fact_9431_log__base__10__eq2,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.20 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % log_base_10_eq2
% 5.82/6.20 thf(fact_9432_tanh__real__altdef,axiom,
% 5.82/6.20 ( tanh_real
% 5.82/6.20 = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % tanh_real_altdef
% 5.82/6.20 thf(fact_9433_log__base__10__eq1,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.82/6.20 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % log_base_10_eq1
% 5.82/6.20 thf(fact_9434_le__arcsin__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ ( arcsin @ X2 ) )
% 5.82/6.20 = ( ord_less_eq_real @ ( sin_real @ Y3 ) @ X2 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % le_arcsin_iff
% 5.82/6.20 thf(fact_9435_arcsin__le__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y3 )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y3 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_le_iff
% 5.82/6.20 thf(fact_9436_arcsin__pi,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ pi )
% 5.82/6.20 & ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.82/6.20 = Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_pi
% 5.82/6.20 thf(fact_9437_arcsin,axiom,
% 5.82/6.20 ! [Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 & ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.82/6.20 = Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin
% 5.82/6.20 thf(fact_9438_arccos__cos__eq__abs__2pi,axiom,
% 5.82/6.20 ! [Theta: real] :
% 5.82/6.20 ~ ! [K2: int] :
% 5.82/6.20 ( ( arccos @ ( cos_real @ Theta ) )
% 5.82/6.20 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_cos_eq_abs_2pi
% 5.82/6.20 thf(fact_9439_sin__arccos,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.82/6.20 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sin_arccos
% 5.82/6.20 thf(fact_9440_Maclaurin__sin__bound,axiom,
% 5.82/6.20 ! [X2: real,N: nat] :
% 5.82/6.20 ( ord_less_eq_real
% 5.82/6.20 @ ( abs_abs_real
% 5.82/6.20 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.82/6.20 @ ( groups6591440286371151544t_real
% 5.82/6.20 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.20 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.82/6.20 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Maclaurin_sin_bound
% 5.82/6.20 thf(fact_9441_cot__less__zero,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cot_less_zero
% 5.82/6.20 thf(fact_9442_cot__periodic,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( cot_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.82/6.20 = ( cot_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % cot_periodic
% 5.82/6.20 thf(fact_9443_inverse__powr,axiom,
% 5.82/6.20 ! [Y3: real,A2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.20 => ( ( powr_real @ ( inverse_inverse_real @ Y3 ) @ A2 )
% 5.82/6.20 = ( inverse_inverse_real @ ( powr_real @ Y3 @ A2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % inverse_powr
% 5.82/6.20 thf(fact_9444_forall__pos__mono__1,axiom,
% 5.82/6.20 ! [P: real > $o,E: real] :
% 5.82/6.20 ( ! [D4: real,E2: real] :
% 5.82/6.20 ( ( ord_less_real @ D4 @ E2 )
% 5.82/6.20 => ( ( P @ D4 )
% 5.82/6.20 => ( P @ E2 ) ) )
% 5.82/6.20 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.82/6.20 => ( P @ E ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % forall_pos_mono_1
% 5.82/6.20 thf(fact_9445_sqrt__divide__self__eq,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( divide_divide_real @ ( sqrt @ X2 ) @ X2 )
% 5.82/6.20 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sqrt_divide_self_eq
% 5.82/6.20 thf(fact_9446_log__inverse,axiom,
% 5.82/6.20 ! [A2: real,X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.20 => ( ( A2 != one_one_real )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( log @ A2 @ ( inverse_inverse_real @ X2 ) )
% 5.82/6.20 = ( uminus_uminus_real @ ( log @ A2 @ X2 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % log_inverse
% 5.82/6.20 thf(fact_9447_exp__plus__inverse__exp,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_plus_inverse_exp
% 5.82/6.20 thf(fact_9448_plus__inverse__ge__2,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % plus_inverse_ge_2
% 5.82/6.20 thf(fact_9449_real__inv__sqrt__pow2,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.20 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_inv_sqrt_pow2
% 5.82/6.20 thf(fact_9450_tan__cot,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.82/6.20 = ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % tan_cot
% 5.82/6.20 thf(fact_9451_real__le__x__sinh,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ X2 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_le_x_sinh
% 5.82/6.20 thf(fact_9452_real__le__abs__sinh,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_le_abs_sinh
% 5.82/6.20 thf(fact_9453_powr__real__of__int,axiom,
% 5.82/6.20 ! [X2: real,N: int] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.82/6.20 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.82/6.20 = ( power_power_real @ X2 @ ( nat2 @ N ) ) ) )
% 5.82/6.20 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.82/6.20 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.82/6.20 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % powr_real_of_int
% 5.82/6.20 thf(fact_9454_cot__gt__zero,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cot_gt_zero
% 5.82/6.20 thf(fact_9455_tan__cot_H,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.82/6.20 = ( cot_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % tan_cot'
% 5.82/6.20 thf(fact_9456_sinh__real__le__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.82/6.20
% 5.82/6.20 % sinh_real_le_iff
% 5.82/6.20 thf(fact_9457_sinh__real__nonneg__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.82/6.20 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % sinh_real_nonneg_iff
% 5.82/6.20 thf(fact_9458_sinh__real__nonpos__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % sinh_real_nonpos_iff
% 5.82/6.20 thf(fact_9459_sinh__le__cosh__real,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % sinh_le_cosh_real
% 5.82/6.20 thf(fact_9460_cosh__real__nonneg,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_nonneg
% 5.82/6.20 thf(fact_9461_cosh__real__nonneg__le__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_nonneg_le_iff
% 5.82/6.20 thf(fact_9462_cosh__real__nonpos__le__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_nonpos_le_iff
% 5.82/6.20 thf(fact_9463_cosh__real__ge__1,axiom,
% 5.82/6.20 ! [X2: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_ge_1
% 5.82/6.20 thf(fact_9464_cosh__real__nonpos__less__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.82/6.20 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ Y3 @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_nonpos_less_iff
% 5.82/6.20 thf(fact_9465_cosh__real__nonneg__less__iff,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.20 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_nonneg_less_iff
% 5.82/6.20 thf(fact_9466_cosh__real__strict__mono,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.20 => ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_real_strict_mono
% 5.82/6.20 thf(fact_9467_arcosh__cosh__real,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( arcosh_real @ ( cosh_real @ X2 ) )
% 5.82/6.20 = X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcosh_cosh_real
% 5.82/6.20 thf(fact_9468_complex__inverse,axiom,
% 5.82/6.20 ! [A2: real,B2: real] :
% 5.82/6.20 ( ( invers8013647133539491842omplex @ ( complex2 @ A2 @ B2 ) )
% 5.82/6.20 = ( complex2 @ ( divide_divide_real @ A2 @ ( plus_plus_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B2 ) @ ( plus_plus_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % complex_inverse
% 5.82/6.20 thf(fact_9469_cosh__ln__real,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.20 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cosh_ln_real
% 5.82/6.20 thf(fact_9470_sinh__ln__real,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.82/6.20 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sinh_ln_real
% 5.82/6.20 thf(fact_9471_divmod__BitM__2__eq,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.82/6.20 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % divmod_BitM_2_eq
% 5.82/6.20 thf(fact_9472_i__even__power,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.82/6.20 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % i_even_power
% 5.82/6.20 thf(fact_9473_norm__ii,axiom,
% 5.82/6.20 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.82/6.20 = one_one_real ) ).
% 5.82/6.20
% 5.82/6.20 % norm_ii
% 5.82/6.20 thf(fact_9474_pred__numeral__simps_I2_J,axiom,
% 5.82/6.20 ! [K: num] :
% 5.82/6.20 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.82/6.20 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % pred_numeral_simps(2)
% 5.82/6.20 thf(fact_9475_i__squared,axiom,
% 5.82/6.20 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.82/6.20 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % i_squared
% 5.82/6.20 thf(fact_9476_exp__pi__i,axiom,
% 5.82/6.20 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.82/6.20 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_pi_i
% 5.82/6.20 thf(fact_9477_exp__pi__i_H,axiom,
% 5.82/6.20 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.82/6.20 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % exp_pi_i'
% 5.82/6.20 thf(fact_9478_exp__two__pi__i,axiom,
% 5.82/6.20 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.82/6.20 = one_one_complex ) ).
% 5.82/6.20
% 5.82/6.20 % exp_two_pi_i
% 5.82/6.20 thf(fact_9479_exp__two__pi__i_H,axiom,
% 5.82/6.20 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.82/6.20 = one_one_complex ) ).
% 5.82/6.20
% 5.82/6.20 % exp_two_pi_i'
% 5.82/6.20 thf(fact_9480_power2__i,axiom,
% 5.82/6.20 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.20 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % power2_i
% 5.82/6.20 thf(fact_9481_semiring__norm_I26_J,axiom,
% 5.82/6.20 ( ( bitM @ one )
% 5.82/6.20 = one ) ).
% 5.82/6.20
% 5.82/6.20 % semiring_norm(26)
% 5.82/6.20 thf(fact_9482_complex__i__not__one,axiom,
% 5.82/6.20 imaginary_unit != one_one_complex ).
% 5.82/6.20
% 5.82/6.20 % complex_i_not_one
% 5.82/6.20 thf(fact_9483_semiring__norm_I28_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bitM @ ( bit1 @ N ) )
% 5.82/6.20 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % semiring_norm(28)
% 5.82/6.20 thf(fact_9484_semiring__norm_I27_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bitM @ ( bit0 @ N ) )
% 5.82/6.20 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % semiring_norm(27)
% 5.82/6.20 thf(fact_9485_eval__nat__numeral_I2_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.82/6.20 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % eval_nat_numeral(2)
% 5.82/6.20 thf(fact_9486_one__plus__BitM,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.82/6.20 = ( bit0 @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % one_plus_BitM
% 5.82/6.20 thf(fact_9487_BitM__plus__one,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.82/6.20 = ( bit0 @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % BitM_plus_one
% 5.82/6.20 thf(fact_9488_Complex__eq__i,axiom,
% 5.82/6.20 ! [X2: real,Y3: real] :
% 5.82/6.20 ( ( ( complex2 @ X2 @ Y3 )
% 5.82/6.20 = imaginary_unit )
% 5.82/6.20 = ( ( X2 = zero_zero_real )
% 5.82/6.20 & ( Y3 = one_one_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Complex_eq_i
% 5.82/6.20 thf(fact_9489_imaginary__unit_Ocode,axiom,
% 5.82/6.20 ( imaginary_unit
% 5.82/6.20 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % imaginary_unit.code
% 5.82/6.20 thf(fact_9490_Complex__eq,axiom,
% 5.82/6.20 ( complex2
% 5.82/6.20 = ( ^ [A5: real,B6: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A5 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B6 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Complex_eq
% 5.82/6.20 thf(fact_9491_complex__split__polar,axiom,
% 5.82/6.20 ! [Z: complex] :
% 5.82/6.20 ? [R3: real,A3: real] :
% 5.82/6.20 ( Z
% 5.82/6.20 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % complex_split_polar
% 5.82/6.20 thf(fact_9492_cmod__unit__one,axiom,
% 5.82/6.20 ! [A2: real] :
% 5.82/6.20 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A2 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A2 ) ) ) ) )
% 5.82/6.20 = one_one_real ) ).
% 5.82/6.20
% 5.82/6.20 % cmod_unit_one
% 5.82/6.20 thf(fact_9493_cmod__complex__polar,axiom,
% 5.82/6.20 ! [R2: real,A2: real] :
% 5.82/6.20 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A2 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A2 ) ) ) ) ) )
% 5.82/6.20 = ( abs_abs_real @ R2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % cmod_complex_polar
% 5.82/6.20 thf(fact_9494_Arg__minus__ii,axiom,
% 5.82/6.20 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.82/6.20 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Arg_minus_ii
% 5.82/6.20 thf(fact_9495_csqrt__ii,axiom,
% 5.82/6.20 ( ( csqrt @ imaginary_unit )
% 5.82/6.20 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % csqrt_ii
% 5.82/6.20 thf(fact_9496_Arg__ii,axiom,
% 5.82/6.20 ( ( arg @ imaginary_unit )
% 5.82/6.20 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Arg_ii
% 5.82/6.20 thf(fact_9497_csqrt__eq__1,axiom,
% 5.82/6.20 ! [Z: complex] :
% 5.82/6.20 ( ( ( csqrt @ Z )
% 5.82/6.20 = one_one_complex )
% 5.82/6.20 = ( Z = one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % csqrt_eq_1
% 5.82/6.20 thf(fact_9498_csqrt__1,axiom,
% 5.82/6.20 ( ( csqrt @ one_one_complex )
% 5.82/6.20 = one_one_complex ) ).
% 5.82/6.20
% 5.82/6.20 % csqrt_1
% 5.82/6.20 thf(fact_9499_power2__csqrt,axiom,
% 5.82/6.20 ! [Z: complex] :
% 5.82/6.20 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.82/6.20 = Z ) ).
% 5.82/6.20
% 5.82/6.20 % power2_csqrt
% 5.82/6.20 thf(fact_9500_of__real__sqrt,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X2 ) )
% 5.82/6.20 = ( csqrt @ ( real_V4546457046886955230omplex @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % of_real_sqrt
% 5.82/6.20 thf(fact_9501_Arg__bounded,axiom,
% 5.82/6.20 ! [Z: complex] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.82/6.20
% 5.82/6.20 % Arg_bounded
% 5.82/6.20 thf(fact_9502_cis__minus__pi__half,axiom,
% 5.82/6.20 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.20 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.82/6.20
% 5.82/6.20 % cis_minus_pi_half
% 5.82/6.20 thf(fact_9503_or__minus__numerals_I5_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.82/6.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_numerals(5)
% 5.82/6.20 thf(fact_9504_or__minus__numerals_I1_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_numerals(1)
% 5.82/6.20 thf(fact_9505_norm__cis,axiom,
% 5.82/6.20 ! [A2: real] :
% 5.82/6.20 ( ( real_V1022390504157884413omplex @ ( cis @ A2 ) )
% 5.82/6.20 = one_one_real ) ).
% 5.82/6.20
% 5.82/6.20 % norm_cis
% 5.82/6.20 thf(fact_9506_cis__zero,axiom,
% 5.82/6.20 ( ( cis @ zero_zero_real )
% 5.82/6.20 = one_one_complex ) ).
% 5.82/6.20
% 5.82/6.20 % cis_zero
% 5.82/6.20 thf(fact_9507_cis__pi,axiom,
% 5.82/6.20 ( ( cis @ pi )
% 5.82/6.20 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % cis_pi
% 5.82/6.20 thf(fact_9508_or__minus__numerals_I8_J,axiom,
% 5.82/6.20 ! [N: num,M: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.82/6.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_numerals(8)
% 5.82/6.20 thf(fact_9509_or__minus__numerals_I4_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_numerals(4)
% 5.82/6.20 thf(fact_9510_or__minus__numerals_I3_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_numerals(3)
% 5.82/6.20 thf(fact_9511_or__minus__numerals_I7_J,axiom,
% 5.82/6.20 ! [N: num,M: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.82/6.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_numerals(7)
% 5.82/6.20 thf(fact_9512_cis__pi__half,axiom,
% 5.82/6.20 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 = imaginary_unit ) ).
% 5.82/6.20
% 5.82/6.20 % cis_pi_half
% 5.82/6.20 thf(fact_9513_cis__2pi,axiom,
% 5.82/6.20 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.82/6.20 = one_one_complex ) ).
% 5.82/6.20
% 5.82/6.20 % cis_2pi
% 5.82/6.20 thf(fact_9514_or__not__num__neg_Osimps_I1_J,axiom,
% 5.82/6.20 ( ( bit_or_not_num_neg @ one @ one )
% 5.82/6.20 = one ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(1)
% 5.82/6.20 thf(fact_9515_or__not__num__neg_Osimps_I4_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.82/6.20 = ( bit0 @ one ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(4)
% 5.82/6.20 thf(fact_9516_or__not__num__neg_Osimps_I6_J,axiom,
% 5.82/6.20 ! [N: num,M: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.82/6.20 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(6)
% 5.82/6.20 thf(fact_9517_or__not__num__neg_Osimps_I7_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.82/6.20 = one ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(7)
% 5.82/6.20 thf(fact_9518_or__not__num__neg_Osimps_I3_J,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.82/6.20 = ( bit1 @ M ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(3)
% 5.82/6.20 thf(fact_9519_or__not__num__neg_Osimps_I5_J,axiom,
% 5.82/6.20 ! [N: num,M: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.82/6.20 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(5)
% 5.82/6.20 thf(fact_9520_cis__mult,axiom,
% 5.82/6.20 ! [A2: real,B2: real] :
% 5.82/6.20 ( ( times_times_complex @ ( cis @ A2 ) @ ( cis @ B2 ) )
% 5.82/6.20 = ( cis @ ( plus_plus_real @ A2 @ B2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cis_mult
% 5.82/6.20 thf(fact_9521_cis__divide,axiom,
% 5.82/6.20 ! [A2: real,B2: real] :
% 5.82/6.20 ( ( divide1717551699836669952omplex @ ( cis @ A2 ) @ ( cis @ B2 ) )
% 5.82/6.20 = ( cis @ ( minus_minus_real @ A2 @ B2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cis_divide
% 5.82/6.20 thf(fact_9522_or__not__num__neg_Osimps_I2_J,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.82/6.20 = ( bit1 @ M ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(2)
% 5.82/6.20 thf(fact_9523_or__not__num__neg_Osimps_I8_J,axiom,
% 5.82/6.20 ! [N: num,M: num] :
% 5.82/6.20 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.82/6.20 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.simps(8)
% 5.82/6.20 thf(fact_9524_or__not__num__neg_Oelims,axiom,
% 5.82/6.20 ! [X2: num,Xa: num,Y3: num] :
% 5.82/6.20 ( ( ( bit_or_not_num_neg @ X2 @ Xa )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( ( X2 = one )
% 5.82/6.20 => ( ( Xa = one )
% 5.82/6.20 => ( Y3 != one ) ) )
% 5.82/6.20 => ( ( ( X2 = one )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit0 @ M5 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bit1 @ M5 ) ) ) )
% 5.82/6.20 => ( ( ( X2 = one )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bit1 @ M5 ) ) ) )
% 5.82/6.20 => ( ( ? [N3: num] :
% 5.82/6.20 ( X2
% 5.82/6.20 = ( bit0 @ N3 ) )
% 5.82/6.20 => ( ( Xa = one )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bit0 @ one ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit0 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit0 @ M5 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit0 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.82/6.20 => ( ( ? [N3: num] :
% 5.82/6.20 ( X2
% 5.82/6.20 = ( bit1 @ N3 ) )
% 5.82/6.20 => ( ( Xa = one )
% 5.82/6.20 => ( Y3 != one ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit1 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit0 @ M5 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.82/6.20 => ~ ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit1 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.elims
% 5.82/6.20 thf(fact_9525_bij__betw__roots__unity,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( bij_betw_nat_complex
% 5.82/6.20 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.82/6.20 @ ( set_ord_lessThan_nat @ N )
% 5.82/6.20 @ ( collect_complex
% 5.82/6.20 @ ^ [Z4: complex] :
% 5.82/6.20 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.20 = one_one_complex ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bij_betw_roots_unity
% 5.82/6.20 thf(fact_9526_set__decode__0,axiom,
% 5.82/6.20 ! [X2: nat] :
% 5.82/6.20 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.82/6.20 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % set_decode_0
% 5.82/6.20 thf(fact_9527_VEBTi_Osize_I3_J,axiom,
% 5.82/6.20 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 5.82/6.20 ( ( size_size_VEBT_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 5.82/6.20 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ size_size_VEBT_VEBTi @ X13 ) @ ( size_size_VEBT_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBTi.size(3)
% 5.82/6.20 thf(fact_9528_set__decode__Suc,axiom,
% 5.82/6.20 ! [N: nat,X2: nat] :
% 5.82/6.20 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X2 ) )
% 5.82/6.20 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % set_decode_Suc
% 5.82/6.20 thf(fact_9529_subset__decode__imp__le,axiom,
% 5.82/6.20 ! [M: nat,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.82/6.20 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % subset_decode_imp_le
% 5.82/6.20 thf(fact_9530_set__decode__plus__power__2,axiom,
% 5.82/6.20 ! [N: nat,Z: nat] :
% 5.82/6.20 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.82/6.20 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.82/6.20 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % set_decode_plus_power_2
% 5.82/6.20 thf(fact_9531_set__decode__def,axiom,
% 5.82/6.20 ( nat_set_decode
% 5.82/6.20 = ( ^ [X3: nat] :
% 5.82/6.20 ( collect_nat
% 5.82/6.20 @ ^ [N4: nat] :
% 5.82/6.20 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % set_decode_def
% 5.82/6.20 thf(fact_9532_VEBTi_Osize__gen_I1_J,axiom,
% 5.82/6.20 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 5.82/6.20 ( ( vEBT_size_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 5.82/6.20 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ vEBT_size_VEBTi @ X13 ) @ ( vEBT_size_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBTi.size_gen(1)
% 5.82/6.20 thf(fact_9533_Suc__0__mod__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ( N
% 5.82/6.20 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Suc_0_mod_eq
% 5.82/6.20 thf(fact_9534_Divides_Oadjust__div__eq,axiom,
% 5.82/6.20 ! [Q3: int,R2: int] :
% 5.82/6.20 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.82/6.20 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Divides.adjust_div_eq
% 5.82/6.20 thf(fact_9535_or__Suc__0__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_Suc_0_eq
% 5.82/6.20 thf(fact_9536_Suc__0__or__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Suc_0_or_eq
% 5.82/6.20 thf(fact_9537_or__nat__rec,axiom,
% 5.82/6.20 ( bit_se1412395901928357646or_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ( plus_plus_nat
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.82/6.20 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.82/6.20 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_nat_rec
% 5.82/6.20 thf(fact_9538_or__int__rec,axiom,
% 5.82/6.20 ( bit_se1409905431419307370or_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.82/6.20 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_int_rec
% 5.82/6.20 thf(fact_9539_bij__betw__nth__root__unity,axiom,
% 5.82/6.20 ! [C2: complex,N: nat] :
% 5.82/6.20 ( ( C2 != zero_zero_complex )
% 5.82/6.20 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C2 ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.82/6.20 @ ( collect_complex
% 5.82/6.20 @ ^ [Z4: complex] :
% 5.82/6.20 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.20 = one_one_complex ) )
% 5.82/6.20 @ ( collect_complex
% 5.82/6.20 @ ^ [Z4: complex] :
% 5.82/6.20 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.20 = C2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bij_betw_nth_root_unity
% 5.82/6.20 thf(fact_9540_and__int_Oelims,axiom,
% 5.82/6.20 ! [X2: int,Xa: int,Y3: int] :
% 5.82/6.20 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( uminus_uminus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int.elims
% 5.82/6.20 thf(fact_9541_and__int_Osimps,axiom,
% 5.82/6.20 ( bit_se725231765392027082nd_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( if_int
% 5.82/6.20 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 @ ( uminus_uminus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 5.82/6.20 @ ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int.simps
% 5.82/6.20 thf(fact_9542_real__root__Suc__0,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.82/6.20 = X2 ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_Suc_0
% 5.82/6.20 thf(fact_9543_real__root__eq__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ( root @ N @ X2 )
% 5.82/6.20 = ( root @ N @ Y3 ) )
% 5.82/6.20 = ( X2 = Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_eq_iff
% 5.82/6.20 thf(fact_9544_and__nonnegative__int__iff,axiom,
% 5.82/6.20 ! [K: int,L: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.82/6.20 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_nonnegative_int_iff
% 5.82/6.20 thf(fact_9545_real__root__eq__0__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ( root @ N @ X2 )
% 5.82/6.20 = zero_zero_real )
% 5.82/6.20 = ( X2 = zero_zero_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_eq_0_iff
% 5.82/6.20 thf(fact_9546_real__root__less__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_less_iff
% 5.82/6.20 thf(fact_9547_real__root__le__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_le_iff
% 5.82/6.20 thf(fact_9548_real__root__eq__1__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ( root @ N @ X2 )
% 5.82/6.20 = one_one_real )
% 5.82/6.20 = ( X2 = one_one_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_eq_1_iff
% 5.82/6.20 thf(fact_9549_real__root__one,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( root @ N @ one_one_real )
% 5.82/6.20 = one_one_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_one
% 5.82/6.20 thf(fact_9550_real__root__gt__0__iff,axiom,
% 5.82/6.20 ! [N: nat,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ zero_zero_real @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_gt_0_iff
% 5.82/6.20 thf(fact_9551_real__root__lt__0__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.82/6.20 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_lt_0_iff
% 5.82/6.20 thf(fact_9552_real__root__le__0__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_le_0_iff
% 5.82/6.20 thf(fact_9553_real__root__ge__0__iff,axiom,
% 5.82/6.20 ! [N: nat,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_ge_0_iff
% 5.82/6.20 thf(fact_9554_real__root__lt__1__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.82/6.20 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_lt_1_iff
% 5.82/6.20 thf(fact_9555_real__root__gt__1__iff,axiom,
% 5.82/6.20 ! [N: nat,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y3 ) )
% 5.82/6.20 = ( ord_less_real @ one_one_real @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_gt_1_iff
% 5.82/6.20 thf(fact_9556_real__root__ge__1__iff,axiom,
% 5.82/6.20 ! [N: nat,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y3 ) )
% 5.82/6.20 = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_ge_1_iff
% 5.82/6.20 thf(fact_9557_real__root__le__1__iff,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_le_1_iff
% 5.82/6.20 thf(fact_9558_and__minus__numerals_I2_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = one_one_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_minus_numerals(2)
% 5.82/6.20 thf(fact_9559_and__minus__numerals_I6_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.82/6.20 = one_one_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_minus_numerals(6)
% 5.82/6.20 thf(fact_9560_real__root__pow__pos2,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.82/6.20 = X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_pow_pos2
% 5.82/6.20 thf(fact_9561_and__minus__numerals_I1_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = zero_zero_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_minus_numerals(1)
% 5.82/6.20 thf(fact_9562_and__minus__numerals_I5_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.82/6.20 = zero_zero_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_minus_numerals(5)
% 5.82/6.20 thf(fact_9563_real__root__mult__exp,axiom,
% 5.82/6.20 ! [M: nat,N: nat,X2: real] :
% 5.82/6.20 ( ( root @ ( times_times_nat @ M @ N ) @ X2 )
% 5.82/6.20 = ( root @ M @ ( root @ N @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_mult_exp
% 5.82/6.20 thf(fact_9564_real__root__pos__pos__le,axiom,
% 5.82/6.20 ! [X2: real,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_pos_pos_le
% 5.82/6.20 thf(fact_9565_AND__upper2_H,axiom,
% 5.82/6.20 ! [Y3: int,Z: int,X2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_upper2'
% 5.82/6.20 thf(fact_9566_AND__upper1_H,axiom,
% 5.82/6.20 ! [Y3: int,Z: int,Ya: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.20 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_upper1'
% 5.82/6.20 thf(fact_9567_AND__upper2,axiom,
% 5.82/6.20 ! [Y3: int,X2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ Y3 ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_upper2
% 5.82/6.20 thf(fact_9568_AND__upper1,axiom,
% 5.82/6.20 ! [X2: int,Y3: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_upper1
% 5.82/6.20 thf(fact_9569_AND__lower,axiom,
% 5.82/6.20 ! [X2: int,Y3: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.20 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_lower
% 5.82/6.20 thf(fact_9570_plus__and__or,axiom,
% 5.82/6.20 ! [X2: int,Y3: int] :
% 5.82/6.20 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ ( bit_se1409905431419307370or_int @ X2 @ Y3 ) )
% 5.82/6.20 = ( plus_plus_int @ X2 @ Y3 ) ) ).
% 5.82/6.20
% 5.82/6.20 % plus_and_or
% 5.82/6.20 thf(fact_9571_real__root__less__mono,axiom,
% 5.82/6.20 ! [N: nat,X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ Y3 )
% 5.82/6.20 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_less_mono
% 5.82/6.20 thf(fact_9572_real__root__le__mono,axiom,
% 5.82/6.20 ! [N: nat,X2: real,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.82/6.20 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_le_mono
% 5.82/6.20 thf(fact_9573_real__root__power,axiom,
% 5.82/6.20 ! [N: nat,X2: real,K: nat] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( root @ N @ ( power_power_real @ X2 @ K ) )
% 5.82/6.20 = ( power_power_real @ ( root @ N @ X2 ) @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_power
% 5.82/6.20 thf(fact_9574_real__root__abs,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( root @ N @ ( abs_abs_real @ X2 ) )
% 5.82/6.20 = ( abs_abs_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_abs
% 5.82/6.20 thf(fact_9575_and__less__eq,axiom,
% 5.82/6.20 ! [L: int,K: int] :
% 5.82/6.20 ( ( ord_less_int @ L @ zero_zero_int )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_less_eq
% 5.82/6.20 thf(fact_9576_AND__upper1_H_H,axiom,
% 5.82/6.20 ! [Y3: int,Z: int,Ya: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.20 => ( ( ord_less_int @ Y3 @ Z )
% 5.82/6.20 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_upper1''
% 5.82/6.20 thf(fact_9577_AND__upper2_H_H,axiom,
% 5.82/6.20 ! [Y3: int,Z: int,X2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.20 => ( ( ord_less_int @ Y3 @ Z )
% 5.82/6.20 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % AND_upper2''
% 5.82/6.20 thf(fact_9578_real__root__gt__zero,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_gt_zero
% 5.82/6.20 thf(fact_9579_real__root__strict__decreasing,axiom,
% 5.82/6.20 ! [N: nat,N7: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_nat @ N @ N7 )
% 5.82/6.20 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.20 => ( ord_less_real @ ( root @ N7 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_strict_decreasing
% 5.82/6.20 thf(fact_9580_sqrt__def,axiom,
% 5.82/6.20 ( sqrt
% 5.82/6.20 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sqrt_def
% 5.82/6.20 thf(fact_9581_root__abs__power,axiom,
% 5.82/6.20 ! [N: nat,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y3 @ N ) ) )
% 5.82/6.20 = ( abs_abs_real @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % root_abs_power
% 5.82/6.20 thf(fact_9582_even__and__iff__int,axiom,
% 5.82/6.20 ! [K: int,L: int] :
% 5.82/6.20 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.82/6.20 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.82/6.20 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % even_and_iff_int
% 5.82/6.20 thf(fact_9583_real__root__pos__pos,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_pos_pos
% 5.82/6.20 thf(fact_9584_real__root__strict__increasing,axiom,
% 5.82/6.20 ! [N: nat,N7: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_nat @ N @ N7 )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N7 @ X2 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_strict_increasing
% 5.82/6.20 thf(fact_9585_real__root__decreasing,axiom,
% 5.82/6.20 ! [N: nat,N7: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.20 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( root @ N7 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_decreasing
% 5.82/6.20 thf(fact_9586_odd__real__root__pow,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.82/6.20 = X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % odd_real_root_pow
% 5.82/6.20 thf(fact_9587_odd__real__root__unique,axiom,
% 5.82/6.20 ! [N: nat,Y3: real,X2: real] :
% 5.82/6.20 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( ( ( power_power_real @ Y3 @ N )
% 5.82/6.20 = X2 )
% 5.82/6.20 => ( ( root @ N @ X2 )
% 5.82/6.20 = Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % odd_real_root_unique
% 5.82/6.20 thf(fact_9588_odd__real__root__power__cancel,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.82/6.20 = X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % odd_real_root_power_cancel
% 5.82/6.20 thf(fact_9589_real__root__pow__pos,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.82/6.20 = X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_pow_pos
% 5.82/6.20 thf(fact_9590_real__root__pos__unique,axiom,
% 5.82/6.20 ! [N: nat,Y3: real,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.82/6.20 => ( ( ( power_power_real @ Y3 @ N )
% 5.82/6.20 = X2 )
% 5.82/6.20 => ( ( root @ N @ X2 )
% 5.82/6.20 = Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_pos_unique
% 5.82/6.20 thf(fact_9591_real__root__power__cancel,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.82/6.20 = X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_power_cancel
% 5.82/6.20 thf(fact_9592_real__root__increasing,axiom,
% 5.82/6.20 ! [N: nat,N7: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.82/6.20 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.20 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N7 @ X2 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % real_root_increasing
% 5.82/6.20 thf(fact_9593_log__root,axiom,
% 5.82/6.20 ! [N: nat,A2: real,B2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.82/6.20 => ( ( log @ B2 @ ( root @ N @ A2 ) )
% 5.82/6.20 = ( divide_divide_real @ ( log @ B2 @ A2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % log_root
% 5.82/6.20 thf(fact_9594_log__base__root,axiom,
% 5.82/6.20 ! [N: nat,B2: real,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.20 => ( ( log @ ( root @ N @ B2 ) @ X2 )
% 5.82/6.20 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ X2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % log_base_root
% 5.82/6.20 thf(fact_9595_ln__root,axiom,
% 5.82/6.20 ! [N: nat,B2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.82/6.20 => ( ( ln_ln_real @ ( root @ N @ B2 ) )
% 5.82/6.20 = ( divide_divide_real @ ( ln_ln_real @ B2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % ln_root
% 5.82/6.20 thf(fact_9596_and__int__rec,axiom,
% 5.82/6.20 ( bit_se725231765392027082nd_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int_rec
% 5.82/6.20 thf(fact_9597_root__powr__inverse,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( ( root @ N @ X2 )
% 5.82/6.20 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % root_powr_inverse
% 5.82/6.20 thf(fact_9598_and__int__unfold,axiom,
% 5.82/6.20 ( bit_se725231765392027082nd_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( if_int
% 5.82/6.20 @ ( ( K3 = zero_zero_int )
% 5.82/6.20 | ( L3 = zero_zero_int ) )
% 5.82/6.20 @ zero_zero_int
% 5.82/6.20 @ ( if_int
% 5.82/6.20 @ ( K3
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 @ L3
% 5.82/6.20 @ ( if_int
% 5.82/6.20 @ ( L3
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 @ K3
% 5.82/6.20 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( 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 @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int_unfold
% 5.82/6.20 thf(fact_9599_and__int_Opsimps,axiom,
% 5.82/6.20 ! [K: int,L: int] :
% 5.82/6.20 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.82/6.20 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.82/6.20 = ( uminus_uminus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.82/6.20 = ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int.psimps
% 5.82/6.20 thf(fact_9600_and__int_Opelims,axiom,
% 5.82/6.20 ! [X2: int,Xa: int,Y3: int] :
% 5.82/6.20 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 5.82/6.20 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( uminus_uminus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.82/6.20 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int.pelims
% 5.82/6.20 thf(fact_9601_forall__finite_I3_J,axiom,
% 5.82/6.20 ! [X2: nat,P: nat > $o] :
% 5.82/6.20 ( ( ! [I4: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I4 @ ( suc @ ( suc @ X2 ) ) )
% 5.82/6.20 => ( P @ I4 ) ) )
% 5.82/6.20 = ( ( P @ zero_zero_nat )
% 5.82/6.20 & ! [I4: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I4 @ ( suc @ X2 ) )
% 5.82/6.20 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % forall_finite(3)
% 5.82/6.20 thf(fact_9602_and__nat__numerals_I1_J,axiom,
% 5.82/6.20 ! [Y3: num] :
% 5.82/6.20 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.82/6.20 = zero_zero_nat ) ).
% 5.82/6.20
% 5.82/6.20 % and_nat_numerals(1)
% 5.82/6.20 thf(fact_9603_and__nat__numerals_I3_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = zero_zero_nat ) ).
% 5.82/6.20
% 5.82/6.20 % and_nat_numerals(3)
% 5.82/6.20 thf(fact_9604_and__nat__numerals_I4_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = one_one_nat ) ).
% 5.82/6.20
% 5.82/6.20 % and_nat_numerals(4)
% 5.82/6.20 thf(fact_9605_and__nat__numerals_I2_J,axiom,
% 5.82/6.20 ! [Y3: num] :
% 5.82/6.20 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.82/6.20 = one_one_nat ) ).
% 5.82/6.20
% 5.82/6.20 % and_nat_numerals(2)
% 5.82/6.20 thf(fact_9606_and__Suc__0__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_Suc_0_eq
% 5.82/6.20 thf(fact_9607_Suc__0__and__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Suc_0_and_eq
% 5.82/6.20 thf(fact_9608_forall__finite_I1_J,axiom,
% 5.82/6.20 ! [P: nat > $o,I5: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I5 @ zero_zero_nat )
% 5.82/6.20 => ( P @ I5 ) ) ).
% 5.82/6.20
% 5.82/6.20 % forall_finite(1)
% 5.82/6.20 thf(fact_9609_and__nat__unfold,axiom,
% 5.82/6.20 ( bit_se727722235901077358nd_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ( if_nat
% 5.82/6.20 @ ( ( M6 = zero_zero_nat )
% 5.82/6.20 | ( N4 = zero_zero_nat ) )
% 5.82/6.20 @ zero_zero_nat
% 5.82/6.20 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_nat_unfold
% 5.82/6.20 thf(fact_9610_and__nat__rec,axiom,
% 5.82/6.20 ( bit_se727722235901077358nd_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ( plus_plus_nat
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.82/6.20 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.82/6.20 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_nat_rec
% 5.82/6.20 thf(fact_9611_and__int_Opinduct,axiom,
% 5.82/6.20 ! [A0: int,A12: int,P: int > int > $o] :
% 5.82/6.20 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.82/6.20 => ( ! [K2: int,L2: int] :
% 5.82/6.20 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L2 ) )
% 5.82/6.20 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.82/6.20 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.82/6.20 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.82/6.20 => ( P @ K2 @ L2 ) ) )
% 5.82/6.20 => ( P @ A0 @ A12 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_int.pinduct
% 5.82/6.20 thf(fact_9612_Comparator__Generator_OAll__less__Suc,axiom,
% 5.82/6.20 ! [X2: nat,P: nat > $o] :
% 5.82/6.20 ( ( ! [I4: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I4 @ ( suc @ X2 ) )
% 5.82/6.20 => ( P @ I4 ) ) )
% 5.82/6.20 = ( ( P @ zero_zero_nat )
% 5.82/6.20 & ! [I4: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I4 @ X2 )
% 5.82/6.20 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Comparator_Generator.All_less_Suc
% 5.82/6.20 thf(fact_9613_forall__finite_I2_J,axiom,
% 5.82/6.20 ! [P: nat > $o] :
% 5.82/6.20 ( ( ! [I4: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I4 @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( P @ I4 ) ) )
% 5.82/6.20 = ( P @ zero_zero_nat ) ) ).
% 5.82/6.20
% 5.82/6.20 % forall_finite(2)
% 5.82/6.20 thf(fact_9614_upto_Opinduct,axiom,
% 5.82/6.20 ! [A0: int,A12: int,P: int > int > $o] :
% 5.82/6.20 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.82/6.20 => ( ! [I2: int,J2: int] :
% 5.82/6.20 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 5.82/6.20 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.82/6.20 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 5.82/6.20 => ( P @ I2 @ J2 ) ) )
% 5.82/6.20 => ( P @ A0 @ A12 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % upto.pinduct
% 5.82/6.20 thf(fact_9615_uint32_Osize__eq,axiom,
% 5.82/6.20 ( size_size_uint32
% 5.82/6.20 = ( ^ [P4: uint32] : ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % uint32.size_eq
% 5.82/6.20 thf(fact_9616_pred__numeral__inc,axiom,
% 5.82/6.20 ! [K: num] :
% 5.82/6.20 ( ( pred_numeral @ ( inc @ K ) )
% 5.82/6.20 = ( numeral_numeral_nat @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % pred_numeral_inc
% 5.82/6.20 thf(fact_9617_take__bit__of__Suc__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_of_Suc_0
% 5.82/6.20 thf(fact_9618_take__bit__diff,axiom,
% 5.82/6.20 ! [N: nat,K: int,L: int] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.82/6.20 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_diff
% 5.82/6.20 thf(fact_9619_nat__take__bit__eq,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.82/6.20 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % nat_take_bit_eq
% 5.82/6.20 thf(fact_9620_take__bit__nat__eq,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.82/6.20 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_eq
% 5.82/6.20 thf(fact_9621_take__bit__tightened__less__eq__nat,axiom,
% 5.82/6.20 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.20 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.20 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_tightened_less_eq_nat
% 5.82/6.20 thf(fact_9622_take__bit__nat__less__eq__self,axiom,
% 5.82/6.20 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_less_eq_self
% 5.82/6.20 thf(fact_9623_num__induct,axiom,
% 5.82/6.20 ! [P: num > $o,X2: num] :
% 5.82/6.20 ( ( P @ one )
% 5.82/6.20 => ( ! [X4: num] :
% 5.82/6.20 ( ( P @ X4 )
% 5.82/6.20 => ( P @ ( inc @ X4 ) ) )
% 5.82/6.20 => ( P @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % num_induct
% 5.82/6.20 thf(fact_9624_add__inc,axiom,
% 5.82/6.20 ! [X2: num,Y3: num] :
% 5.82/6.20 ( ( plus_plus_num @ X2 @ ( inc @ Y3 ) )
% 5.82/6.20 = ( inc @ ( plus_plus_num @ X2 @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % add_inc
% 5.82/6.20 thf(fact_9625_take__bit__tightened__less__eq__int,axiom,
% 5.82/6.20 ! [M: nat,N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_tightened_less_eq_int
% 5.82/6.20 thf(fact_9626_take__bit__nonnegative,axiom,
% 5.82/6.20 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nonnegative
% 5.82/6.20 thf(fact_9627_take__bit__int__less__eq__self__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.82/6.20 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_less_eq_self_iff
% 5.82/6.20 thf(fact_9628_inc_Osimps_I1_J,axiom,
% 5.82/6.20 ( ( inc @ one )
% 5.82/6.20 = ( bit0 @ one ) ) ).
% 5.82/6.20
% 5.82/6.20 % inc.simps(1)
% 5.82/6.20 thf(fact_9629_inc_Osimps_I3_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( inc @ ( bit1 @ X2 ) )
% 5.82/6.20 = ( bit0 @ ( inc @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % inc.simps(3)
% 5.82/6.20 thf(fact_9630_inc_Osimps_I2_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( inc @ ( bit0 @ X2 ) )
% 5.82/6.20 = ( bit1 @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % inc.simps(2)
% 5.82/6.20 thf(fact_9631_add__One,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( plus_plus_num @ X2 @ one )
% 5.82/6.20 = ( inc @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % add_One
% 5.82/6.20 thf(fact_9632_inc__BitM__eq,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( inc @ ( bitM @ N ) )
% 5.82/6.20 = ( bit0 @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % inc_BitM_eq
% 5.82/6.20 thf(fact_9633_BitM__inc__eq,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bitM @ ( inc @ N ) )
% 5.82/6.20 = ( bit1 @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % BitM_inc_eq
% 5.82/6.20 thf(fact_9634_mult__inc,axiom,
% 5.82/6.20 ! [X2: num,Y3: num] :
% 5.82/6.20 ( ( times_times_num @ X2 @ ( inc @ Y3 ) )
% 5.82/6.20 = ( plus_plus_num @ ( times_times_num @ X2 @ Y3 ) @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % mult_inc
% 5.82/6.20 thf(fact_9635_take__bit__decr__eq,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.82/6.20 != zero_zero_int )
% 5.82/6.20 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.82/6.20 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_decr_eq
% 5.82/6.20 thf(fact_9636_take__bit__nat__eq__self__iff,axiom,
% 5.82/6.20 ! [N: nat,M: nat] :
% 5.82/6.20 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.82/6.20 = M )
% 5.82/6.20 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_eq_self_iff
% 5.82/6.20 thf(fact_9637_take__bit__nat__less__exp,axiom,
% 5.82/6.20 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_less_exp
% 5.82/6.20 thf(fact_9638_take__bit__nat__eq__self,axiom,
% 5.82/6.20 ! [M: nat,N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.20 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.82/6.20 = M ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_eq_self
% 5.82/6.20 thf(fact_9639_take__bit__nat__def,axiom,
% 5.82/6.20 ( bit_se2925701944663578781it_nat
% 5.82/6.20 = ( ^ [N4: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_def
% 5.82/6.20 thf(fact_9640_take__bit__Suc__minus__bit1,axiom,
% 5.82/6.20 ! [N: nat,K: num] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.82/6.20 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_Suc_minus_bit1
% 5.82/6.20 thf(fact_9641_take__bit__int__less__exp,axiom,
% 5.82/6.20 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_less_exp
% 5.82/6.20 thf(fact_9642_take__bit__int__def,axiom,
% 5.82/6.20 ( bit_se2923211474154528505it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_def
% 5.82/6.20 thf(fact_9643_take__bit__numeral__minus__bit1,axiom,
% 5.82/6.20 ! [L: num,K: num] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.82/6.20 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_numeral_minus_bit1
% 5.82/6.20 thf(fact_9644_take__bit__nat__less__self__iff,axiom,
% 5.82/6.20 ! [N: nat,M: nat] :
% 5.82/6.20 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.82/6.20 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_nat_less_self_iff
% 5.82/6.20 thf(fact_9645_take__bit__Suc__minus__bit0,axiom,
% 5.82/6.20 ! [N: nat,K: num] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.82/6.20 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_Suc_minus_bit0
% 5.82/6.20 thf(fact_9646_take__bit__int__less__self__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.82/6.20 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_less_self_iff
% 5.82/6.20 thf(fact_9647_take__bit__int__greater__eq__self__iff,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.82/6.20 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_greater_eq_self_iff
% 5.82/6.20 thf(fact_9648_take__bit__int__eq__self__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.82/6.20 = K )
% 5.82/6.20 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_eq_self_iff
% 5.82/6.20 thf(fact_9649_take__bit__int__eq__self,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.20 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.82/6.20 = K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_eq_self
% 5.82/6.20 thf(fact_9650_take__bit__incr__eq,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.82/6.20 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.82/6.20 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.82/6.20 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_incr_eq
% 5.82/6.20 thf(fact_9651_take__bit__numeral__minus__bit0,axiom,
% 5.82/6.20 ! [L: num,K: num] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.82/6.20 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_numeral_minus_bit0
% 5.82/6.20 thf(fact_9652_take__bit__int__less__eq,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.82/6.20 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_less_eq
% 5.82/6.20 thf(fact_9653_take__bit__int__greater__eq,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( ord_less_int @ K @ zero_zero_int )
% 5.82/6.20 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_int_greater_eq
% 5.82/6.20 thf(fact_9654_divmod__step__nat__def,axiom,
% 5.82/6.20 ( unique5026877609467782581ep_nat
% 5.82/6.20 = ( ^ [L3: num] :
% 5.82/6.20 ( produc2626176000494625587at_nat
% 5.82/6.20 @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divmod_step_nat_def
% 5.82/6.20 thf(fact_9655_signed__take__bit__eq__take__bit__shift,axiom,
% 5.82/6.20 ( bit_ri631733984087533419it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % signed_take_bit_eq_take_bit_shift
% 5.82/6.20 thf(fact_9656_divmod__step__int__def,axiom,
% 5.82/6.20 ( unique5024387138958732305ep_int
% 5.82/6.20 = ( ^ [L3: num] :
% 5.82/6.20 ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divmod_step_int_def
% 5.82/6.20 thf(fact_9657_take__bit__minus__small__eq,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( ord_less_int @ zero_zero_int @ K )
% 5.82/6.20 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.20 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.82/6.20 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_minus_small_eq
% 5.82/6.20 thf(fact_9658_divmod__step__integer__def,axiom,
% 5.82/6.20 ( unique4921790084139445826nteger
% 5.82/6.20 = ( ^ [L3: num] :
% 5.82/6.20 ( produc6916734918728496179nteger
% 5.82/6.20 @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divmod_step_integer_def
% 5.82/6.20 thf(fact_9659_divmod__nat__if,axiom,
% 5.82/6.20 ( divmod_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ( if_Pro6206227464963214023at_nat
% 5.82/6.20 @ ( ( N4 = zero_zero_nat )
% 5.82/6.20 | ( ord_less_nat @ M6 @ N4 ) )
% 5.82/6.20 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.82/6.20 @ ( produc2626176000494625587at_nat
% 5.82/6.20 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 5.82/6.20 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divmod_nat_if
% 5.82/6.20 thf(fact_9660_mask__nat__positive__iff,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.82/6.20 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % mask_nat_positive_iff
% 5.82/6.20 thf(fact_9661_less__eq__mask,axiom,
% 5.82/6.20 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % less_eq_mask
% 5.82/6.20 thf(fact_9662_mask__nonnegative__int,axiom,
% 5.82/6.20 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % mask_nonnegative_int
% 5.82/6.20 thf(fact_9663_less__mask,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % less_mask
% 5.82/6.20 thf(fact_9664_take__bit__eq__mask__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.82/6.20 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.82/6.20 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.82/6.20 = zero_zero_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_eq_mask_iff
% 5.82/6.20 thf(fact_9665_one__natural_Orsp,axiom,
% 5.82/6.20 one_one_nat = one_one_nat ).
% 5.82/6.20
% 5.82/6.20 % one_natural.rsp
% 5.82/6.20 thf(fact_9666_one__integer_Orsp,axiom,
% 5.82/6.20 one_one_int = one_one_int ).
% 5.82/6.20
% 5.82/6.20 % one_integer.rsp
% 5.82/6.20 thf(fact_9667_less__eq__integer__code_I1_J,axiom,
% 5.82/6.20 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.82/6.20
% 5.82/6.20 % less_eq_integer_code(1)
% 5.82/6.20 thf(fact_9668_Divides_Oadjust__div__def,axiom,
% 5.82/6.20 ( adjust_div
% 5.82/6.20 = ( produc8211389475949308722nt_int
% 5.82/6.20 @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Divides.adjust_div_def
% 5.82/6.20 thf(fact_9669_Suc__mask__eq__exp,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.82/6.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % Suc_mask_eq_exp
% 5.82/6.20 thf(fact_9670_mask__nat__less__exp,axiom,
% 5.82/6.20 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % mask_nat_less_exp
% 5.82/6.20 thf(fact_9671_mask__half__int,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.20 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % mask_half_int
% 5.82/6.20 thf(fact_9672_mask__int__def,axiom,
% 5.82/6.20 ( bit_se2000444600071755411sk_int
% 5.82/6.20 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % mask_int_def
% 5.82/6.20 thf(fact_9673_mask__nat__def,axiom,
% 5.82/6.20 ( bit_se2002935070580805687sk_nat
% 5.82/6.20 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % mask_nat_def
% 5.82/6.20 thf(fact_9674_divmod__nat__def,axiom,
% 5.82/6.20 ( divmod_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N4 ) @ ( modulo_modulo_nat @ M6 @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divmod_nat_def
% 5.82/6.20 thf(fact_9675_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.82/6.20 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.82/6.20 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_eq_mask_iff_exp_dvd
% 5.82/6.20 thf(fact_9676_plus__integer__code_I1_J,axiom,
% 5.82/6.20 ! [K: code_integer] :
% 5.82/6.20 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.82/6.20 = K ) ).
% 5.82/6.20
% 5.82/6.20 % plus_integer_code(1)
% 5.82/6.20 thf(fact_9677_plus__integer__code_I2_J,axiom,
% 5.82/6.20 ! [L: code_integer] :
% 5.82/6.20 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 5.82/6.20 = L ) ).
% 5.82/6.20
% 5.82/6.20 % plus_integer_code(2)
% 5.82/6.20 thf(fact_9678_minus__integer__code_I1_J,axiom,
% 5.82/6.20 ! [K: code_integer] :
% 5.82/6.20 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.82/6.20 = K ) ).
% 5.82/6.20
% 5.82/6.20 % minus_integer_code(1)
% 5.82/6.20 thf(fact_9679_minus__integer__code_I2_J,axiom,
% 5.82/6.20 ! [L: code_integer] :
% 5.82/6.20 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 5.82/6.20 = ( uminus1351360451143612070nteger @ L ) ) ).
% 5.82/6.20
% 5.82/6.20 % minus_integer_code(2)
% 5.82/6.20 thf(fact_9680_integer__of__int__code,axiom,
% 5.82/6.20 ( code_integer_of_int
% 5.82/6.20 = ( ^ [K3: int] :
% 5.82/6.20 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.82/6.20 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.82/6.20 @ ( if_Code_integer
% 5.82/6.20 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.82/6.20 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % integer_of_int_code
% 5.82/6.20 thf(fact_9681_int__ge__less__than__def,axiom,
% 5.82/6.20 ( int_ge_less_than
% 5.82/6.20 = ( ^ [D3: int] :
% 5.82/6.20 ( collec213857154873943460nt_int
% 5.82/6.20 @ ( produc4947309494688390418_int_o
% 5.82/6.20 @ ^ [Z8: int,Z4: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ D3 @ Z8 )
% 5.82/6.20 & ( ord_less_int @ Z8 @ Z4 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_ge_less_than_def
% 5.82/6.20 thf(fact_9682_one__integer__def,axiom,
% 5.82/6.20 ( one_one_Code_integer
% 5.82/6.20 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % one_integer_def
% 5.82/6.20 thf(fact_9683_less__eq__integer_Oabs__eq,axiom,
% 5.82/6.20 ! [Xa: int,X2: int] :
% 5.82/6.20 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.82/6.20 = ( ord_less_eq_int @ Xa @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % less_eq_integer.abs_eq
% 5.82/6.20 thf(fact_9684_plus__integer_Oabs__eq,axiom,
% 5.82/6.20 ! [Xa: int,X2: int] :
% 5.82/6.20 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.82/6.20 = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % plus_integer.abs_eq
% 5.82/6.20 thf(fact_9685_minus__integer_Oabs__eq,axiom,
% 5.82/6.20 ! [Xa: int,X2: int] :
% 5.82/6.20 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.82/6.20 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % minus_integer.abs_eq
% 5.82/6.20 thf(fact_9686_int__ge__less__than2__def,axiom,
% 5.82/6.20 ( int_ge_less_than2
% 5.82/6.20 = ( ^ [D3: int] :
% 5.82/6.20 ( collec213857154873943460nt_int
% 5.82/6.20 @ ( produc4947309494688390418_int_o
% 5.82/6.20 @ ^ [Z8: int,Z4: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ D3 @ Z4 )
% 5.82/6.20 & ( ord_less_int @ Z8 @ Z4 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_ge_less_than2_def
% 5.82/6.20 thf(fact_9687_VEBT__internal_Ospace_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_VEBT_space @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( 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 ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.space.pelims
% 5.82/6.20 thf(fact_9688_VEBT__internal_OT__vebt__buildupi_H_Opelims,axiom,
% 5.82/6.20 ! [X2: nat,Y3: int] :
% 5.82/6.20 ( ( ( vEBT_V9176841429113362141ildupi @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_V3352910403632780892pi_rel @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3 = one_one_int )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3 = one_one_int )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [N3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ ( suc @ ( suc @ N3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.T_vebt_buildupi'.pelims
% 5.82/6.20 thf(fact_9689_vebt__buildup_Opelims,axiom,
% 5.82/6.20 ! [X2: nat,Y3: vEBT_VEBT] :
% 5.82/6.20 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [Va3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % vebt_buildup.pelims
% 5.82/6.20 thf(fact_9690_VEBT__internal_Ospace_H_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_VEBT_space2 @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( 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 ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.space'.pelims
% 5.82/6.20 thf(fact_9691_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,
% 5.82/6.20 ! [X2: nat,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_V8646137997579335489_i_l_d @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_V5144397997797733112_d_rel @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [Va3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.pelims
% 5.82/6.20 thf(fact_9692_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,
% 5.82/6.20 ! [X2: nat,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_V8346862874174094_d_u_p @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_V1247956027447740395_p_rel @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [Va3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( 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 @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.pelims
% 5.82/6.20 thf(fact_9693_VEBT__internal_OTb_Opelims,axiom,
% 5.82/6.20 ! [X2: nat,Y3: int] :
% 5.82/6.20 ( ( ( vEBT_VEBT_Tb @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_VEBT_Tb_rel2 @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_int @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_int @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [N3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ ( suc @ ( suc @ N3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.Tb.pelims
% 5.82/6.20 thf(fact_9694_VEBT__internal_OTb_H_Opelims,axiom,
% 5.82/6.20 ! [X2: nat,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_VEBT_Tb2 @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_VEBT_Tb_rel @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [N3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ ( suc @ ( suc @ N3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.Tb'.pelims
% 5.82/6.20 thf(fact_9695_VEBT__internal_Ocnt_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: real] :
% 5.82/6.20 ( ( ( vEBT_VEBT_cnt @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3 = one_one_real )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( 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 ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.cnt.pelims
% 5.82/6.20 thf(fact_9696_VEBT__internal_OT__vebt__buildupi_Opelims,axiom,
% 5.82/6.20 ! [X2: nat,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_V441764108873111860ildupi @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_nat @ vEBT_V2957053500504383685pi_rel @ X2 )
% 5.82/6.20 => ( ( ( X2 = zero_zero_nat )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ zero_zero_nat ) ) )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( suc @ zero_zero_nat ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 => ~ ! [N3: nat] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( suc @ ( suc @ N3 ) ) )
% 5.82/6.20 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.20 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N3 @ ( 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 @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ ( suc @ N3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.T_vebt_buildupi.pelims
% 5.82/6.20 thf(fact_9697_VEBT__internal_Ocnt_H_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_VEBT_cnt2 @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( 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 ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.cnt'.pelims
% 5.82/6.20 thf(fact_9698_vebt__minti_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBTi,Y3: heap_T2636463487746394924on_nat] :
% 5.82/6.20 ( ( ( vEBT_vebt_minti @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.20 => ( ( ( A3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 5.82/6.20 & ( ~ A3
% 5.82/6.20 => ( ( B3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 5.82/6.20 & ( ~ B3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Leafi @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ none_nat ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.82/6.20 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi2 ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % vebt_minti.pelims
% 5.82/6.20 thf(fact_9699_vebt__maxti_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBTi,Y3: heap_T2636463487746394924on_nat] :
% 5.82/6.20 ( ( ( vEBT_vebt_maxti @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leafi @ A3 @ B3 ) )
% 5.82/6.20 => ( ( ( B3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 5.82/6.20 & ( ~ B3
% 5.82/6.20 => ( ( A3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 5.82/6.20 & ( ~ A3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Leafi @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ none_nat ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.82/6.20 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma2 ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % vebt_maxti.pelims
% 5.82/6.20 thf(fact_9700_vebt__maxt_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.82/6.20 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( ( B3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.20 & ( ~ B3
% 5.82/6.20 => ( ( A3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.20 & ( ~ A3
% 5.82/6.20 => ( Y3 = none_nat ) ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.20 => ( ( Y3 = none_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.82/6.20 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( some_nat @ Ma2 ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % vebt_maxt.pelims
% 5.82/6.20 thf(fact_9701_vebt__mint_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.82/6.20 ( ( ( vEBT_vebt_mint @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( ( A3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( some_nat @ zero_zero_nat ) ) )
% 5.82/6.20 & ( ~ A3
% 5.82/6.20 => ( ( B3
% 5.82/6.20 => ( Y3
% 5.82/6.20 = ( some_nat @ one_one_nat ) ) )
% 5.82/6.20 & ( ~ B3
% 5.82/6.20 => ( Y3 = none_nat ) ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.20 => ( ( Y3 = none_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.82/6.20 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( some_nat @ Mi2 ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % vebt_mint.pelims
% 5.82/6.20 thf(fact_9702_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_T_m_i_n_t @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.82/6.20 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 5.82/6.20 thf(fact_9703_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_T_m_a_x_t @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.82/6.20 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 5.82/6.20 thf(fact_9704_VEBT__internal_OminNulli_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBTi,Y3: heap_Time_Heap_o] :
% 5.82/6.20 ( ( ( vEBT_VEBT_minNulli @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBTi @ vEBT_V5740978063120863272li_rel @ X2 )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( vEBT_Leafi @ $false @ $false ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_Time_return_o @ $true ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_V5740978063120863272li_rel @ ( vEBT_Leafi @ $false @ $false ) ) ) )
% 5.82/6.20 => ( ! [Uv2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leafi @ $true @ Uv2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_Time_return_o @ $false ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_V5740978063120863272li_rel @ ( vEBT_Leafi @ $true @ Uv2 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leafi @ Uu2 @ $true ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_Time_return_o @ $false ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_V5740978063120863272li_rel @ ( vEBT_Leafi @ Uu2 @ $true ) ) ) )
% 5.82/6.20 => ( ! [Uw2: nat,Ux2: array_VEBT_VEBTi,Uy2: vEBT_VEBTi] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_Time_return_o @ $true ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_V5740978063120863272li_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.82/6.20 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: array_VEBT_VEBTi,Vc2: vEBT_VEBTi] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( heap_Time_return_o @ $false ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBTi @ vEBT_V5740978063120863272li_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.minNulli.pelims
% 5.82/6.20 thf(fact_9705_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X2 )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.82/6.20 => ( ! [Uv2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.82/6.20 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.82/6.20 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.20 => ( ( Y3 = one_one_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 5.82/6.20 thf(fact_9706_or__not__num__neg_Opelims,axiom,
% 5.82/6.20 ! [X2: num,Xa: num,Y3: num] :
% 5.82/6.20 ( ( ( bit_or_not_num_neg @ X2 @ Xa )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X2 @ Xa ) )
% 5.82/6.20 => ( ( ( X2 = one )
% 5.82/6.20 => ( ( Xa = one )
% 5.82/6.20 => ( ( Y3 = one )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.82/6.20 => ( ( ( X2 = one )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit0 @ M5 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 5.82/6.20 => ( ( ( X2 = one )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit0 @ N3 ) )
% 5.82/6.20 => ( ( Xa = one )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bit0 @ one ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit0 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit0 @ M5 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit0 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit1 @ N3 ) )
% 5.82/6.20 => ( ( Xa = one )
% 5.82/6.20 => ( ( Y3 = one )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.82/6.20 => ( ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit1 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit0 @ M5 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.82/6.20 => ~ ! [N3: num] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( bit1 @ N3 ) )
% 5.82/6.20 => ! [M5: num] :
% 5.82/6.20 ( ( Xa
% 5.82/6.20 = ( bit1 @ M5 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.82/6.20 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_num_neg.pelims
% 5.82/6.20 thf(fact_9707_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: $o] :
% 5.82/6.20 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.82/6.20 => ( ! [Uv2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.20 => ( ~ Y3
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.82/6.20 => ( ! [Uu2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.20 => ( ~ Y3
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.82/6.20 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.82/6.20 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.20 => ( ~ Y3
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.minNull.pelims(1)
% 5.82/6.20 thf(fact_9708_arctan__def,axiom,
% 5.82/6.20 ( arctan
% 5.82/6.20 = ( ^ [Y: real] :
% 5.82/6.20 ( the_real
% 5.82/6.20 @ ^ [X3: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.82/6.20 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 & ( ( tan_real @ X3 )
% 5.82/6.20 = Y ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arctan_def
% 5.82/6.20 thf(fact_9709_modulo__int__def,axiom,
% 5.82/6.20 ( modulo_modulo_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( if_int @ ( L3 = zero_zero_int ) @ K3
% 5.82/6.20 @ ( if_int
% 5.82/6.20 @ ( ( sgn_sgn_int @ K3 )
% 5.82/6.20 = ( sgn_sgn_int @ L3 ) )
% 5.82/6.20 @ ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) ) )
% 5.82/6.20 @ ( times_times_int @ ( sgn_sgn_int @ L3 )
% 5.82/6.20 @ ( minus_minus_int
% 5.82/6.20 @ ( times_times_int @ ( abs_abs_int @ L3 )
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ~ ( dvd_dvd_int @ L3 @ K3 ) ) )
% 5.82/6.20 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % modulo_int_def
% 5.82/6.20 thf(fact_9710_ln__real__def,axiom,
% 5.82/6.20 ( ln_ln_real
% 5.82/6.20 = ( ^ [X3: real] :
% 5.82/6.20 ( the_real
% 5.82/6.20 @ ^ [U2: real] :
% 5.82/6.20 ( ( exp_real @ U2 )
% 5.82/6.20 = X3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % ln_real_def
% 5.82/6.20 thf(fact_9711_sgn__mod,axiom,
% 5.82/6.20 ! [L: int,K: int] :
% 5.82/6.20 ( ( L != zero_zero_int )
% 5.82/6.20 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.82/6.20 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.82/6.20 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_mod
% 5.82/6.20 thf(fact_9712_ln__neg__is__const,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( ( ln_ln_real @ X2 )
% 5.82/6.20 = ( the_real
% 5.82/6.20 @ ^ [X3: real] : $false ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % ln_neg_is_const
% 5.82/6.20 thf(fact_9713_zsgn__def,axiom,
% 5.82/6.20 ( sgn_sgn_int
% 5.82/6.20 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % zsgn_def
% 5.82/6.20 thf(fact_9714_arccos__def,axiom,
% 5.82/6.20 ( arccos
% 5.82/6.20 = ( ^ [Y: real] :
% 5.82/6.20 ( the_real
% 5.82/6.20 @ ^ [X3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.82/6.20 & ( ord_less_eq_real @ X3 @ pi )
% 5.82/6.20 & ( ( cos_real @ X3 )
% 5.82/6.20 = Y ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arccos_def
% 5.82/6.20 thf(fact_9715_eucl__rel__int__remainderI,axiom,
% 5.82/6.20 ! [R2: int,L: int,K: int,Q3: int] :
% 5.82/6.20 ( ( ( sgn_sgn_int @ R2 )
% 5.82/6.20 = ( sgn_sgn_int @ L ) )
% 5.82/6.20 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 5.82/6.20 => ( ( K
% 5.82/6.20 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 5.82/6.20 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % eucl_rel_int_remainderI
% 5.82/6.20 thf(fact_9716_div__noneq__sgn__abs,axiom,
% 5.82/6.20 ! [L: int,K: int] :
% 5.82/6.20 ( ( L != zero_zero_int )
% 5.82/6.20 => ( ( ( sgn_sgn_int @ K )
% 5.82/6.20 != ( sgn_sgn_int @ L ) )
% 5.82/6.20 => ( ( divide_divide_int @ K @ L )
% 5.82/6.20 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % div_noneq_sgn_abs
% 5.82/6.20 thf(fact_9717_eucl__rel__int_Ocases,axiom,
% 5.82/6.20 ! [A12: int,A23: int,A32: product_prod_int_int] :
% 5.82/6.20 ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 5.82/6.20 => ( ( ( A23 = zero_zero_int )
% 5.82/6.20 => ( A32
% 5.82/6.20 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.82/6.20 => ( ! [Q4: int] :
% 5.82/6.20 ( ( A32
% 5.82/6.20 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.82/6.20 => ( ( A23 != zero_zero_int )
% 5.82/6.20 => ( A12
% 5.82/6.20 != ( times_times_int @ Q4 @ A23 ) ) ) )
% 5.82/6.20 => ~ ! [R3: int,Q4: int] :
% 5.82/6.20 ( ( A32
% 5.82/6.20 = ( product_Pair_int_int @ Q4 @ R3 ) )
% 5.82/6.20 => ( ( ( sgn_sgn_int @ R3 )
% 5.82/6.20 = ( sgn_sgn_int @ A23 ) )
% 5.82/6.20 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.82/6.20 => ( A12
% 5.82/6.20 != ( plus_plus_int @ ( times_times_int @ Q4 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % eucl_rel_int.cases
% 5.82/6.20 thf(fact_9718_eucl__rel__int_Osimps,axiom,
% 5.82/6.20 ( eucl_rel_int
% 5.82/6.20 = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 5.82/6.20 ( ? [K3: int] :
% 5.82/6.20 ( ( A1 = K3 )
% 5.82/6.20 & ( A22 = zero_zero_int )
% 5.82/6.20 & ( A33
% 5.82/6.20 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.82/6.20 | ? [L3: int,K3: int,Q5: int] :
% 5.82/6.20 ( ( A1 = K3 )
% 5.82/6.20 & ( A22 = L3 )
% 5.82/6.20 & ( A33
% 5.82/6.20 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 5.82/6.20 & ( L3 != zero_zero_int )
% 5.82/6.20 & ( K3
% 5.82/6.20 = ( times_times_int @ Q5 @ L3 ) ) )
% 5.82/6.20 | ? [R5: int,L3: int,K3: int,Q5: int] :
% 5.82/6.20 ( ( A1 = K3 )
% 5.82/6.20 & ( A22 = L3 )
% 5.82/6.20 & ( A33
% 5.82/6.20 = ( product_Pair_int_int @ Q5 @ R5 ) )
% 5.82/6.20 & ( ( sgn_sgn_int @ R5 )
% 5.82/6.20 = ( sgn_sgn_int @ L3 ) )
% 5.82/6.20 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L3 ) )
% 5.82/6.20 & ( K3
% 5.82/6.20 = ( plus_plus_int @ ( times_times_int @ Q5 @ L3 ) @ R5 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % eucl_rel_int.simps
% 5.82/6.20 thf(fact_9719_pi__half,axiom,
% 5.82/6.20 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.20 = ( the_real
% 5.82/6.20 @ ^ [X3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.82/6.20 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.20 & ( ( cos_real @ X3 )
% 5.82/6.20 = zero_zero_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % pi_half
% 5.82/6.20 thf(fact_9720_pi__def,axiom,
% 5.82/6.20 ( pi
% 5.82/6.20 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.82/6.20 @ ( the_real
% 5.82/6.20 @ ^ [X3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.82/6.20 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.82/6.20 & ( ( cos_real @ X3 )
% 5.82/6.20 = zero_zero_real ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % pi_def
% 5.82/6.20 thf(fact_9721_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT] :
% 5.82/6.20 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.82/6.20 => ( ! [Uv2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.82/6.20 => ( ! [Uu2: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.82/6.20 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.minNull.pelims(3)
% 5.82/6.20 thf(fact_9722_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT] :
% 5.82/6.20 ( ( vEBT_VEBT_minNull @ X2 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.82/6.20 => ( ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ $false @ $false ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.82/6.20 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.minNull.pelims(2)
% 5.82/6.20 thf(fact_9723_divide__int__unfold,axiom,
% 5.82/6.20 ! [L: int,K: int,N: nat,M: nat] :
% 5.82/6.20 ( ( ( ( ( sgn_sgn_int @ L )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( ( sgn_sgn_int @ K )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( N = zero_zero_nat ) )
% 5.82/6.20 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.20 = zero_zero_int ) )
% 5.82/6.20 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( ( sgn_sgn_int @ K )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( N = zero_zero_nat ) )
% 5.82/6.20 => ( ( ( ( sgn_sgn_int @ K )
% 5.82/6.20 = ( sgn_sgn_int @ L ) )
% 5.82/6.20 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.20 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.82/6.20 & ( ( ( sgn_sgn_int @ K )
% 5.82/6.20 != ( sgn_sgn_int @ L ) )
% 5.82/6.20 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.20 = ( uminus_uminus_int
% 5.82/6.20 @ ( semiri1314217659103216013at_int
% 5.82/6.20 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divide_int_unfold
% 5.82/6.20 thf(fact_9724_modulo__int__unfold,axiom,
% 5.82/6.20 ! [L: int,K: int,N: nat,M: nat] :
% 5.82/6.20 ( ( ( ( ( sgn_sgn_int @ L )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( ( sgn_sgn_int @ K )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( N = zero_zero_nat ) )
% 5.82/6.20 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.20 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.82/6.20 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( ( sgn_sgn_int @ K )
% 5.82/6.20 = zero_zero_int )
% 5.82/6.20 | ( N = zero_zero_nat ) )
% 5.82/6.20 => ( ( ( ( sgn_sgn_int @ K )
% 5.82/6.20 = ( sgn_sgn_int @ L ) )
% 5.82/6.20 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.20 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.82/6.20 & ( ( ( sgn_sgn_int @ K )
% 5.82/6.20 != ( sgn_sgn_int @ L ) )
% 5.82/6.20 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.82/6.20 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.82/6.20 @ ( minus_minus_int
% 5.82/6.20 @ ( semiri1314217659103216013at_int
% 5.82/6.20 @ ( times_times_nat @ N
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.82/6.20 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % modulo_int_unfold
% 5.82/6.20 thf(fact_9725_divide__int__def,axiom,
% 5.82/6.20 ( divide_divide_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( if_int @ ( L3 = zero_zero_int ) @ zero_zero_int
% 5.82/6.20 @ ( if_int
% 5.82/6.20 @ ( ( sgn_sgn_int @ K3 )
% 5.82/6.20 = ( sgn_sgn_int @ L3 ) )
% 5.82/6.20 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) )
% 5.82/6.20 @ ( uminus_uminus_int
% 5.82/6.20 @ ( semiri1314217659103216013at_int
% 5.82/6.20 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) )
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ~ ( dvd_dvd_int @ L3 @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divide_int_def
% 5.82/6.20 thf(fact_9726_arcsin__def,axiom,
% 5.82/6.20 ( arcsin
% 5.82/6.20 = ( ^ [Y: real] :
% 5.82/6.20 ( the_real
% 5.82/6.20 @ ^ [X3: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.82/6.20 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 & ( ( sin_real @ X3 )
% 5.82/6.20 = Y ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcsin_def
% 5.82/6.20 thf(fact_9727_zero__le__sgn__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X2 ) )
% 5.82/6.20 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % zero_le_sgn_iff
% 5.82/6.20 thf(fact_9728_sgn__le__0__iff,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X2 ) @ zero_zero_real )
% 5.82/6.20 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_le_0_iff
% 5.82/6.20 thf(fact_9729_sgn__root,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( sgn_sgn_real @ ( root @ N @ X2 ) )
% 5.82/6.20 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_root
% 5.82/6.20 thf(fact_9730_sgn__real__def,axiom,
% 5.82/6.20 ( sgn_sgn_real
% 5.82/6.20 = ( ^ [A5: real] : ( if_real @ ( A5 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A5 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_real_def
% 5.82/6.20 thf(fact_9731_sgn__integer__code,axiom,
% 5.82/6.20 ( sgn_sgn_Code_integer
% 5.82/6.20 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_integer_code
% 5.82/6.20 thf(fact_9732_sgn__power__injE,axiom,
% 5.82/6.20 ! [A2: real,N: nat,X2: real,B2: real] :
% 5.82/6.20 ( ( ( times_times_real @ ( sgn_sgn_real @ A2 ) @ ( power_power_real @ ( abs_abs_real @ A2 ) @ N ) )
% 5.82/6.20 = X2 )
% 5.82/6.20 => ( ( X2
% 5.82/6.20 = ( times_times_real @ ( sgn_sgn_real @ B2 ) @ ( power_power_real @ ( abs_abs_real @ B2 ) @ N ) ) )
% 5.82/6.20 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( A2 = B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_power_injE
% 5.82/6.20 thf(fact_9733_sgn__power__root,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X2 ) ) @ N ) )
% 5.82/6.20 = X2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_power_root
% 5.82/6.20 thf(fact_9734_root__sgn__power,axiom,
% 5.82/6.20 ! [N: nat,Y3: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) ) )
% 5.82/6.20 = Y3 ) ) ).
% 5.82/6.20
% 5.82/6.20 % root_sgn_power
% 5.82/6.20 thf(fact_9735_cis__Arg__unique,axiom,
% 5.82/6.20 ! [Z: complex,X2: real] :
% 5.82/6.20 ( ( ( sgn_sgn_complex @ Z )
% 5.82/6.20 = ( cis @ X2 ) )
% 5.82/6.20 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.82/6.20 => ( ( arg @ Z )
% 5.82/6.20 = X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % cis_Arg_unique
% 5.82/6.20 thf(fact_9736_split__root,axiom,
% 5.82/6.20 ! [P: real > $o,N: nat,X2: real] :
% 5.82/6.20 ( ( P @ ( root @ N @ X2 ) )
% 5.82/6.20 = ( ( ( N = zero_zero_nat )
% 5.82/6.20 => ( P @ zero_zero_real ) )
% 5.82/6.20 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ! [Y: real] :
% 5.82/6.20 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.82/6.20 = X2 )
% 5.82/6.20 => ( P @ Y ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % split_root
% 5.82/6.20 thf(fact_9737_floor__real__def,axiom,
% 5.82/6.20 ( archim6058952711729229775r_real
% 5.82/6.20 = ( ^ [X3: real] :
% 5.82/6.20 ( the_int
% 5.82/6.20 @ ^ [Z4: int] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X3 )
% 5.82/6.20 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % floor_real_def
% 5.82/6.20 thf(fact_9738_Arg__correct,axiom,
% 5.82/6.20 ! [Z: complex] :
% 5.82/6.20 ( ( Z != zero_zero_complex )
% 5.82/6.20 => ( ( ( sgn_sgn_complex @ Z )
% 5.82/6.20 = ( cis @ ( arg @ Z ) ) )
% 5.82/6.20 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.82/6.20 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Arg_correct
% 5.82/6.20 thf(fact_9739_arctan__inverse,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( X2 != zero_zero_real )
% 5.82/6.20 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X2 ) )
% 5.82/6.20 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arctan_inverse
% 5.82/6.20 thf(fact_9740_signed__take__bit__eq__take__bit__minus,axiom,
% 5.82/6.20 ( bit_ri631733984087533419it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % signed_take_bit_eq_take_bit_minus
% 5.82/6.20 thf(fact_9741_signed__take__bit__nonnegative__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.82/6.20 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % signed_take_bit_nonnegative_iff
% 5.82/6.20 thf(fact_9742_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.82/6.20 ! [W: num,N: nat] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.82/6.20 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_minus_numeral_Bit0_Suc_iff
% 5.82/6.20 thf(fact_9743_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.82/6.20 ! [W: num,N: nat] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.82/6.20 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_minus_numeral_Bit1_Suc_iff
% 5.82/6.20 thf(fact_9744_bit__minus__numeral__int_I1_J,axiom,
% 5.82/6.20 ! [W: num,N: num] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.20 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_minus_numeral_int(1)
% 5.82/6.20 thf(fact_9745_bit__minus__numeral__int_I2_J,axiom,
% 5.82/6.20 ! [W: num,N: num] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.82/6.20 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_minus_numeral_int(2)
% 5.82/6.20 thf(fact_9746_bin__nth__minus__Bit0,axiom,
% 5.82/6.20 ! [N: nat,W: num] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ N )
% 5.82/6.20 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_nth_minus_Bit0
% 5.82/6.20 thf(fact_9747_bin__nth__minus__Bit1,axiom,
% 5.82/6.20 ! [N: nat,W: num] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ N )
% 5.82/6.20 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_nth_minus_Bit1
% 5.82/6.20 thf(fact_9748_bit__not__int__iff_H,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.82/6.20 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_not_int_iff'
% 5.82/6.20 thf(fact_9749_bit__imp__take__bit__positive,axiom,
% 5.82/6.20 ! [N: nat,M: nat,K: int] :
% 5.82/6.20 ( ( ord_less_nat @ N @ M )
% 5.82/6.20 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.82/6.20 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_imp_take_bit_positive
% 5.82/6.20 thf(fact_9750_int__bit__bound,axiom,
% 5.82/6.20 ! [K: int] :
% 5.82/6.20 ~ ! [N3: nat] :
% 5.82/6.20 ( ! [M3: nat] :
% 5.82/6.20 ( ( ord_less_eq_nat @ N3 @ M3 )
% 5.82/6.20 => ( ( bit_se1146084159140164899it_int @ K @ M3 )
% 5.82/6.20 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.82/6.20 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.82/6.20 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.82/6.20 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_bit_bound
% 5.82/6.20 thf(fact_9751_bit__int__def,axiom,
% 5.82/6.20 ( bit_se1146084159140164899it_int
% 5.82/6.20 = ( ^ [K3: int,N4: nat] :
% 5.82/6.20 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_int_def
% 5.82/6.20 thf(fact_9752_Bit__Operations_Oset__bit__eq,axiom,
% 5.82/6.20 ( bit_se7879613467334960850it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] :
% 5.82/6.20 ( plus_plus_int @ K3
% 5.82/6.20 @ ( times_times_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N4 ) )
% 5.82/6.20 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Bit_Operations.set_bit_eq
% 5.82/6.20 thf(fact_9753_unset__bit__eq,axiom,
% 5.82/6.20 ( bit_se4203085406695923979it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % unset_bit_eq
% 5.82/6.20 thf(fact_9754_take__bit__Suc__from__most,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.82/6.20 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_Suc_from_most
% 5.82/6.20 thf(fact_9755_floor__rat__def,axiom,
% 5.82/6.20 ( archim3151403230148437115or_rat
% 5.82/6.20 = ( ^ [X3: rat] :
% 5.82/6.20 ( the_int
% 5.82/6.20 @ ^ [Z4: int] :
% 5.82/6.20 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X3 )
% 5.82/6.20 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % floor_rat_def
% 5.82/6.20 thf(fact_9756_root__def,axiom,
% 5.82/6.20 ( root
% 5.82/6.20 = ( ^ [N4: nat,X3: real] :
% 5.82/6.20 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 5.82/6.20 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.82/6.20 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N4 ) )
% 5.82/6.20 @ X3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % root_def
% 5.82/6.20 thf(fact_9757_Arg__def,axiom,
% 5.82/6.20 ( arg
% 5.82/6.20 = ( ^ [Z4: complex] :
% 5.82/6.20 ( if_real @ ( Z4 = zero_zero_complex ) @ zero_zero_real
% 5.82/6.20 @ ( fChoice_real
% 5.82/6.20 @ ^ [A5: real] :
% 5.82/6.20 ( ( ( sgn_sgn_complex @ Z4 )
% 5.82/6.20 = ( cis @ A5 ) )
% 5.82/6.20 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A5 )
% 5.82/6.20 & ( ord_less_eq_real @ A5 @ pi ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Arg_def
% 5.82/6.20 thf(fact_9758_not__nonnegative__int__iff,axiom,
% 5.82/6.20 ! [K: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.82/6.20 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_nonnegative_int_iff
% 5.82/6.20 thf(fact_9759_not__negative__int__iff,axiom,
% 5.82/6.20 ! [K: int] :
% 5.82/6.20 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.82/6.20 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_negative_int_iff
% 5.82/6.20 thf(fact_9760_and__minus__minus__numerals,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_minus_minus_numerals
% 5.82/6.20 thf(fact_9761_or__minus__minus__numerals,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_minus_minus_numerals
% 5.82/6.20 thf(fact_9762_sgn__rat__def,axiom,
% 5.82/6.20 ( sgn_sgn_rat
% 5.82/6.20 = ( ^ [A5: rat] : ( if_rat @ ( A5 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A5 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % sgn_rat_def
% 5.82/6.20 thf(fact_9763_not__bit__Suc__0__Suc,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_bit_Suc_0_Suc
% 5.82/6.20 thf(fact_9764_bit__Suc__0__iff,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( N = zero_zero_nat ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_Suc_0_iff
% 5.82/6.20 thf(fact_9765_less__eq__rat__def,axiom,
% 5.82/6.20 ( ord_less_eq_rat
% 5.82/6.20 = ( ^ [X3: rat,Y: rat] :
% 5.82/6.20 ( ( ord_less_rat @ X3 @ Y )
% 5.82/6.20 | ( X3 = Y ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % less_eq_rat_def
% 5.82/6.20 thf(fact_9766_obtain__pos__sum,axiom,
% 5.82/6.20 ! [R2: rat] :
% 5.82/6.20 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.82/6.20 => ~ ! [S3: rat] :
% 5.82/6.20 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.82/6.20 => ! [T7: rat] :
% 5.82/6.20 ( ( ord_less_rat @ zero_zero_rat @ T7 )
% 5.82/6.20 => ( R2
% 5.82/6.20 != ( plus_plus_rat @ S3 @ T7 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % obtain_pos_sum
% 5.82/6.20 thf(fact_9767_not__bit__Suc__0__numeral,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_bit_Suc_0_numeral
% 5.82/6.20 thf(fact_9768_not__int__def,axiom,
% 5.82/6.20 ( bit_ri7919022796975470100ot_int
% 5.82/6.20 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_int_def
% 5.82/6.20 thf(fact_9769_and__not__numerals_I1_J,axiom,
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.82/6.20 = zero_zero_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(1)
% 5.82/6.20 thf(fact_9770_or__not__numerals_I1_J,axiom,
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(1)
% 5.82/6.20 thf(fact_9771_not__int__div__2,axiom,
% 5.82/6.20 ! [K: int] :
% 5.82/6.20 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_int_div_2
% 5.82/6.20 thf(fact_9772_even__not__iff__int,axiom,
% 5.82/6.20 ! [K: int] :
% 5.82/6.20 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.82/6.20 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % even_not_iff_int
% 5.82/6.20 thf(fact_9773_and__not__numerals_I4_J,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.82/6.20 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(4)
% 5.82/6.20 thf(fact_9774_and__not__numerals_I2_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = one_one_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(2)
% 5.82/6.20 thf(fact_9775_or__not__numerals_I2_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(2)
% 5.82/6.20 thf(fact_9776_or__not__numerals_I4_J,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(4)
% 5.82/6.20 thf(fact_9777_bit__nat__iff,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.82/6.20 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_nat_iff
% 5.82/6.20 thf(fact_9778_bit__minus__int__iff,axiom,
% 5.82/6.20 ! [K: int,N: nat] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.82/6.20 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_minus_int_iff
% 5.82/6.20 thf(fact_9779_and__not__numerals_I5_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(5)
% 5.82/6.20 thf(fact_9780_and__not__numerals_I7_J,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.82/6.20 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(7)
% 5.82/6.20 thf(fact_9781_or__not__numerals_I3_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(3)
% 5.82/6.20 thf(fact_9782_and__not__numerals_I3_J,axiom,
% 5.82/6.20 ! [N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = zero_zero_int ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(3)
% 5.82/6.20 thf(fact_9783_or__not__numerals_I7_J,axiom,
% 5.82/6.20 ! [M: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.82/6.20 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(7)
% 5.82/6.20 thf(fact_9784_bit__nat__def,axiom,
% 5.82/6.20 ( bit_se1148574629649215175it_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_nat_def
% 5.82/6.20 thf(fact_9785_and__not__numerals_I9_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(9)
% 5.82/6.20 thf(fact_9786_and__not__numerals_I6_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(6)
% 5.82/6.20 thf(fact_9787_or__not__numerals_I6_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(6)
% 5.82/6.20 thf(fact_9788_or__not__numerals_I5_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(5)
% 5.82/6.20 thf(fact_9789_and__not__numerals_I8_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % and_not_numerals(8)
% 5.82/6.20 thf(fact_9790_or__not__numerals_I9_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.82/6.20 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(9)
% 5.82/6.20 thf(fact_9791_or__not__numerals_I8_J,axiom,
% 5.82/6.20 ! [M: num,N: num] :
% 5.82/6.20 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.82/6.20 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % or_not_numerals(8)
% 5.82/6.20 thf(fact_9792_not__int__rec,axiom,
% 5.82/6.20 ( bit_ri7919022796975470100ot_int
% 5.82/6.20 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % not_int_rec
% 5.82/6.20 thf(fact_9793_int__not__code_I1_J,axiom,
% 5.82/6.20 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_not_code(1)
% 5.82/6.20 thf(fact_9794_bitNOT__integer__code,axiom,
% 5.82/6.20 ( bit_ri7632146776885996613nteger
% 5.82/6.20 = ( ^ [I4: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ I4 ) @ one_one_Code_integer ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bitNOT_integer_code
% 5.82/6.20 thf(fact_9795_xor__int__unfold,axiom,
% 5.82/6.20 ( bit_se6526347334894502574or_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( if_int
% 5.82/6.20 @ ( K3
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 @ ( bit_ri7919022796975470100ot_int @ L3 )
% 5.82/6.20 @ ( if_int
% 5.82/6.20 @ ( L3
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.82/6.20 @ ( if_int @ ( K3 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = 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 @ L3 @ ( 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 @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_int_unfold
% 5.82/6.20 thf(fact_9796_xor__nonnegative__int__iff,axiom,
% 5.82/6.20 ! [K: int,L: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.82/6.20 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.82/6.20 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nonnegative_int_iff
% 5.82/6.20 thf(fact_9797_XOR__lower,axiom,
% 5.82/6.20 ! [X2: int,Y3: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.20 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.82/6.20 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % XOR_lower
% 5.82/6.20 thf(fact_9798_diff__rat__def,axiom,
% 5.82/6.20 ( minus_minus_rat
% 5.82/6.20 = ( ^ [Q5: rat,R5: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % diff_rat_def
% 5.82/6.20 thf(fact_9799_XOR__upper,axiom,
% 5.82/6.20 ! [X2: int,N: nat,Y3: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.82/6.20 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.20 => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.82/6.20 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % XOR_upper
% 5.82/6.20 thf(fact_9800_xor__int__rec,axiom,
% 5.82/6.20 ( bit_se6526347334894502574or_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] :
% 5.82/6.20 ( plus_plus_int
% 5.82/6.20 @ ( zero_n2684676970156552555ol_int
% 5.82/6.20 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.82/6.20 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 5.82/6.20 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_int_rec
% 5.82/6.20 thf(fact_9801_Bit__integer_Oabs__eq,axiom,
% 5.82/6.20 ! [Xa: int,X2: $o] :
% 5.82/6.20 ( ( bits_Bit_integer @ ( code_integer_of_int @ Xa ) @ X2 )
% 5.82/6.20 = ( code_integer_of_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ X2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Bit_integer.abs_eq
% 5.82/6.20 thf(fact_9802_xor__nat__numerals_I1_J,axiom,
% 5.82/6.20 ! [Y3: num] :
% 5.82/6.20 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nat_numerals(1)
% 5.82/6.20 thf(fact_9803_xor__nat__numerals_I2_J,axiom,
% 5.82/6.20 ! [Y3: num] :
% 5.82/6.20 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nat_numerals(2)
% 5.82/6.20 thf(fact_9804_xor__nat__numerals_I3_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nat_numerals(3)
% 5.82/6.20 thf(fact_9805_xor__nat__numerals_I4_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nat_numerals(4)
% 5.82/6.20 thf(fact_9806_xor__nat__unfold,axiom,
% 5.82/6.20 ( bit_se6528837805403552850or_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nat_unfold
% 5.82/6.20 thf(fact_9807_xor__nat__rec,axiom,
% 5.82/6.20 ( bit_se6528837805403552850or_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ( plus_plus_nat
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.82/6.20 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.82/6.20 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_nat_rec
% 5.82/6.20 thf(fact_9808_Suc__0__xor__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Suc_0_xor_eq
% 5.82/6.20 thf(fact_9809_xor__Suc__0__eq,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.20 @ ( zero_n2687167440665602831ol_nat
% 5.82/6.20 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % xor_Suc_0_eq
% 5.82/6.20 thf(fact_9810_num_Osize__gen_I3_J,axiom,
% 5.82/6.20 ! [X33: num] :
% 5.82/6.20 ( ( size_num @ ( bit1 @ X33 ) )
% 5.82/6.20 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % num.size_gen(3)
% 5.82/6.20 thf(fact_9811_num_Osize__gen_I1_J,axiom,
% 5.82/6.20 ( ( size_num @ one )
% 5.82/6.20 = zero_zero_nat ) ).
% 5.82/6.20
% 5.82/6.20 % num.size_gen(1)
% 5.82/6.20 thf(fact_9812_num_Osize__gen_I2_J,axiom,
% 5.82/6.20 ! [X22: num] :
% 5.82/6.20 ( ( size_num @ ( bit0 @ X22 ) )
% 5.82/6.20 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % num.size_gen(2)
% 5.82/6.20 thf(fact_9813_dup__1,axiom,
% 5.82/6.20 ( ( code_dup @ one_one_Code_integer )
% 5.82/6.20 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % dup_1
% 5.82/6.20 thf(fact_9814_pow_Osimps_I1_J,axiom,
% 5.82/6.20 ! [X2: num] :
% 5.82/6.20 ( ( pow @ X2 @ one )
% 5.82/6.20 = X2 ) ).
% 5.82/6.20
% 5.82/6.20 % pow.simps(1)
% 5.82/6.20 thf(fact_9815_dup_Oabs__eq,axiom,
% 5.82/6.20 ! [X2: int] :
% 5.82/6.20 ( ( code_dup @ ( code_integer_of_int @ X2 ) )
% 5.82/6.20 = ( code_integer_of_int @ ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % dup.abs_eq
% 5.82/6.20 thf(fact_9816_cis__multiple__2pi,axiom,
% 5.82/6.20 ! [N: real] :
% 5.82/6.20 ( ( member_real @ N @ ring_1_Ints_real )
% 5.82/6.20 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.82/6.20 = one_one_complex ) ) ).
% 5.82/6.20
% 5.82/6.20 % cis_multiple_2pi
% 5.82/6.20 thf(fact_9817_sin__integer__2pi,axiom,
% 5.82/6.20 ! [N: real] :
% 5.82/6.20 ( ( member_real @ N @ ring_1_Ints_real )
% 5.82/6.20 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.82/6.20 = zero_zero_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % sin_integer_2pi
% 5.82/6.20 thf(fact_9818_cos__integer__2pi,axiom,
% 5.82/6.20 ! [N: real] :
% 5.82/6.20 ( ( member_real @ N @ ring_1_Ints_real )
% 5.82/6.20 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.82/6.20 = one_one_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % cos_integer_2pi
% 5.82/6.20 thf(fact_9819_rat__inverse__code,axiom,
% 5.82/6.20 ! [P6: rat] :
% 5.82/6.20 ( ( quotient_of @ ( inverse_inverse_rat @ P6 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int,B6: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B6 ) @ ( abs_abs_int @ A5 ) ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_inverse_code
% 5.82/6.20 thf(fact_9820_setceilmax,axiom,
% 5.82/6.20 ! [S2: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 5.82/6.20 ( ( vEBT_invar_vebt @ S2 @ M )
% 5.82/6.20 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.20 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.82/6.20 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.82/6.20 => ( ( M
% 5.82/6.20 = ( suc @ N ) )
% 5.82/6.20 => ( ! [X4: vEBT_VEBT] :
% 5.82/6.20 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.82/6.20 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X4 ) )
% 5.82/6.20 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.82/6.20 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S2 ) )
% 5.82/6.20 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 5.82/6.20 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S2 @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 5.82/6.20 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % setceilmax
% 5.82/6.20 thf(fact_9821_height__compose__list,axiom,
% 5.82/6.20 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.20 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.82/6.20 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % height_compose_list
% 5.82/6.20 thf(fact_9822_max__ins__scaled,axiom,
% 5.82/6.20 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % max_ins_scaled
% 5.82/6.20 thf(fact_9823_height__i__max,axiom,
% 5.82/6.20 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 5.82/6.20 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.82/6.20 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % height_i_max
% 5.82/6.20 thf(fact_9824_max__idx__list,axiom,
% 5.82/6.20 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 5.82/6.20 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.82/6.20 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % max_idx_list
% 5.82/6.20 thf(fact_9825_Max__divisors__self__nat,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( N != zero_zero_nat )
% 5.82/6.20 => ( ( lattic8265883725875713057ax_nat
% 5.82/6.20 @ ( collect_nat
% 5.82/6.20 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ N ) ) )
% 5.82/6.20 = N ) ) ).
% 5.82/6.20
% 5.82/6.20 % Max_divisors_self_nat
% 5.82/6.20 thf(fact_9826_quotient__of__number_I3_J,axiom,
% 5.82/6.20 ! [K: num] :
% 5.82/6.20 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.82/6.20 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % quotient_of_number(3)
% 5.82/6.20 thf(fact_9827_rat__one__code,axiom,
% 5.82/6.20 ( ( quotient_of @ one_one_rat )
% 5.82/6.20 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_one_code
% 5.82/6.20 thf(fact_9828_rat__zero__code,axiom,
% 5.82/6.20 ( ( quotient_of @ zero_zero_rat )
% 5.82/6.20 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_zero_code
% 5.82/6.20 thf(fact_9829_quotient__of__number_I5_J,axiom,
% 5.82/6.20 ! [K: num] :
% 5.82/6.20 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.82/6.20 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % quotient_of_number(5)
% 5.82/6.20 thf(fact_9830_quotient__of__number_I4_J,axiom,
% 5.82/6.20 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.82/6.20 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % quotient_of_number(4)
% 5.82/6.20 thf(fact_9831_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 5.82/6.20 ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.82/6.20 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 5.82/6.20 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.height.simps(2)
% 5.82/6.20 thf(fact_9832_VEBT__internal_Oheight_Oelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_VEBT_height @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( ? [A3: $o,B3: $o] :
% 5.82/6.20 ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( Y3 != zero_zero_nat ) )
% 5.82/6.20 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.20 => ( Y3
% 5.82/6.20 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.height.elims
% 5.82/6.20 thf(fact_9833_divide__nat__def,axiom,
% 5.82/6.20 ( divide_divide_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] :
% 5.82/6.20 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 5.82/6.20 @ ( lattic8265883725875713057ax_nat
% 5.82/6.20 @ ( collect_nat
% 5.82/6.20 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M6 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % divide_nat_def
% 5.82/6.20 thf(fact_9834_rat__abs__code,axiom,
% 5.82/6.20 ! [P6: rat] :
% 5.82/6.20 ( ( quotient_of @ ( abs_abs_rat @ P6 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_abs_code
% 5.82/6.20 thf(fact_9835_rat__uminus__code,axiom,
% 5.82/6.20 ! [P6: rat] :
% 5.82/6.20 ( ( quotient_of @ ( uminus_uminus_rat @ P6 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_uminus_code
% 5.82/6.20 thf(fact_9836_rat__less__code,axiom,
% 5.82/6.20 ( ord_less_rat
% 5.82/6.20 = ( ^ [P4: rat,Q5: rat] :
% 5.82/6.20 ( produc4947309494688390418_int_o
% 5.82/6.20 @ ^ [A5: int,C4: int] :
% 5.82/6.20 ( produc4947309494688390418_int_o
% 5.82/6.20 @ ^ [B6: int,D3: int] : ( ord_less_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B6 ) )
% 5.82/6.20 @ ( quotient_of @ Q5 ) )
% 5.82/6.20 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_less_code
% 5.82/6.20 thf(fact_9837_rat__floor__code,axiom,
% 5.82/6.20 ( archim3151403230148437115or_rat
% 5.82/6.20 = ( ^ [P4: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_floor_code
% 5.82/6.20 thf(fact_9838_rat__less__eq__code,axiom,
% 5.82/6.20 ( ord_less_eq_rat
% 5.82/6.20 = ( ^ [P4: rat,Q5: rat] :
% 5.82/6.20 ( produc4947309494688390418_int_o
% 5.82/6.20 @ ^ [A5: int,C4: int] :
% 5.82/6.20 ( produc4947309494688390418_int_o
% 5.82/6.20 @ ^ [B6: int,D3: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B6 ) )
% 5.82/6.20 @ ( quotient_of @ Q5 ) )
% 5.82/6.20 @ ( quotient_of @ P4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_less_eq_code
% 5.82/6.20 thf(fact_9839_VEBT__internal_Oheight_Opelims,axiom,
% 5.82/6.20 ! [X2: vEBT_VEBT,Y3: nat] :
% 5.82/6.20 ( ( ( vEBT_VEBT_height @ X2 )
% 5.82/6.20 = Y3 )
% 5.82/6.20 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X2 )
% 5.82/6.20 => ( ! [A3: $o,B3: $o] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.82/6.20 => ( ( Y3 = zero_zero_nat )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.82/6.20 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.82/6.20 ( ( X2
% 5.82/6.20 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.82/6.20 => ( ( Y3
% 5.82/6.20 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 5.82/6.20 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.height.pelims
% 5.82/6.20 thf(fact_9840_quotient__of__int,axiom,
% 5.82/6.20 ! [A2: int] :
% 5.82/6.20 ( ( quotient_of @ ( of_int @ A2 ) )
% 5.82/6.20 = ( product_Pair_int_int @ A2 @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % quotient_of_int
% 5.82/6.20 thf(fact_9841_bij__betw__Suc,axiom,
% 5.82/6.20 ! [M8: set_nat,N7: set_nat] :
% 5.82/6.20 ( ( bij_betw_nat_nat @ suc @ M8 @ N7 )
% 5.82/6.20 = ( ( image_nat_nat @ suc @ M8 )
% 5.82/6.20 = N7 ) ) ).
% 5.82/6.20
% 5.82/6.20 % bij_betw_Suc
% 5.82/6.20 thf(fact_9842_image__Suc__atLeastLessThan,axiom,
% 5.82/6.20 ! [I: nat,J: nat] :
% 5.82/6.20 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.82/6.20 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_Suc_atLeastLessThan
% 5.82/6.20 thf(fact_9843_image__Suc__atLeastAtMost,axiom,
% 5.82/6.20 ! [I: nat,J: nat] :
% 5.82/6.20 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.82/6.20 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_Suc_atLeastAtMost
% 5.82/6.20 thf(fact_9844_Max__divisors__self__int,axiom,
% 5.82/6.20 ! [N: int] :
% 5.82/6.20 ( ( N != zero_zero_int )
% 5.82/6.20 => ( ( lattic8263393255366662781ax_int
% 5.82/6.20 @ ( collect_int
% 5.82/6.20 @ ^ [D3: int] : ( dvd_dvd_int @ D3 @ N ) ) )
% 5.82/6.20 = ( abs_abs_int @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Max_divisors_self_int
% 5.82/6.20 thf(fact_9845_zero__notin__Suc__image,axiom,
% 5.82/6.20 ! [A: set_nat] :
% 5.82/6.20 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A ) ) ).
% 5.82/6.20
% 5.82/6.20 % zero_notin_Suc_image
% 5.82/6.20 thf(fact_9846_finite__int__iff__bounded,axiom,
% 5.82/6.20 ( finite_finite_int
% 5.82/6.20 = ( ^ [S8: set_int] :
% 5.82/6.20 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S8 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % finite_int_iff_bounded
% 5.82/6.20 thf(fact_9847_finite__int__iff__bounded__le,axiom,
% 5.82/6.20 ( finite_finite_int
% 5.82/6.20 = ( ^ [S8: set_int] :
% 5.82/6.20 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S8 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % finite_int_iff_bounded_le
% 5.82/6.20 thf(fact_9848_image__Suc__lessThan,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.20 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_Suc_lessThan
% 5.82/6.20 thf(fact_9849_image__Suc__atMost,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.82/6.20 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_Suc_atMost
% 5.82/6.20 thf(fact_9850_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.82/6.20 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % atLeast0_lessThan_Suc_eq_insert_0
% 5.82/6.20 thf(fact_9851_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.82/6.20 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % atLeast0_atMost_Suc_eq_insert_0
% 5.82/6.20 thf(fact_9852_lessThan__Suc__eq__insert__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.82/6.20 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % lessThan_Suc_eq_insert_0
% 5.82/6.20 thf(fact_9853_atMost__Suc__eq__insert__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.82/6.20 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % atMost_Suc_eq_insert_0
% 5.82/6.20 thf(fact_9854_range__mod,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( image_nat_nat
% 5.82/6.20 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 5.82/6.20 @ top_top_set_nat )
% 5.82/6.20 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % range_mod
% 5.82/6.20 thf(fact_9855_image__add__int__atLeastLessThan,axiom,
% 5.82/6.20 ! [L: int,U: int] :
% 5.82/6.20 ( ( image_int_int
% 5.82/6.20 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 5.82/6.20 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.82/6.20 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_add_int_atLeastLessThan
% 5.82/6.20 thf(fact_9856_image__add__integer__atLeastLessThan,axiom,
% 5.82/6.20 ! [L: code_integer,U: code_integer] :
% 5.82/6.20 ( ( image_4470545334726330049nteger
% 5.82/6.20 @ ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ X3 @ L )
% 5.82/6.20 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 5.82/6.20 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_add_integer_atLeastLessThan
% 5.82/6.20 thf(fact_9857_image__atLeastZeroLessThan__int,axiom,
% 5.82/6.20 ! [U: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.82/6.20 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.82/6.20 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_atLeastZeroLessThan_int
% 5.82/6.20 thf(fact_9858_image__minus__const__atLeastLessThan__nat,axiom,
% 5.82/6.20 ! [C2: nat,Y3: nat,X2: nat] :
% 5.82/6.20 ( ( ( ord_less_nat @ C2 @ Y3 )
% 5.82/6.20 => ( ( image_nat_nat
% 5.82/6.20 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C2 )
% 5.82/6.20 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 5.82/6.20 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C2 ) @ ( minus_minus_nat @ Y3 @ C2 ) ) ) )
% 5.82/6.20 & ( ~ ( ord_less_nat @ C2 @ Y3 )
% 5.82/6.20 => ( ( ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.20 => ( ( image_nat_nat
% 5.82/6.20 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C2 )
% 5.82/6.20 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 5.82/6.20 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.82/6.20 & ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.82/6.20 => ( ( image_nat_nat
% 5.82/6.20 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C2 )
% 5.82/6.20 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 5.82/6.20 = bot_bot_set_nat ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % image_minus_const_atLeastLessThan_nat
% 5.82/6.20 thf(fact_9859_rat__minus__code,axiom,
% 5.82/6.20 ! [P6: rat,Q3: rat] :
% 5.82/6.20 ( ( quotient_of @ ( minus_minus_rat @ P6 @ Q3 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int,C4: int] :
% 5.82/6.20 ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [B6: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ B6 @ C4 ) ) @ ( times_times_int @ C4 @ D3 ) ) )
% 5.82/6.20 @ ( quotient_of @ Q3 ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_minus_code
% 5.82/6.20 thf(fact_9860_rat__plus__code,axiom,
% 5.82/6.20 ! [P6: rat,Q3: rat] :
% 5.82/6.20 ( ( quotient_of @ ( plus_plus_rat @ P6 @ Q3 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int,C4: int] :
% 5.82/6.20 ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [B6: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ B6 @ C4 ) ) @ ( times_times_int @ C4 @ D3 ) ) )
% 5.82/6.20 @ ( quotient_of @ Q3 ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_plus_code
% 5.82/6.20 thf(fact_9861_normalize__denom__zero,axiom,
% 5.82/6.20 ! [P6: int] :
% 5.82/6.20 ( ( normalize @ ( product_Pair_int_int @ P6 @ zero_zero_int ) )
% 5.82/6.20 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % normalize_denom_zero
% 5.82/6.20 thf(fact_9862_rat__times__code,axiom,
% 5.82/6.20 ! [P6: rat,Q3: rat] :
% 5.82/6.20 ( ( quotient_of @ ( times_times_rat @ P6 @ Q3 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int,C4: int] :
% 5.82/6.20 ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [B6: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B6 ) @ ( times_times_int @ C4 @ D3 ) ) )
% 5.82/6.20 @ ( quotient_of @ Q3 ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_times_code
% 5.82/6.20 thf(fact_9863_rat__divide__code,axiom,
% 5.82/6.20 ! [P6: rat,Q3: rat] :
% 5.82/6.20 ( ( quotient_of @ ( divide_divide_rat @ P6 @ Q3 ) )
% 5.82/6.20 = ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [A5: int,C4: int] :
% 5.82/6.20 ( produc4245557441103728435nt_int
% 5.82/6.20 @ ^ [B6: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B6 ) ) )
% 5.82/6.20 @ ( quotient_of @ Q3 ) )
% 5.82/6.20 @ ( quotient_of @ P6 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % rat_divide_code
% 5.82/6.20 thf(fact_9864_UNIV__nat__eq,axiom,
% 5.82/6.20 ( top_top_set_nat
% 5.82/6.20 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % UNIV_nat_eq
% 5.82/6.20 thf(fact_9865_Frct__code__post_I5_J,axiom,
% 5.82/6.20 ! [K: num] :
% 5.82/6.20 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.82/6.20 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Frct_code_post(5)
% 5.82/6.20 thf(fact_9866_Frct__code__post_I3_J,axiom,
% 5.82/6.20 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.82/6.20 = one_one_rat ) ).
% 5.82/6.20
% 5.82/6.20 % Frct_code_post(3)
% 5.82/6.20 thf(fact_9867_Frct__code__post_I4_J,axiom,
% 5.82/6.20 ! [K: num] :
% 5.82/6.20 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.82/6.20 = ( numeral_numeral_rat @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % Frct_code_post(4)
% 5.82/6.20 thf(fact_9868_bin__rest__integer_Oabs__eq,axiom,
% 5.82/6.20 ! [X2: int] :
% 5.82/6.20 ( ( bits_b2549910563261871055nteger @ ( code_integer_of_int @ X2 ) )
% 5.82/6.20 = ( code_integer_of_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_rest_integer.abs_eq
% 5.82/6.20 thf(fact_9869_bin__rest__integer__code,axiom,
% 5.82/6.20 ( bits_b2549910563261871055nteger
% 5.82/6.20 = ( ^ [I4: code_integer] : ( divide6298287555418463151nteger @ I4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_rest_integer_code
% 5.82/6.20 thf(fact_9870_bitXOR__integer__unfold,axiom,
% 5.82/6.20 ( bit_se3222712562003087583nteger
% 5.82/6.20 = ( ^ [X3: code_integer,Y: code_integer] :
% 5.82/6.20 ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ Y
% 5.82/6.20 @ ( if_Code_integer
% 5.82/6.20 @ ( X3
% 5.82/6.20 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.82/6.20 @ ( bit_ri7632146776885996613nteger @ Y )
% 5.82/6.20 @ ( bits_Bit_integer @ ( bit_se3222712562003087583nteger @ ( bits_b2549910563261871055nteger @ X3 ) @ ( bits_b2549910563261871055nteger @ Y ) )
% 5.82/6.20 @ ( ( ~ ( bits_b8758750999018896077nteger @ X3 ) )
% 5.82/6.20 = ( bits_b8758750999018896077nteger @ Y ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bitXOR_integer_unfold
% 5.82/6.20 thf(fact_9871_drop__bit__nonnegative__int__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.82/6.20 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_nonnegative_int_iff
% 5.82/6.20 thf(fact_9872_drop__bit__minus__one,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_minus_one
% 5.82/6.20 thf(fact_9873_drop__bit__of__Suc__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_of_Suc_0
% 5.82/6.20 thf(fact_9874_drop__bit__Suc__minus__bit0,axiom,
% 5.82/6.20 ! [N: nat,K: num] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.82/6.20 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_Suc_minus_bit0
% 5.82/6.20 thf(fact_9875_drop__bit__numeral__minus__bit0,axiom,
% 5.82/6.20 ! [L: num,K: num] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.82/6.20 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_numeral_minus_bit0
% 5.82/6.20 thf(fact_9876_drop__bit__Suc__minus__bit1,axiom,
% 5.82/6.20 ! [N: nat,K: num] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.82/6.20 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_Suc_minus_bit1
% 5.82/6.20 thf(fact_9877_drop__bit__numeral__minus__bit1,axiom,
% 5.82/6.20 ! [L: num,K: num] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.82/6.20 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_numeral_minus_bit1
% 5.82/6.20 thf(fact_9878_drop__bit__int__code_I2_J,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ zero_zero_int )
% 5.82/6.20 = zero_zero_int ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_int_code(2)
% 5.82/6.20 thf(fact_9879_bitval__bin__last__integer,axiom,
% 5.82/6.20 ! [I: code_integer] :
% 5.82/6.20 ( ( zero_n356916108424825756nteger @ ( bits_b8758750999018896077nteger @ I ) )
% 5.82/6.20 = ( bit_se3949692690581998587nteger @ I @ one_one_Code_integer ) ) ).
% 5.82/6.20
% 5.82/6.20 % bitval_bin_last_integer
% 5.82/6.20 thf(fact_9880_shiftr__integer__conv__div__pow2,axiom,
% 5.82/6.20 ( bit_se3928097537394005634nteger
% 5.82/6.20 = ( ^ [N4: nat,X3: code_integer] : ( divide6298287555418463151nteger @ X3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % shiftr_integer_conv_div_pow2
% 5.82/6.20 thf(fact_9881_bin__last__integer__code,axiom,
% 5.82/6.20 ( bits_b8758750999018896077nteger
% 5.82/6.20 = ( ^ [I4: code_integer] :
% 5.82/6.20 ( ( bit_se3949692690581998587nteger @ I4 @ one_one_Code_integer )
% 5.82/6.20 != zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_last_integer_code
% 5.82/6.20 thf(fact_9882_bin__rest__code,axiom,
% 5.82/6.20 ! [I: int] :
% 5.82/6.20 ( ( divide_divide_int @ I @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.82/6.20 = ( bit_se8568078237143864401it_int @ one_one_nat @ I ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_rest_code
% 5.82/6.20 thf(fact_9883_drop__bit__int__def,axiom,
% 5.82/6.20 ( bit_se8568078237143864401it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_int_def
% 5.82/6.20 thf(fact_9884_drop__bit__nat__def,axiom,
% 5.82/6.20 ( bit_se8570568707652914677it_nat
% 5.82/6.20 = ( ^ [N4: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_nat_def
% 5.82/6.20 thf(fact_9885_bin__last__integer__nbe,axiom,
% 5.82/6.20 ( bits_b8758750999018896077nteger
% 5.82/6.20 = ( ^ [I4: code_integer] :
% 5.82/6.20 ( ( modulo364778990260209775nteger @ I4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.82/6.20 != zero_z3403309356797280102nteger ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_last_integer_nbe
% 5.82/6.20 thf(fact_9886_bin__last__integer_Oabs__eq,axiom,
% 5.82/6.20 ! [X2: int] :
% 5.82/6.20 ( ( bits_b8758750999018896077nteger @ ( code_integer_of_int @ X2 ) )
% 5.82/6.20 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bin_last_integer.abs_eq
% 5.82/6.20 thf(fact_9887_bitOR__integer__unfold,axiom,
% 5.82/6.20 ( bit_se1080825931792720795nteger
% 5.82/6.20 = ( ^ [X3: code_integer,Y: code_integer] :
% 5.82/6.20 ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ Y
% 5.82/6.20 @ ( if_Code_integer
% 5.82/6.20 @ ( X3
% 5.82/6.20 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.82/6.20 @ ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.82/6.20 @ ( bits_Bit_integer @ ( bit_se1080825931792720795nteger @ ( bits_b2549910563261871055nteger @ X3 ) @ ( bits_b2549910563261871055nteger @ Y ) )
% 5.82/6.20 @ ( ( bits_b8758750999018896077nteger @ X3 )
% 5.82/6.20 | ( bits_b8758750999018896077nteger @ Y ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bitOR_integer_unfold
% 5.82/6.20 thf(fact_9888_bitAND__integer__unfold,axiom,
% 5.82/6.20 ( bit_se3949692690581998587nteger
% 5.82/6.20 = ( ^ [X3: code_integer,Y: code_integer] :
% 5.82/6.20 ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger
% 5.82/6.20 @ ( if_Code_integer
% 5.82/6.20 @ ( X3
% 5.82/6.20 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.82/6.20 @ Y
% 5.82/6.20 @ ( bits_Bit_integer @ ( bit_se3949692690581998587nteger @ ( bits_b2549910563261871055nteger @ X3 ) @ ( bits_b2549910563261871055nteger @ Y ) )
% 5.82/6.20 @ ( ( bits_b8758750999018896077nteger @ X3 )
% 5.82/6.20 & ( bits_b8758750999018896077nteger @ Y ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bitAND_integer_unfold
% 5.82/6.20 thf(fact_9889_push__bit__nonnegative__int__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.82/6.20 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % push_bit_nonnegative_int_iff
% 5.82/6.20 thf(fact_9890_push__bit__of__Suc__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.82/6.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % push_bit_of_Suc_0
% 5.82/6.20 thf(fact_9891_drop__bit__push__bit__int,axiom,
% 5.82/6.20 ! [M: nat,N: nat,K: int] :
% 5.82/6.20 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.82/6.20 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % drop_bit_push_bit_int
% 5.82/6.20 thf(fact_9892_set__bit__nat__def,axiom,
% 5.82/6.20 ( bit_se7882103937844011126it_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % set_bit_nat_def
% 5.82/6.20 thf(fact_9893_flip__bit__nat__def,axiom,
% 5.82/6.20 ( bit_se2161824704523386999it_nat
% 5.82/6.20 = ( ^ [M6: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % flip_bit_nat_def
% 5.82/6.20 thf(fact_9894_Bit__integer__code_I1_J,axiom,
% 5.82/6.20 ! [I: code_integer] :
% 5.82/6.20 ( ( bits_Bit_integer @ I @ $false )
% 5.82/6.20 = ( bit_se7788150548672797655nteger @ one_one_nat @ I ) ) ).
% 5.82/6.20
% 5.82/6.20 % Bit_integer_code(1)
% 5.82/6.20 thf(fact_9895_bit__push__bit__iff__int,axiom,
% 5.82/6.20 ! [M: nat,K: int,N: nat] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.82/6.20 = ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.20 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_push_bit_iff_int
% 5.82/6.20 thf(fact_9896_Bit__Operations_Oset__bit__int__def,axiom,
% 5.82/6.20 ( bit_se7879613467334960850it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Bit_Operations.set_bit_int_def
% 5.82/6.20 thf(fact_9897_bit__push__bit__iff__nat,axiom,
% 5.82/6.20 ! [M: nat,Q3: nat,N: nat] :
% 5.82/6.20 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 5.82/6.20 = ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.20 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_push_bit_iff_nat
% 5.82/6.20 thf(fact_9898_flip__bit__int__def,axiom,
% 5.82/6.20 ( bit_se2159334234014336723it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % flip_bit_int_def
% 5.82/6.20 thf(fact_9899_shiftl__integer__conv__mult__pow2,axiom,
% 5.82/6.20 ( bit_se7788150548672797655nteger
% 5.82/6.20 = ( ^ [N4: nat,X3: code_integer] : ( times_3573771949741848930nteger @ X3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % shiftl_integer_conv_mult_pow2
% 5.82/6.20 thf(fact_9900_unset__bit__int__def,axiom,
% 5.82/6.20 ( bit_se4203085406695923979it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % unset_bit_int_def
% 5.82/6.20 thf(fact_9901_push__bit__int__def,axiom,
% 5.82/6.20 ( bit_se545348938243370406it_int
% 5.82/6.20 = ( ^ [N4: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % push_bit_int_def
% 5.82/6.20 thf(fact_9902_Bit__integer__code_I2_J,axiom,
% 5.82/6.20 ! [I: code_integer] :
% 5.82/6.20 ( ( bits_Bit_integer @ I @ $true )
% 5.82/6.20 = ( plus_p5714425477246183910nteger @ ( bit_se7788150548672797655nteger @ one_one_nat @ I ) @ one_one_Code_integer ) ) ).
% 5.82/6.20
% 5.82/6.20 % Bit_integer_code(2)
% 5.82/6.20 thf(fact_9903_push__bit__nat__def,axiom,
% 5.82/6.20 ( bit_se547839408752420682it_nat
% 5.82/6.20 = ( ^ [N4: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % push_bit_nat_def
% 5.82/6.20 thf(fact_9904_push__bit__minus__one,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % push_bit_minus_one
% 5.82/6.20 thf(fact_9905_set__bit__integer__conv__masks,axiom,
% 5.82/6.20 ( generi2397576812484419408nteger
% 5.82/6.20 = ( ^ [X3: code_integer,I4: nat,B6: $o] : ( if_Code_integer @ B6 @ ( bit_se1080825931792720795nteger @ X3 @ ( bit_se7788150548672797655nteger @ I4 @ one_one_Code_integer ) ) @ ( bit_se3949692690581998587nteger @ X3 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ I4 @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % set_bit_integer_conv_masks
% 5.82/6.20 thf(fact_9906_int__set__bit__True__conv__OR,axiom,
% 5.82/6.20 ! [I: int,N: nat] :
% 5.82/6.20 ( ( generi8991105624351003935it_int @ I @ N @ $true )
% 5.82/6.20 = ( bit_se1409905431419307370or_int @ I @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_set_bit_True_conv_OR
% 5.82/6.20 thf(fact_9907_int__set__bit__False__conv__NAND,axiom,
% 5.82/6.20 ! [I: int,N: nat] :
% 5.82/6.20 ( ( generi8991105624351003935it_int @ I @ N @ $false )
% 5.82/6.20 = ( bit_se725231765392027082nd_int @ I @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_set_bit_False_conv_NAND
% 5.82/6.20 thf(fact_9908_int__set__bit__conv__ops,axiom,
% 5.82/6.20 ( generi8991105624351003935it_int
% 5.82/6.20 = ( ^ [I4: int,N4: nat,B6: $o] : ( if_int @ B6 @ ( bit_se1409905431419307370or_int @ I4 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) @ ( bit_se725231765392027082nd_int @ I4 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_set_bit_conv_ops
% 5.82/6.20 thf(fact_9909_upto__aux__rec,axiom,
% 5.82/6.20 ( upto_aux
% 5.82/6.20 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % upto_aux_rec
% 5.82/6.20 thf(fact_9910_concat__bit__Suc,axiom,
% 5.82/6.20 ! [N: nat,K: int,L: int] :
% 5.82/6.20 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 5.82/6.20 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % concat_bit_Suc
% 5.82/6.20 thf(fact_9911_concat__bit__nonnegative__iff,axiom,
% 5.82/6.20 ! [N: nat,K: int,L: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 5.82/6.20 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.82/6.20
% 5.82/6.20 % concat_bit_nonnegative_iff
% 5.82/6.20 thf(fact_9912_concat__bit__assoc,axiom,
% 5.82/6.20 ! [N: nat,K: int,M: nat,L: int,R2: int] :
% 5.82/6.20 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 5.82/6.20 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % concat_bit_assoc
% 5.82/6.20 thf(fact_9913_concat__bit__eq,axiom,
% 5.82/6.20 ( bit_concat_bit
% 5.82/6.20 = ( ^ [N4: nat,K3: int,L3: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N4 @ K3 ) @ ( bit_se545348938243370406it_int @ N4 @ L3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % concat_bit_eq
% 5.82/6.20 thf(fact_9914_bit__concat__bit__iff,axiom,
% 5.82/6.20 ! [M: nat,K: int,L: int,N: nat] :
% 5.82/6.20 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 5.82/6.20 = ( ( ( ord_less_nat @ N @ M )
% 5.82/6.20 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.82/6.20 | ( ( ord_less_eq_nat @ M @ N )
% 5.82/6.20 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % bit_concat_bit_iff
% 5.82/6.20 thf(fact_9915_int__lsb__numeral_I2_J,axiom,
% 5.82/6.20 least_4859182151741483524sb_int @ one_one_int ).
% 5.82/6.20
% 5.82/6.20 % int_lsb_numeral(2)
% 5.82/6.20 thf(fact_9916_int__lsb__numeral_I6_J,axiom,
% 5.82/6.20 ! [W: num] :
% 5.82/6.20 ~ ( least_4859182151741483524sb_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_lsb_numeral(6)
% 5.82/6.20 thf(fact_9917_int__lsb__numeral_I3_J,axiom,
% 5.82/6.20 least_4859182151741483524sb_int @ ( numeral_numeral_int @ one ) ).
% 5.82/6.20
% 5.82/6.20 % int_lsb_numeral(3)
% 5.82/6.20 thf(fact_9918_int__lsb__numeral_I4_J,axiom,
% 5.82/6.20 least_4859182151741483524sb_int @ ( uminus_uminus_int @ one_one_int ) ).
% 5.82/6.20
% 5.82/6.20 % int_lsb_numeral(4)
% 5.82/6.20 thf(fact_9919_int__lsb__numeral_I8_J,axiom,
% 5.82/6.20 ! [W: num] :
% 5.82/6.20 ~ ( least_4859182151741483524sb_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_lsb_numeral(8)
% 5.82/6.20 thf(fact_9920_int__lsb__numeral_I5_J,axiom,
% 5.82/6.20 least_4859182151741483524sb_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_lsb_numeral(5)
% 5.82/6.20 thf(fact_9921_bin__last__conv__lsb,axiom,
% 5.82/6.20 ( ( ^ [A5: int] :
% 5.82/6.20 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) )
% 5.82/6.20 = least_4859182151741483524sb_int ) ).
% 5.82/6.20
% 5.82/6.20 % bin_last_conv_lsb
% 5.82/6.20 thf(fact_9922_horner__sum__of__bool__2__less,axiom,
% 5.82/6.20 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % horner_sum_of_bool_2_less
% 5.82/6.20 thf(fact_9923_Cauchy__iff2,axiom,
% 5.82/6.20 ( topolo4055970368930404560y_real
% 5.82/6.20 = ( ^ [X7: nat > real] :
% 5.82/6.20 ! [J3: nat] :
% 5.82/6.20 ? [M10: nat] :
% 5.82/6.20 ! [M6: nat] :
% 5.82/6.20 ( ( ord_less_eq_nat @ M10 @ M6 )
% 5.82/6.20 => ! [N4: nat] :
% 5.82/6.20 ( ( ord_less_eq_nat @ M10 @ N4 )
% 5.82/6.20 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Cauchy_iff2
% 5.82/6.20 thf(fact_9924_int__sdiv__negated__is__minus1,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( A2 != zero_zero_int )
% 5.82/6.20 => ( ( ( signed6714573509424544716de_int @ A2 @ B2 )
% 5.82/6.20 = ( uminus_uminus_int @ A2 ) )
% 5.82/6.20 = ( B2
% 5.82/6.20 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_sdiv_negated_is_minus1
% 5.82/6.20 thf(fact_9925_int__sdiv__simps_I3_J,axiom,
% 5.82/6.20 ! [A2: int] :
% 5.82/6.20 ( ( signed6714573509424544716de_int @ A2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.82/6.20 = ( uminus_uminus_int @ A2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_sdiv_simps(3)
% 5.82/6.20 thf(fact_9926_int__sdiv__simps_I1_J,axiom,
% 5.82/6.20 ! [A2: int] :
% 5.82/6.20 ( ( signed6714573509424544716de_int @ A2 @ one_one_int )
% 5.82/6.20 = A2 ) ).
% 5.82/6.20
% 5.82/6.20 % int_sdiv_simps(1)
% 5.82/6.20 thf(fact_9927_int__sdiv__same__is__1,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( A2 != zero_zero_int )
% 5.82/6.20 => ( ( ( signed6714573509424544716de_int @ A2 @ B2 )
% 5.82/6.20 = A2 )
% 5.82/6.20 = ( B2 = one_one_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % int_sdiv_same_is_1
% 5.82/6.20 thf(fact_9928_entails__solve__init_I1_J,axiom,
% 5.82/6.20 ! [P: assn,Q: assn] :
% 5.82/6.20 ( ( fI_QUERY @ P @ Q @ top_top_assn )
% 5.82/6.20 => ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % entails_solve_init(1)
% 5.82/6.20 thf(fact_9929_frame__inference__init,axiom,
% 5.82/6.20 ! [P: assn,Q: assn,F3: assn] :
% 5.82/6.20 ( ( fI_QUERY @ P @ Q @ F3 )
% 5.82/6.20 => ( entails @ P @ ( times_times_assn @ Q @ F3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % frame_inference_init
% 5.82/6.20 thf(fact_9930_FI__QUERY__def,axiom,
% 5.82/6.20 ( fI_QUERY
% 5.82/6.20 = ( ^ [P3: assn,Q7: assn,F8: assn] : ( entails @ P3 @ ( times_times_assn @ Q7 @ F8 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % FI_QUERY_def
% 5.82/6.20 thf(fact_9931_entails__solve__init_I2_J,axiom,
% 5.82/6.20 ! [P: assn,Q: assn] :
% 5.82/6.20 ( ( fI_QUERY @ P @ Q @ one_one_assn )
% 5.82/6.20 => ( entails @ P @ Q ) ) ).
% 5.82/6.20
% 5.82/6.20 % entails_solve_init(2)
% 5.82/6.20 thf(fact_9932_smod__int__range,axiom,
% 5.82/6.20 ! [B2: int,A2: int] :
% 5.82/6.20 ( ( B2 != zero_zero_int )
% 5.82/6.20 => ( member_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ ( uminus_uminus_int @ ( abs_abs_int @ B2 ) ) @ one_one_int ) @ ( minus_minus_int @ ( abs_abs_int @ B2 ) @ one_one_int ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_range
% 5.82/6.20 thf(fact_9933_smod__int__compares_I1_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.20 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.20 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) @ B2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(1)
% 5.82/6.20 thf(fact_9934_smod__int__compares_I2_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.20 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.20 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(2)
% 5.82/6.20 thf(fact_9935_smod__int__compares_I4_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.20 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.20 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(4)
% 5.82/6.20 thf(fact_9936_smod__int__compares_I6_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.20 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.20 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(6)
% 5.82/6.20 thf(fact_9937_smod__int__compares_I7_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.20 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.20 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(7)
% 5.82/6.20 thf(fact_9938_smod__int__compares_I8_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.20 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.20 => ( ord_less_eq_int @ B2 @ ( signed6292675348222524329lo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(8)
% 5.82/6.20 thf(fact_9939_smod__mod__positive,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.20 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.82/6.20 => ( ( signed6292675348222524329lo_int @ A2 @ B2 )
% 5.82/6.20 = ( modulo_modulo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_mod_positive
% 5.82/6.20 thf(fact_9940_signed__modulo__int__def,axiom,
% 5.82/6.20 ( signed6292675348222524329lo_int
% 5.82/6.20 = ( ^ [K3: int,L3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( signed6714573509424544716de_int @ K3 @ L3 ) @ L3 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % signed_modulo_int_def
% 5.82/6.20 thf(fact_9941_smod__int__compares_I5_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.82/6.20 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.82/6.20 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A2 @ B2 ) @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(5)
% 5.82/6.20 thf(fact_9942_smod__int__compares_I3_J,axiom,
% 5.82/6.20 ! [A2: int,B2: int] :
% 5.82/6.20 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.82/6.20 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.82/6.20 => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( signed6292675348222524329lo_int @ A2 @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % smod_int_compares(3)
% 5.82/6.20 thf(fact_9943_uint32_Osize__eq__length,axiom,
% 5.82/6.20 ( ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.20 = ( type_l796852477590012082l_num1 @ type_N8448461349408098053l_num1 ) ) ).
% 5.82/6.20
% 5.82/6.20 % uint32.size_eq_length
% 5.82/6.20 thf(fact_9944_len__num1,axiom,
% 5.82/6.20 ( type_l4264026598287037465l_num1
% 5.82/6.20 = ( ^ [Uu4: itself_Numeral_num1] : one_one_nat ) ) ).
% 5.82/6.20
% 5.82/6.20 % len_num1
% 5.82/6.20 thf(fact_9945_len__of__finite__1__def,axiom,
% 5.82/6.20 ( type_l31302759751748491nite_1
% 5.82/6.20 = ( ^ [X3: itself_finite_1] : one_one_nat ) ) ).
% 5.82/6.20
% 5.82/6.20 % len_of_finite_1_def
% 5.82/6.20 thf(fact_9946_len__of__finite__2__def,axiom,
% 5.82/6.20 ( type_l31302759751748492nite_2
% 5.82/6.20 = ( ^ [X3: itself_finite_2] : ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % len_of_finite_2_def
% 5.82/6.20 thf(fact_9947_len__of__finite__3__def,axiom,
% 5.82/6.20 ( type_l31302759751748493nite_3
% 5.82/6.20 = ( ^ [X3: itself_finite_3] : ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % len_of_finite_3_def
% 5.82/6.20 thf(fact_9948_min__Suc__Suc,axiom,
% 5.82/6.20 ! [M: nat,N: nat] :
% 5.82/6.20 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.82/6.20 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_Suc_Suc
% 5.82/6.20 thf(fact_9949_min__0L,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.82/6.20 = zero_zero_nat ) ).
% 5.82/6.20
% 5.82/6.20 % min_0L
% 5.82/6.20 thf(fact_9950_min__0R,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.82/6.20 = zero_zero_nat ) ).
% 5.82/6.20
% 5.82/6.20 % min_0R
% 5.82/6.20 thf(fact_9951_min__minus,axiom,
% 5.82/6.20 ! [M: nat,K: nat] :
% 5.82/6.20 ( ( ord_min_nat @ M @ ( minus_minus_nat @ M @ K ) )
% 5.82/6.20 = ( minus_minus_nat @ M @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_minus
% 5.82/6.20 thf(fact_9952_min__minus_H,axiom,
% 5.82/6.20 ! [M: nat,K: nat] :
% 5.82/6.20 ( ( ord_min_nat @ ( minus_minus_nat @ M @ K ) @ M )
% 5.82/6.20 = ( minus_minus_nat @ M @ K ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_minus'
% 5.82/6.20 thf(fact_9953_min__Suc__gt_I1_J,axiom,
% 5.82/6.20 ! [A2: nat,B2: nat] :
% 5.82/6.20 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.20 => ( ( ord_min_nat @ ( suc @ A2 ) @ B2 )
% 5.82/6.20 = ( suc @ A2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_Suc_gt(1)
% 5.82/6.20 thf(fact_9954_min__Suc__gt_I2_J,axiom,
% 5.82/6.20 ! [A2: nat,B2: nat] :
% 5.82/6.20 ( ( ord_less_nat @ A2 @ B2 )
% 5.82/6.20 => ( ( ord_min_nat @ B2 @ ( suc @ A2 ) )
% 5.82/6.20 = ( suc @ A2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_Suc_gt(2)
% 5.82/6.20 thf(fact_9955_rev__min__pm1,axiom,
% 5.82/6.20 ! [A2: nat,B2: nat] :
% 5.82/6.20 ( ( plus_plus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ ( ord_min_nat @ B2 @ A2 ) )
% 5.82/6.20 = A2 ) ).
% 5.82/6.20
% 5.82/6.20 % rev_min_pm1
% 5.82/6.20 thf(fact_9956_rev__min__pm,axiom,
% 5.82/6.20 ! [B2: nat,A2: nat] :
% 5.82/6.20 ( ( plus_plus_nat @ ( ord_min_nat @ B2 @ A2 ) @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.20 = A2 ) ).
% 5.82/6.20
% 5.82/6.20 % rev_min_pm
% 5.82/6.20 thf(fact_9957_min__pm1,axiom,
% 5.82/6.20 ! [A2: nat,B2: nat] :
% 5.82/6.20 ( ( plus_plus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ ( ord_min_nat @ A2 @ B2 ) )
% 5.82/6.20 = A2 ) ).
% 5.82/6.20
% 5.82/6.20 % min_pm1
% 5.82/6.20 thf(fact_9958_min__pm,axiom,
% 5.82/6.20 ! [A2: nat,B2: nat] :
% 5.82/6.20 ( ( plus_plus_nat @ ( ord_min_nat @ A2 @ B2 ) @ ( minus_minus_nat @ A2 @ B2 ) )
% 5.82/6.20 = A2 ) ).
% 5.82/6.20
% 5.82/6.20 % min_pm
% 5.82/6.20 thf(fact_9959_min__numeral__Suc,axiom,
% 5.82/6.20 ! [K: num,N: nat] :
% 5.82/6.20 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.82/6.20 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_numeral_Suc
% 5.82/6.20 thf(fact_9960_min__Suc__numeral,axiom,
% 5.82/6.20 ! [N: nat,K: num] :
% 5.82/6.20 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.82/6.20 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_Suc_numeral
% 5.82/6.20 thf(fact_9961_min__diff,axiom,
% 5.82/6.20 ! [M: nat,I: nat,N: nat] :
% 5.82/6.20 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.82/6.20 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.82/6.20
% 5.82/6.20 % min_diff
% 5.82/6.20 thf(fact_9962_nat__mult__min__right,axiom,
% 5.82/6.20 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.20 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 5.82/6.20 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % nat_mult_min_right
% 5.82/6.20 thf(fact_9963_nat__mult__min__left,axiom,
% 5.82/6.20 ! [M: nat,N: nat,Q3: nat] :
% 5.82/6.20 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 5.82/6.20 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % nat_mult_min_left
% 5.82/6.20 thf(fact_9964_concat__bit__assoc__sym,axiom,
% 5.82/6.20 ! [M: nat,N: nat,K: int,L: int,R2: int] :
% 5.82/6.20 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L ) @ R2 )
% 5.82/6.20 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L @ R2 ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % concat_bit_assoc_sym
% 5.82/6.20 thf(fact_9965_take__bit__concat__bit__eq,axiom,
% 5.82/6.20 ! [M: nat,N: nat,K: int,L: int] :
% 5.82/6.20 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L ) )
% 5.82/6.20 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % take_bit_concat_bit_eq
% 5.82/6.20 thf(fact_9966_mod__mod__power,axiom,
% 5.82/6.20 ! [K: nat,M: nat,N: nat] :
% 5.82/6.20 ( ( 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 ) )
% 5.82/6.20 = ( modulo_modulo_nat @ K @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( ord_min_nat @ M @ N ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % mod_mod_power
% 5.82/6.20 thf(fact_9967_min__enat__simps_I3_J,axiom,
% 5.82/6.20 ! [Q3: extended_enat] :
% 5.82/6.20 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.82/6.20 = zero_z5237406670263579293d_enat ) ).
% 5.82/6.20
% 5.82/6.20 % min_enat_simps(3)
% 5.82/6.20 thf(fact_9968_min__enat__simps_I2_J,axiom,
% 5.82/6.20 ! [Q3: extended_enat] :
% 5.82/6.20 ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.82/6.20 = zero_z5237406670263579293d_enat ) ).
% 5.82/6.20
% 5.82/6.20 % min_enat_simps(2)
% 5.82/6.20 thf(fact_9969_shiftl__Suc__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_Sh3965577149348748681tl_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.82/6.20
% 5.82/6.20 % shiftl_Suc_0
% 5.82/6.20 thf(fact_9970_shiftr__Suc__0,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( bit_Sh2154871086232339855tr_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.82/6.20 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % shiftr_Suc_0
% 5.82/6.20 thf(fact_9971_inj__on__diff__nat,axiom,
% 5.82/6.20 ! [N7: set_nat,K: nat] :
% 5.82/6.20 ( ! [N3: nat] :
% 5.82/6.20 ( ( member_nat @ N3 @ N7 )
% 5.82/6.20 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.82/6.20 => ( inj_on_nat_nat
% 5.82/6.20 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K )
% 5.82/6.20 @ N7 ) ) ).
% 5.82/6.20
% 5.82/6.20 % inj_on_diff_nat
% 5.82/6.20 thf(fact_9972_inj__Suc,axiom,
% 5.82/6.20 ! [N7: set_nat] : ( inj_on_nat_nat @ suc @ N7 ) ).
% 5.82/6.20
% 5.82/6.20 % inj_Suc
% 5.82/6.20 thf(fact_9973_inj__sgn__power,axiom,
% 5.82/6.20 ! [N: nat] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( inj_on_real_real
% 5.82/6.20 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.82/6.20 @ top_top_set_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % inj_sgn_power
% 5.82/6.20 thf(fact_9974_valid__eq2,axiom,
% 5.82/6.20 ! [T: vEBT_VEBT,D2: nat] :
% 5.82/6.20 ( ( vEBT_VEBT_valid @ T @ D2 )
% 5.82/6.20 => ( vEBT_invar_vebt @ T @ D2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % valid_eq2
% 5.82/6.20 thf(fact_9975_valid__eq1,axiom,
% 5.82/6.20 ! [T: vEBT_VEBT,D2: nat] :
% 5.82/6.20 ( ( vEBT_invar_vebt @ T @ D2 )
% 5.82/6.20 => ( vEBT_VEBT_valid @ T @ D2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % valid_eq1
% 5.82/6.20 thf(fact_9976_valid__eq,axiom,
% 5.82/6.20 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.82/6.20
% 5.82/6.20 % valid_eq
% 5.82/6.20 thf(fact_9977_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.82/6.20 ! [Uu: $o,Uv: $o,D2: nat] :
% 5.82/6.20 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 )
% 5.82/6.20 = ( D2 = one_one_nat ) ) ).
% 5.82/6.20
% 5.82/6.20 % VEBT_internal.valid'.simps(1)
% 5.82/6.20 thf(fact_9978_DERIV__real__root__generic,axiom,
% 5.82/6.20 ! [N: nat,X2: real,D: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( X2 != zero_zero_real )
% 5.82/6.20 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( D
% 5.82/6.20 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.82/6.20 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( D
% 5.82/6.20 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.82/6.20 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( D
% 5.82/6.20 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_real_root_generic
% 5.82/6.20 thf(fact_9979_DERIV__even__real__root,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_even_real_root
% 5.82/6.20 thf(fact_9980_has__real__derivative__pos__inc__right,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( member_real @ ( plus_plus_real @ X2 @ H6 ) @ S )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H6 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % has_real_derivative_pos_inc_right
% 5.82/6.20 thf(fact_9981_has__real__derivative__neg__dec__right,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.82/6.20 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( member_real @ ( plus_plus_real @ X2 @ H6 ) @ S )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H6 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % has_real_derivative_neg_dec_right
% 5.82/6.20 thf(fact_9982_has__real__derivative__neg__dec__left,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.82/6.20 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( member_real @ ( minus_minus_real @ X2 @ H6 ) @ S )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H6 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % has_real_derivative_neg_dec_left
% 5.82/6.20 thf(fact_9983_has__real__derivative__pos__inc__left,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( member_real @ ( minus_minus_real @ X2 @ H6 ) @ S )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H6 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % has_real_derivative_pos_inc_left
% 5.82/6.20 thf(fact_9984_DERIV__local__const,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,D2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.82/6.20 => ( ! [Y4: real] :
% 5.82/6.20 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D2 )
% 5.82/6.20 => ( ( F @ X2 )
% 5.82/6.20 = ( F @ Y4 ) ) )
% 5.82/6.20 => ( L = zero_zero_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_local_const
% 5.82/6.20 thf(fact_9985_MVT2,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real,F5: real > real] :
% 5.82/6.20 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.20 => ( ! [X4: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.82/6.20 => ? [Z2: real] :
% 5.82/6.20 ( ( ord_less_real @ A2 @ Z2 )
% 5.82/6.20 & ( ord_less_real @ Z2 @ B2 )
% 5.82/6.20 & ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) )
% 5.82/6.20 = ( times_times_real @ ( minus_minus_real @ B2 @ A2 ) @ ( F5 @ Z2 ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % MVT2
% 5.82/6.20 thf(fact_9986_DERIV__mirror,axiom,
% 5.82/6.20 ! [F: real > real,Y3: real,X2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ X2 ) @ top_top_set_real ) )
% 5.82/6.20 = ( has_fi5821293074295781190e_real
% 5.82/6.20 @ ^ [X3: real] : ( F @ ( uminus_uminus_real @ X3 ) )
% 5.82/6.20 @ ( uminus_uminus_real @ Y3 )
% 5.82/6.20 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_mirror
% 5.82/6.20 thf(fact_9987_deriv__nonneg__imp__mono,axiom,
% 5.82/6.20 ! [A2: real,B2: real,G: real > real,G2: real > real] :
% 5.82/6.20 ( ! [X4: real] :
% 5.82/6.20 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A2 @ B2 ) )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.82/6.20 => ( ! [X4: real] :
% 5.82/6.20 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A2 @ B2 ) )
% 5.82/6.20 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 5.82/6.20 => ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( G @ A2 ) @ ( G @ B2 ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % deriv_nonneg_imp_mono
% 5.82/6.20 thf(fact_9988_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.20 => ( ! [X4: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.20 => ? [Y5: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 & ( ord_less_eq_real @ Y5 @ zero_zero_real ) ) ) )
% 5.82/6.20 => ( ord_less_eq_real @ ( F @ B2 ) @ ( F @ A2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_nonpos_imp_nonincreasing
% 5.82/6.20 thf(fact_9989_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.20 => ( ! [X4: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.20 => ? [Y5: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 & ( ord_less_eq_real @ zero_zero_real @ Y5 ) ) ) )
% 5.82/6.20 => ( ord_less_eq_real @ ( F @ A2 ) @ ( F @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_nonneg_imp_nondecreasing
% 5.82/6.20 thf(fact_9990_DERIV__neg__imp__decreasing,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.20 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.20 => ( ! [X4: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.20 => ? [Y5: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.82/6.20 => ( ord_less_real @ ( F @ B2 ) @ ( F @ A2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_neg_imp_decreasing
% 5.82/6.20 thf(fact_9991_DERIV__pos__imp__increasing,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.20 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.20 => ( ! [X4: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.20 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.20 => ? [Y5: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.82/6.20 => ( ord_less_real @ ( F @ A2 ) @ ( F @ B2 ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_pos_imp_increasing
% 5.82/6.20 thf(fact_9992_DERIV__neg__dec__left,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H6 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_neg_dec_left
% 5.82/6.20 thf(fact_9993_DERIV__pos__inc__left,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H6 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_pos_inc_left
% 5.82/6.20 thf(fact_9994_DERIV__neg__dec__right,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H6 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_neg_dec_right
% 5.82/6.20 thf(fact_9995_DERIV__pos__inc__right,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.82/6.20 => ? [D4: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.82/6.20 & ! [H6: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ H6 )
% 5.82/6.20 => ( ( ord_less_real @ H6 @ D4 )
% 5.82/6.20 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H6 ) ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_pos_inc_right
% 5.82/6.20 thf(fact_9996_DERIV__const__ratio__const,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real,K: real] :
% 5.82/6.20 ( ( A2 != B2 )
% 5.82/6.20 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 => ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) )
% 5.82/6.20 = ( times_times_real @ ( minus_minus_real @ B2 @ A2 ) @ K ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_const_ratio_const
% 5.82/6.20 thf(fact_9997_DERIV__const__ratio__const2,axiom,
% 5.82/6.20 ! [A2: real,B2: real,F: real > real,K: real] :
% 5.82/6.20 ( ( A2 != B2 )
% 5.82/6.20 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) ) @ ( minus_minus_real @ B2 @ A2 ) )
% 5.82/6.20 = K ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_const_ratio_const2
% 5.82/6.20 thf(fact_9998_DERIV__const__average,axiom,
% 5.82/6.20 ! [A2: real,B2: real,V: real > real,K: real] :
% 5.82/6.20 ( ( A2 != B2 )
% 5.82/6.20 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A2 @ B2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.82/6.20 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A2 ) @ ( V @ B2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_const_average
% 5.82/6.20 thf(fact_9999_DERIV__local__min,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,D2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.82/6.20 => ( ! [Y4: real] :
% 5.82/6.20 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 5.82/6.20 => ( L = zero_zero_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_local_min
% 5.82/6.20 thf(fact_10000_DERIV__local__max,axiom,
% 5.82/6.20 ! [F: real > real,L: real,X2: real,D2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.82/6.20 => ( ! [Y4: real] :
% 5.82/6.20 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D2 )
% 5.82/6.20 => ( ord_less_eq_real @ ( F @ Y4 ) @ ( F @ X2 ) ) )
% 5.82/6.20 => ( L = zero_zero_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_local_max
% 5.82/6.20 thf(fact_10001_DERIV__ln__divide,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_ln_divide
% 5.82/6.20 thf(fact_10002_DERIV__pow,axiom,
% 5.82/6.20 ! [N: nat,X2: real,S2: set_real] :
% 5.82/6.20 ( has_fi5821293074295781190e_real
% 5.82/6.20 @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 5.82/6.20 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.82/6.20 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_pow
% 5.82/6.20 thf(fact_10003_DERIV__fun__pow,axiom,
% 5.82/6.20 ! [G: real > real,M: real,X2: real,N: nat] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( has_fi5821293074295781190e_real
% 5.82/6.20 @ ^ [X3: real] : ( power_power_real @ ( G @ X3 ) @ N )
% 5.82/6.20 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.82/6.20 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_fun_pow
% 5.82/6.20 thf(fact_10004_has__real__derivative__powr,axiom,
% 5.82/6.20 ! [Z: real,R2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.82/6.20 => ( has_fi5821293074295781190e_real
% 5.82/6.20 @ ^ [Z4: real] : ( powr_real @ Z4 @ R2 )
% 5.82/6.20 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.82/6.20 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % has_real_derivative_powr
% 5.82/6.20 thf(fact_10005_DERIV__fun__powr,axiom,
% 5.82/6.20 ! [G: real > real,M: real,X2: real,R2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.82/6.20 => ( has_fi5821293074295781190e_real
% 5.82/6.20 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ R2 )
% 5.82/6.20 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X2 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.82/6.20 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_fun_powr
% 5.82/6.20 thf(fact_10006_DERIV__log,axiom,
% 5.82/6.20 ! [X2: real,B2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ ( log @ B2 ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B2 ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_log
% 5.82/6.20 thf(fact_10007_DERIV__powr,axiom,
% 5.82/6.20 ! [G: real > real,M: real,X2: real,F: real > real,R2: real] :
% 5.82/6.20 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.82/6.20 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.20 => ( has_fi5821293074295781190e_real
% 5.82/6.20 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) )
% 5.82/6.20 @ ( times_times_real @ ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G @ X2 ) ) ) )
% 5.82/6.20 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_powr
% 5.82/6.20 thf(fact_10008_DERIV__real__sqrt,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_real_sqrt
% 5.82/6.20 thf(fact_10009_DERIV__arctan,axiom,
% 5.82/6.20 ! [X2: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_arctan
% 5.82/6.20 thf(fact_10010_arsinh__real__has__field__derivative,axiom,
% 5.82/6.20 ! [X2: real,A: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A ) ) ).
% 5.82/6.20
% 5.82/6.20 % arsinh_real_has_field_derivative
% 5.82/6.20 thf(fact_10011_DERIV__real__sqrt__generic,axiom,
% 5.82/6.20 ! [X2: real,D: real] :
% 5.82/6.20 ( ( X2 != zero_zero_real )
% 5.82/6.20 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( D
% 5.82/6.20 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.20 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.82/6.20 => ( D
% 5.82/6.20 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ sqrt @ D @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_real_sqrt_generic
% 5.82/6.20 thf(fact_10012_arcosh__real__has__field__derivative,axiom,
% 5.82/6.20 ! [X2: real,A: set_real] :
% 5.82/6.20 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % arcosh_real_has_field_derivative
% 5.82/6.20 thf(fact_10013_artanh__real__has__field__derivative,axiom,
% 5.82/6.20 ! [X2: real,A: set_real] :
% 5.82/6.20 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % artanh_real_has_field_derivative
% 5.82/6.20 thf(fact_10014_DERIV__real__root,axiom,
% 5.82/6.20 ! [N: nat,X2: real] :
% 5.82/6.20 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.20 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_real_root
% 5.82/6.20 thf(fact_10015_DERIV__arccos,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_arccos
% 5.82/6.20 thf(fact_10016_DERIV__arcsin,axiom,
% 5.82/6.20 ! [X2: real] :
% 5.82/6.20 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.20 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.20 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % DERIV_arcsin
% 5.82/6.20 thf(fact_10017_Maclaurin__all__le,axiom,
% 5.82/6.20 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.82/6.20 ( ( ( Diff @ zero_zero_nat )
% 5.82/6.20 = F )
% 5.82/6.20 => ( ! [M5: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.20 => ? [T7: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.20 & ( ( F @ X2 )
% 5.82/6.20 = ( plus_plus_real
% 5.82/6.20 @ ( groups6591440286371151544t_real
% 5.82/6.20 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.20 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.20 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.82/6.20
% 5.82/6.20 % Maclaurin_all_le
% 5.82/6.20 thf(fact_10018_Maclaurin__all__le__objl,axiom,
% 5.82/6.20 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.82/6.20 ( ( ( ( Diff @ zero_zero_nat )
% 5.82/6.20 = F )
% 5.82/6.20 & ! [M5: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.82/6.20 => ? [T7: real] :
% 5.82/6.20 ( ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.20 & ( ( F @ X2 )
% 5.82/6.20 = ( plus_plus_real
% 5.82/6.20 @ ( groups6591440286371151544t_real
% 5.82/6.20 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.20 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.20 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin_all_le_objl
% 5.82/6.21 thf(fact_10019_DERIV__odd__real__root,axiom,
% 5.82/6.21 ! [N: nat,X2: real] :
% 5.82/6.21 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.21 => ( ( X2 != zero_zero_real )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_odd_real_root
% 5.82/6.21 thf(fact_10020_Maclaurin,axiom,
% 5.82/6.21 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.82/6.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ T7 )
% 5.82/6.21 & ( ord_less_real @ T7 @ H2 )
% 5.82/6.21 & ( ( F @ H2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin
% 5.82/6.21 thf(fact_10021_Maclaurin2,axiom,
% 5.82/6.21 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.82/6.21 => ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ H2 )
% 5.82/6.21 & ( ( F @ H2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin2
% 5.82/6.21 thf(fact_10022_Maclaurin__minus,axiom,
% 5.82/6.21 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.82/6.21 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.82/6.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ H2 @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ zero_zero_real ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_real @ H2 @ T7 )
% 5.82/6.21 & ( ord_less_real @ T7 @ zero_zero_real )
% 5.82/6.21 & ( ( F @ H2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin_minus
% 5.82/6.21 thf(fact_10023_Maclaurin__all__lt,axiom,
% 5.82/6.21 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.82/6.21 ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( X2 != zero_zero_real )
% 5.82/6.21 => ( ! [M5: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T7 ) )
% 5.82/6.21 & ( ord_less_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.21 & ( ( F @ X2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin_all_lt
% 5.82/6.21 thf(fact_10024_Maclaurin__bi__le,axiom,
% 5.82/6.21 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.82/6.21 ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ ( abs_abs_real @ T7 ) @ ( abs_abs_real @ X2 ) )
% 5.82/6.21 & ( ( F @ X2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin_bi_le
% 5.82/6.21 thf(fact_10025_Taylor__down,axiom,
% 5.82/6.21 ! [N: nat,Diff: nat > real > real,F: real > real,A2: real,B2: real,C2: real] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ A2 @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ B2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ( ( ord_less_real @ A2 @ C2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ C2 @ B2 )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ T7 )
% 5.82/6.21 & ( ord_less_real @ T7 @ C2 )
% 5.82/6.21 & ( ( F @ A2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A2 @ C2 ) @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A2 @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Taylor_down
% 5.82/6.21 thf(fact_10026_Taylor__up,axiom,
% 5.82/6.21 ! [N: nat,Diff: nat > real > real,F: real > real,A2: real,B2: real,C2: real] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ A2 @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ B2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ( ( ord_less_eq_real @ A2 @ C2 )
% 5.82/6.21 => ( ( ord_less_real @ C2 @ B2 )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ord_less_real @ C2 @ T7 )
% 5.82/6.21 & ( ord_less_real @ T7 @ B2 )
% 5.82/6.21 & ( ( F @ B2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B2 @ C2 ) @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B2 @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Taylor_up
% 5.82/6.21 thf(fact_10027_Taylor,axiom,
% 5.82/6.21 ! [N: nat,Diff: nat > real > real,F: real > real,A2: real,B2: real,C2: real,X2: real] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( ( Diff @ zero_zero_nat )
% 5.82/6.21 = F )
% 5.82/6.21 => ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ A2 @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ B2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ( ( ord_less_eq_real @ A2 @ C2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ C2 @ B2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ A2 @ X2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ X2 @ B2 )
% 5.82/6.21 => ( ( X2 != C2 )
% 5.82/6.21 => ? [T7: real] :
% 5.82/6.21 ( ( ( ord_less_real @ X2 @ C2 )
% 5.82/6.21 => ( ( ord_less_real @ X2 @ T7 )
% 5.82/6.21 & ( ord_less_real @ T7 @ C2 ) ) )
% 5.82/6.21 & ( ~ ( ord_less_real @ X2 @ C2 )
% 5.82/6.21 => ( ( ord_less_real @ C2 @ T7 )
% 5.82/6.21 & ( ord_less_real @ T7 @ X2 ) ) )
% 5.82/6.21 & ( ( F @ X2 )
% 5.82/6.21 = ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C2 ) @ M6 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ N ) )
% 5.82/6.21 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T7 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Taylor
% 5.82/6.21 thf(fact_10028_Maclaurin__lemma2,axiom,
% 5.82/6.21 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B: real] :
% 5.82/6.21 ( ! [M5: nat,T7: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M5 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.82/6.21 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T7 ) @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) )
% 5.82/6.21 => ( ( N
% 5.82/6.21 = ( suc @ K ) )
% 5.82/6.21 => ! [M3: nat,T8: real] :
% 5.82/6.21 ( ( ( ord_less_nat @ M3 @ N )
% 5.82/6.21 & ( ord_less_eq_real @ zero_zero_real @ T8 )
% 5.82/6.21 & ( ord_less_eq_real @ T8 @ H2 ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real
% 5.82/6.21 @ ^ [U2: real] :
% 5.82/6.21 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 5.82/6.21 @ ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ U2 @ P4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 5.82/6.21 @ ( times_times_real @ B @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 5.82/6.21 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T8 )
% 5.82/6.21 @ ( plus_plus_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T8 @ P4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 5.82/6.21 @ ( times_times_real @ B @ ( divide_divide_real @ ( power_power_real @ T8 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ T8 @ top_top_set_real ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Maclaurin_lemma2
% 5.82/6.21 thf(fact_10029_DERIV__arctan__series,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.21 => ( has_fi5821293074295781190e_real
% 5.82/6.21 @ ^ [X10: real] :
% 5.82/6.21 ( suminf_real
% 5.82/6.21 @ ^ [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 ) ) ) ) )
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X2 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_arctan_series
% 5.82/6.21 thf(fact_10030_DERIV__power__series_H,axiom,
% 5.82/6.21 ! [R: real,F: nat > real,X0: real] :
% 5.82/6.21 ( ! [X4: real] :
% 5.82/6.21 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.82/6.21 => ( summable_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X4 @ N4 ) ) ) )
% 5.82/6.21 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.82/6.21 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.82/6.21 => ( has_fi5821293074295781190e_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( suminf_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ X3 @ ( suc @ N4 ) ) ) )
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_power_series'
% 5.82/6.21 thf(fact_10031_tanh__real__bounds,axiom,
% 5.82/6.21 ! [X2: real] : ( member_real @ ( tanh_real @ X2 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % tanh_real_bounds
% 5.82/6.21 thf(fact_10032_DERIV__series_H,axiom,
% 5.82/6.21 ! [F: real > nat > real,F5: real > nat > real,X0: real,A2: real,B2: real,L5: nat > real] :
% 5.82/6.21 ( ! [N3: nat] :
% 5.82/6.21 ( has_fi5821293074295781190e_real
% 5.82/6.21 @ ^ [X3: real] : ( F @ X3 @ N3 )
% 5.82/6.21 @ ( F5 @ X0 @ N3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A2 @ B2 ) )
% 5.82/6.21 => ( summable_real @ ( F @ X4 ) ) )
% 5.82/6.21 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A2 @ B2 ) )
% 5.82/6.21 => ( ( summable_real @ ( F5 @ X0 ) )
% 5.82/6.21 => ( ( summable_real @ L5 )
% 5.82/6.21 => ( ! [N3: nat,X4: real,Y4: real] :
% 5.82/6.21 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A2 @ B2 ) )
% 5.82/6.21 => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A2 @ B2 ) )
% 5.82/6.21 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N3 ) @ ( F @ Y4 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) ) ) ) )
% 5.82/6.21 => ( has_fi5821293074295781190e_real
% 5.82/6.21 @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 5.82/6.21 @ ( suminf_real @ ( F5 @ X0 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_series'
% 5.82/6.21 thf(fact_10033_finite__greaterThanLessThan__integer,axiom,
% 5.82/6.21 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % finite_greaterThanLessThan_integer
% 5.82/6.21 thf(fact_10034_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.82/6.21 ! [L: nat,U: nat] :
% 5.82/6.21 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.82/6.21 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeastSucLessThan_greaterThanLessThan
% 5.82/6.21 thf(fact_10035_isCont__Lb__Ub,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.21 & ( ord_less_eq_real @ X4 @ B2 ) )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.82/6.21 => ? [L6: real,M9: real] :
% 5.82/6.21 ( ! [X8: real] :
% 5.82/6.21 ( ( ( ord_less_eq_real @ A2 @ X8 )
% 5.82/6.21 & ( ord_less_eq_real @ X8 @ B2 ) )
% 5.82/6.21 => ( ( ord_less_eq_real @ L6 @ ( F @ X8 ) )
% 5.82/6.21 & ( ord_less_eq_real @ ( F @ X8 ) @ M9 ) ) )
% 5.82/6.21 & ! [Y5: real] :
% 5.82/6.21 ( ( ( ord_less_eq_real @ L6 @ Y5 )
% 5.82/6.21 & ( ord_less_eq_real @ Y5 @ M9 ) )
% 5.82/6.21 => ? [X4: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.21 & ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.21 & ( ( F @ X4 )
% 5.82/6.21 = Y5 ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_Lb_Ub
% 5.82/6.21 thf(fact_10036_LIM__fun__gt__zero,axiom,
% 5.82/6.21 ! [F: real > real,L: real,C2: real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.82/6.21 => ? [R3: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.82/6.21 & ! [X8: real] :
% 5.82/6.21 ( ( ( X8 != C2 )
% 5.82/6.21 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X8 ) ) @ R3 ) )
% 5.82/6.21 => ( ord_less_real @ zero_zero_real @ ( F @ X8 ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIM_fun_gt_zero
% 5.82/6.21 thf(fact_10037_LIM__fun__not__zero,axiom,
% 5.82/6.21 ! [F: real > real,L: real,C2: real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( L != zero_zero_real )
% 5.82/6.21 => ? [R3: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.82/6.21 & ! [X8: real] :
% 5.82/6.21 ( ( ( X8 != C2 )
% 5.82/6.21 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X8 ) ) @ R3 ) )
% 5.82/6.21 => ( ( F @ X8 )
% 5.82/6.21 != zero_zero_real ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIM_fun_not_zero
% 5.82/6.21 thf(fact_10038_LIM__fun__less__zero,axiom,
% 5.82/6.21 ! [F: real > real,L: real,C2: real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.82/6.21 => ? [R3: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.82/6.21 & ! [X8: real] :
% 5.82/6.21 ( ( ( X8 != C2 )
% 5.82/6.21 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X8 ) ) @ R3 ) )
% 5.82/6.21 => ( ord_less_real @ ( F @ X8 ) @ zero_zero_real ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIM_fun_less_zero
% 5.82/6.21 thf(fact_10039_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.82/6.21 ! [L: int,U: int] :
% 5.82/6.21 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.82/6.21 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.82/6.21 thf(fact_10040_isCont__inverse__function2,axiom,
% 5.82/6.21 ! [A2: real,X2: real,B2: real,G: real > real,F: real > real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ X2 )
% 5.82/6.21 => ( ( ord_less_real @ X2 @ B2 )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ Z2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.82/6.21 => ( ( G @ ( F @ Z2 ) )
% 5.82/6.21 = Z2 ) ) )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ Z2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_inverse_function2
% 5.82/6.21 thf(fact_10041_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 5.82/6.21 ! [L: code_integer,U: code_integer] :
% 5.82/6.21 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 5.82/6.21 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 5.82/6.21 thf(fact_10042_isCont__arcosh,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_arcosh
% 5.82/6.21 thf(fact_10043_LIM__cos__div__sin,axiom,
% 5.82/6.21 ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIM_cos_div_sin
% 5.82/6.21 thf(fact_10044_isCont__arccos,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.21 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_arccos
% 5.82/6.21 thf(fact_10045_isCont__arcsin,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.21 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_arcsin
% 5.82/6.21 thf(fact_10046_LIM__less__bound,axiom,
% 5.82/6.21 ! [B2: real,X2: real,F: real > real] :
% 5.82/6.21 ( ( ord_less_real @ B2 @ X2 )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B2 @ X2 ) )
% 5.82/6.21 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.82/6.21 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ F )
% 5.82/6.21 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIM_less_bound
% 5.82/6.21 thf(fact_10047_isCont__artanh,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.82/6.21 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_artanh
% 5.82/6.21 thf(fact_10048_isCont__inverse__function,axiom,
% 5.82/6.21 ! [D2: real,X2: real,G: real > real,F: real > real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X2 ) ) @ D2 )
% 5.82/6.21 => ( ( G @ ( F @ Z2 ) )
% 5.82/6.21 = Z2 ) )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X2 ) ) @ D2 )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % isCont_inverse_function
% 5.82/6.21 thf(fact_10049_GMVT_H,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real,G: real > real,G2: real > real,F5: real > real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ Z2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ Z2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ Z2 )
% 5.82/6.21 => ( ( ord_less_real @ Z2 @ B2 )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.82/6.21 => ( ! [Z2: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ Z2 )
% 5.82/6.21 => ( ( ord_less_real @ Z2 @ B2 )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ F @ ( F5 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.82/6.21 => ? [C3: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ C3 )
% 5.82/6.21 & ( ord_less_real @ C3 @ B2 )
% 5.82/6.21 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) ) @ ( G2 @ C3 ) )
% 5.82/6.21 = ( times_times_real @ ( minus_minus_real @ ( G @ B2 ) @ ( G @ A2 ) ) @ ( F5 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % GMVT'
% 5.82/6.21 thf(fact_10050_summable__Leibniz_I2_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.82/6.21 => ( ( ord_less_real @ zero_zero_real @ ( A2 @ zero_zero_nat ) )
% 5.82/6.21 => ! [N9: nat] :
% 5.82/6.21 ( member_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) )
% 5.82/6.21 @ ( set_or1222579329274155063t_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz(2)
% 5.82/6.21 thf(fact_10051_summable__Leibniz_I3_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.82/6.21 => ( ( ord_less_real @ ( A2 @ zero_zero_nat ) @ zero_zero_real )
% 5.82/6.21 => ! [N9: nat] :
% 5.82/6.21 ( member_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) )
% 5.82/6.21 @ ( set_or1222579329274155063t_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz(3)
% 5.82/6.21 thf(fact_10052_mult__nat__right__at__top,axiom,
% 5.82/6.21 ! [C2: nat] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.21 => ( filterlim_nat_nat
% 5.82/6.21 @ ^ [X3: nat] : ( times_times_nat @ X3 @ C2 )
% 5.82/6.21 @ at_top_nat
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % mult_nat_right_at_top
% 5.82/6.21 thf(fact_10053_mult__nat__left__at__top,axiom,
% 5.82/6.21 ! [C2: nat] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 5.82/6.21 => ( filterlim_nat_nat @ ( times_times_nat @ C2 ) @ at_top_nat @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % mult_nat_left_at_top
% 5.82/6.21 thf(fact_10054_monoseq__convergent,axiom,
% 5.82/6.21 ! [X: nat > real,B: real] :
% 5.82/6.21 ( ( topolo6980174941875973593q_real @ X )
% 5.82/6.21 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X @ I2 ) ) @ B )
% 5.82/6.21 => ~ ! [L6: real] :
% 5.82/6.21 ~ ( filterlim_nat_real @ X @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % monoseq_convergent
% 5.82/6.21 thf(fact_10055_LIMSEQ__root,axiom,
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( root @ N4 @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_root
% 5.82/6.21 thf(fact_10056_nested__sequence__unique,axiom,
% 5.82/6.21 ! [F: nat > real,G: nat > real] :
% 5.82/6.21 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.82/6.21 => ( ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat )
% 5.82/6.21 => ? [L2: real] :
% 5.82/6.21 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L2 )
% 5.82/6.21 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat )
% 5.82/6.21 & ! [N9: nat] : ( ord_less_eq_real @ L2 @ ( G @ N9 ) )
% 5.82/6.21 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % nested_sequence_unique
% 5.82/6.21 thf(fact_10057_LIMSEQ__inverse__zero,axiom,
% 5.82/6.21 ! [X: nat > real] :
% 5.82/6.21 ( ! [R3: real] :
% 5.82/6.21 ? [N10: nat] :
% 5.82/6.21 ! [N3: nat] :
% 5.82/6.21 ( ( ord_less_eq_nat @ N10 @ N3 )
% 5.82/6.21 => ( ord_less_real @ R3 @ ( X @ N3 ) ) )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X @ N4 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_inverse_zero
% 5.82/6.21 thf(fact_10058_lim__inverse__n_H,axiom,
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % lim_inverse_n'
% 5.82/6.21 thf(fact_10059_LIMSEQ__inverse__real__of__nat,axiom,
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_inverse_real_of_nat
% 5.82/6.21 thf(fact_10060_LIMSEQ__root__const,axiom,
% 5.82/6.21 ! [C2: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ C2 )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( root @ N4 @ C2 )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_root_const
% 5.82/6.21 thf(fact_10061_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.82/6.21 ! [R2: real] :
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ R2 )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_inverse_real_of_nat_add
% 5.82/6.21 thf(fact_10062_increasing__LIMSEQ,axiom,
% 5.82/6.21 ! [F: nat > real,L: real] :
% 5.82/6.21 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 5.82/6.21 => ( ! [E2: real] :
% 5.82/6.21 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.82/6.21 => ? [N9: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 5.82/6.21 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % increasing_LIMSEQ
% 5.82/6.21 thf(fact_10063_LIMSEQ__realpow__zero,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.21 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.82/6.21 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_realpow_zero
% 5.82/6.21 thf(fact_10064_LIMSEQ__divide__realpow__zero,axiom,
% 5.82/6.21 ! [X2: real,A2: real] :
% 5.82/6.21 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( divide_divide_real @ A2 @ ( power_power_real @ X2 @ N4 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_divide_realpow_zero
% 5.82/6.21 thf(fact_10065_LIMSEQ__abs__realpow__zero2,axiom,
% 5.82/6.21 ! [C2: real] :
% 5.82/6.21 ( ( ord_less_real @ ( abs_abs_real @ C2 ) @ one_one_real )
% 5.82/6.21 => ( filterlim_nat_real @ ( power_power_real @ C2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_abs_realpow_zero2
% 5.82/6.21 thf(fact_10066_LIMSEQ__abs__realpow__zero,axiom,
% 5.82/6.21 ! [C2: real] :
% 5.82/6.21 ( ( ord_less_real @ ( abs_abs_real @ C2 ) @ one_one_real )
% 5.82/6.21 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C2 ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_abs_realpow_zero
% 5.82/6.21 thf(fact_10067_LIMSEQ__inverse__realpow__zero,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_real @ one_one_real @ X2 )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N4 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_inverse_realpow_zero
% 5.82/6.21 thf(fact_10068_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.82/6.21 ! [R2: real] :
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ R2 )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.82/6.21 thf(fact_10069_tendsto__exp__limit__sequentially,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N4 ) ) ) @ N4 )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % tendsto_exp_limit_sequentially
% 5.82/6.21 thf(fact_10070_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.82/6.21 ! [R2: real] :
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ R2 )
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.82/6.21 thf(fact_10071_summable__Leibniz_I1_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.82/6.21 => ( summable_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A2 @ N4 ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz(1)
% 5.82/6.21 thf(fact_10072_summable,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.82/6.21 => ( summable_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A2 @ N4 ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable
% 5.82/6.21 thf(fact_10073_cos__diff__limit__1,axiom,
% 5.82/6.21 ! [Theta: nat > real,Theta2: real] :
% 5.82/6.21 ( ( filterlim_nat_real
% 5.82/6.21 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.82/6.21 @ at_top_nat )
% 5.82/6.21 => ~ ! [K2: nat > int] :
% 5.82/6.21 ~ ( filterlim_nat_real
% 5.82/6.21 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % cos_diff_limit_1
% 5.82/6.21 thf(fact_10074_cos__limit__1,axiom,
% 5.82/6.21 ! [Theta: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real
% 5.82/6.21 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.82/6.21 @ at_top_nat )
% 5.82/6.21 => ? [K2: nat > int] :
% 5.82/6.21 ( filterlim_nat_real
% 5.82/6.21 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % cos_limit_1
% 5.82/6.21 thf(fact_10075_summable__Leibniz_I4_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] :
% 5.82/6.21 ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) )
% 5.82/6.21 @ at_top_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz(4)
% 5.82/6.21 thf(fact_10076_zeroseq__arctan__series,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % zeroseq_arctan_series
% 5.82/6.21 thf(fact_10077_summable__Leibniz_H_I3_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] :
% 5.82/6.21 ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) )
% 5.82/6.21 @ at_top_nat ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz'(3)
% 5.82/6.21 thf(fact_10078_summable__Leibniz_H_I2_J,axiom,
% 5.82/6.21 ! [A2: nat > real,N: nat] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ord_less_eq_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz'(2)
% 5.82/6.21 thf(fact_10079_sums__alternating__upper__lower,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ? [L2: real] :
% 5.82/6.21 ( ! [N9: nat] :
% 5.82/6.21 ( ord_less_eq_real
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.82/6.21 @ L2 )
% 5.82/6.21 & ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] :
% 5.82/6.21 ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ L2 )
% 5.82/6.21 @ at_top_nat )
% 5.82/6.21 & ! [N9: nat] :
% 5.82/6.21 ( ord_less_eq_real @ L2
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 5.82/6.21 & ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] :
% 5.82/6.21 ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ L2 )
% 5.82/6.21 @ at_top_nat ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % sums_alternating_upper_lower
% 5.82/6.21 thf(fact_10080_summable__Leibniz_I5_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] :
% 5.82/6.21 ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) )
% 5.82/6.21 @ at_top_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz(5)
% 5.82/6.21 thf(fact_10081_summable__Leibniz_H_I5_J,axiom,
% 5.82/6.21 ! [A2: nat > real] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.82/6.21 => ( filterlim_nat_real
% 5.82/6.21 @ ^ [N4: nat] :
% 5.82/6.21 ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) )
% 5.82/6.21 @ at_top_nat ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz'(5)
% 5.82/6.21 thf(fact_10082_summable__Leibniz_H_I4_J,axiom,
% 5.82/6.21 ! [A2: nat > real,N: nat] :
% 5.82/6.21 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.82/6.21 => ( ord_less_eq_real
% 5.82/6.21 @ ( suminf_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) )
% 5.82/6.21 @ ( groups6591440286371151544t_real
% 5.82/6.21 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.82/6.21 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % summable_Leibniz'(4)
% 5.82/6.21 thf(fact_10083_filterlim__Suc,axiom,
% 5.82/6.21 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.82/6.21
% 5.82/6.21 % filterlim_Suc
% 5.82/6.21 thf(fact_10084_dist__complex__def,axiom,
% 5.82/6.21 ( real_V3694042436643373181omplex
% 5.82/6.21 = ( ^ [X3: complex,Y: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % dist_complex_def
% 5.82/6.21 thf(fact_10085_dist__real__def,axiom,
% 5.82/6.21 ( real_V975177566351809787t_real
% 5.82/6.21 = ( ^ [X3: real,Y: real] : ( abs_abs_real @ ( minus_minus_real @ X3 @ Y ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % dist_real_def
% 5.82/6.21 thf(fact_10086_tendsto__exp__limit__at__right,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( filterlim_real_real
% 5.82/6.21 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X2 @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % tendsto_exp_limit_at_right
% 5.82/6.21 thf(fact_10087_tendsto__arctan__at__bot,axiom,
% 5.82/6.21 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.82/6.21
% 5.82/6.21 % tendsto_arctan_at_bot
% 5.82/6.21 thf(fact_10088_artanh__real__at__right__1,axiom,
% 5.82/6.21 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % artanh_real_at_right_1
% 5.82/6.21 thf(fact_10089_ln__at__0,axiom,
% 5.82/6.21 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % ln_at_0
% 5.82/6.21 thf(fact_10090_filterlim__tan__at__right,axiom,
% 5.82/6.21 filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % filterlim_tan_at_right
% 5.82/6.21 thf(fact_10091_filterlim__inverse__at__bot__neg,axiom,
% 5.82/6.21 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % filterlim_inverse_at_bot_neg
% 5.82/6.21 thf(fact_10092_log__inj,axiom,
% 5.82/6.21 ! [B2: real] :
% 5.82/6.21 ( ( ord_less_real @ one_one_real @ B2 )
% 5.82/6.21 => ( inj_on_real_real @ ( log @ B2 ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % log_inj
% 5.82/6.21 thf(fact_10093_tanh__real__at__bot,axiom,
% 5.82/6.21 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.82/6.21
% 5.82/6.21 % tanh_real_at_bot
% 5.82/6.21 thf(fact_10094_tendsto__arcosh__at__left__1,axiom,
% 5.82/6.21 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % tendsto_arcosh_at_left_1
% 5.82/6.21 thf(fact_10095_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.82/6.21 ! [B2: real,F: real > real,Flim: real] :
% 5.82/6.21 ( ! [X4: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ X4 @ B2 )
% 5.82/6.21 => ? [Y5: real] :
% 5.82/6.21 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.21 & ( ord_less_real @ zero_zero_real @ Y5 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.82/6.21 => ( ord_less_real @ Flim @ ( F @ B2 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_pos_imp_increasing_at_bot
% 5.82/6.21 thf(fact_10096_filterlim__pow__at__bot__odd,axiom,
% 5.82/6.21 ! [N: nat,F: real > real,F3: filter_real] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 5.82/6.21 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ F3 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % filterlim_pow_at_bot_odd
% 5.82/6.21 thf(fact_10097_filterlim__pow__at__bot__even,axiom,
% 5.82/6.21 ! [N: nat,F: real > real,F3: filter_real] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 5.82/6.21 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ F3 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % filterlim_pow_at_bot_even
% 5.82/6.21 thf(fact_10098_at__bot__le__at__infinity,axiom,
% 5.82/6.21 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.82/6.21
% 5.82/6.21 % at_bot_le_at_infinity
% 5.82/6.21 thf(fact_10099_at__top__le__at__infinity,axiom,
% 5.82/6.21 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.82/6.21
% 5.82/6.21 % at_top_le_at_infinity
% 5.82/6.21 thf(fact_10100_ln__at__top,axiom,
% 5.82/6.21 filterlim_real_real @ ln_ln_real @ at_top_real @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % ln_at_top
% 5.82/6.21 thf(fact_10101_sqrt__at__top,axiom,
% 5.82/6.21 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % sqrt_at_top
% 5.82/6.21 thf(fact_10102_exp__at__top,axiom,
% 5.82/6.21 filterlim_real_real @ exp_real @ at_top_real @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % exp_at_top
% 5.82/6.21 thf(fact_10103_filterlim__real__sequentially,axiom,
% 5.82/6.21 filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 5.82/6.21
% 5.82/6.21 % filterlim_real_sequentially
% 5.82/6.21 thf(fact_10104_filterlim__uminus__at__bot__at__top,axiom,
% 5.82/6.21 filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % filterlim_uminus_at_bot_at_top
% 5.82/6.21 thf(fact_10105_filterlim__uminus__at__top__at__bot,axiom,
% 5.82/6.21 filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real ).
% 5.82/6.21
% 5.82/6.21 % filterlim_uminus_at_top_at_bot
% 5.82/6.21 thf(fact_10106_greaterThan__0,axiom,
% 5.82/6.21 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.82/6.21 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % greaterThan_0
% 5.82/6.21 thf(fact_10107_greaterThan__Suc,axiom,
% 5.82/6.21 ! [K: nat] :
% 5.82/6.21 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.82/6.21 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % greaterThan_Suc
% 5.82/6.21 thf(fact_10108_tanh__real__at__top,axiom,
% 5.82/6.21 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % tanh_real_at_top
% 5.82/6.21 thf(fact_10109_artanh__real__at__left__1,axiom,
% 5.82/6.21 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % artanh_real_at_left_1
% 5.82/6.21 thf(fact_10110_ln__x__over__x__tendsto__0,axiom,
% 5.82/6.21 ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_real ) ).
% 5.82/6.21
% 5.82/6.21 % ln_x_over_x_tendsto_0
% 5.82/6.21 thf(fact_10111_filterlim__inverse__at__right__top,axiom,
% 5.82/6.21 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % filterlim_inverse_at_right_top
% 5.82/6.21 thf(fact_10112_filterlim__inverse__at__top__right,axiom,
% 5.82/6.21 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % filterlim_inverse_at_top_right
% 5.82/6.21 thf(fact_10113_tendsto__power__div__exp__0,axiom,
% 5.82/6.21 ! [K: nat] :
% 5.82/6.21 ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( power_power_real @ X3 @ K ) @ ( exp_real @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.82/6.21 @ at_top_real ) ).
% 5.82/6.21
% 5.82/6.21 % tendsto_power_div_exp_0
% 5.82/6.21 thf(fact_10114_tendsto__exp__limit__at__top,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( filterlim_real_real
% 5.82/6.21 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ Y ) ) @ Y )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.82/6.21 @ at_top_real ) ).
% 5.82/6.21
% 5.82/6.21 % tendsto_exp_limit_at_top
% 5.82/6.21 thf(fact_10115_filterlim__tan__at__left,axiom,
% 5.82/6.21 filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % filterlim_tan_at_left
% 5.82/6.21 thf(fact_10116_tendsto__arctan__at__top,axiom,
% 5.82/6.21 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.82/6.21
% 5.82/6.21 % tendsto_arctan_at_top
% 5.82/6.21 thf(fact_10117_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.82/6.21 ! [B2: real,F: real > real,Flim: real] :
% 5.82/6.21 ( ! [X4: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ B2 @ X4 )
% 5.82/6.21 => ? [Y5: real] :
% 5.82/6.21 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.82/6.21 & ( ord_less_real @ Y5 @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.82/6.21 => ( ord_less_real @ Flim @ ( F @ B2 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_neg_imp_decreasing_at_top
% 5.82/6.21 thf(fact_10118_lhopital__left__at__top,axiom,
% 5.82/6.21 ! [G: real > real,X2: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 5.82/6.21 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_left_at_top
% 5.82/6.21 thf(fact_10119_eventually__sequentially__Suc,axiom,
% 5.82/6.21 ! [P: nat > $o] :
% 5.82/6.21 ( ( eventually_nat
% 5.82/6.21 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 5.82/6.21 @ at_top_nat )
% 5.82/6.21 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_sequentially_Suc
% 5.82/6.21 thf(fact_10120_eventually__sequentially__seg,axiom,
% 5.82/6.21 ! [P: nat > $o,K: nat] :
% 5.82/6.21 ( ( eventually_nat
% 5.82/6.21 @ ^ [N4: nat] : ( P @ ( plus_plus_nat @ N4 @ K ) )
% 5.82/6.21 @ at_top_nat )
% 5.82/6.21 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_sequentially_seg
% 5.82/6.21 thf(fact_10121_sequentially__offset,axiom,
% 5.82/6.21 ! [P: nat > $o,K: nat] :
% 5.82/6.21 ( ( eventually_nat @ P @ at_top_nat )
% 5.82/6.21 => ( eventually_nat
% 5.82/6.21 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 5.82/6.21 @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % sequentially_offset
% 5.82/6.21 thf(fact_10122_le__sequentially,axiom,
% 5.82/6.21 ! [F3: filter_nat] :
% 5.82/6.21 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 5.82/6.21 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F3 ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % le_sequentially
% 5.82/6.21 thf(fact_10123_eventually__sequentially,axiom,
% 5.82/6.21 ! [P: nat > $o] :
% 5.82/6.21 ( ( eventually_nat @ P @ at_top_nat )
% 5.82/6.21 = ( ? [N8: nat] :
% 5.82/6.21 ! [N4: nat] :
% 5.82/6.21 ( ( ord_less_eq_nat @ N8 @ N4 )
% 5.82/6.21 => ( P @ N4 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_sequentially
% 5.82/6.21 thf(fact_10124_eventually__sequentiallyI,axiom,
% 5.82/6.21 ! [C2: nat,P: nat > $o] :
% 5.82/6.21 ( ! [X4: nat] :
% 5.82/6.21 ( ( ord_less_eq_nat @ C2 @ X4 )
% 5.82/6.21 => ( P @ X4 ) )
% 5.82/6.21 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_sequentiallyI
% 5.82/6.21 thf(fact_10125_eventually__False__sequentially,axiom,
% 5.82/6.21 ~ ( eventually_nat
% 5.82/6.21 @ ^ [N4: nat] : $false
% 5.82/6.21 @ at_top_nat ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_False_sequentially
% 5.82/6.21 thf(fact_10126_eventually__at__right__to__0,axiom,
% 5.82/6.21 ! [P: real > $o,A2: real] :
% 5.82/6.21 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 = ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( P @ ( plus_plus_real @ X3 @ A2 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_at_right_to_0
% 5.82/6.21 thf(fact_10127_eventually__at__left__to__right,axiom,
% 5.82/6.21 ! [P: real > $o,A2: real] :
% 5.82/6.21 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 = ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( P @ ( uminus_uminus_real @ X3 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A2 ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A2 ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_at_left_to_right
% 5.82/6.21 thf(fact_10128_eventually__at__right__real,axiom,
% 5.82/6.21 ! [A2: real,B2: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.21 => ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A2 @ B2 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_at_right_real
% 5.82/6.21 thf(fact_10129_eventually__at__left__real,axiom,
% 5.82/6.21 ! [B2: real,A2: real] :
% 5.82/6.21 ( ( ord_less_real @ B2 @ A2 )
% 5.82/6.21 => ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B2 @ A2 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_at_left_real
% 5.82/6.21 thf(fact_10130_eventually__at__right__to__top,axiom,
% 5.82/6.21 ! [P: real > $o] :
% 5.82/6.21 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 = ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.82/6.21 @ at_top_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_at_right_to_top
% 5.82/6.21 thf(fact_10131_eventually__at__top__to__right,axiom,
% 5.82/6.21 ! [P: real > $o] :
% 5.82/6.21 ( ( eventually_real @ P @ at_top_real )
% 5.82/6.21 = ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % eventually_at_top_to_right
% 5.82/6.21 thf(fact_10132_lhopital__at__top__at__top,axiom,
% 5.82/6.21 ! [F: real > real,A2: real,G: real > real,F5: real > real,G2: real > real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_at_top_at_top
% 5.82/6.21 thf(fact_10133_lhopital,axiom,
% 5.82/6.21 ! [F: real > real,X2: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital
% 5.82/6.21 thf(fact_10134_lhopital__right__at__top__at__top,axiom,
% 5.82/6.21 ! [F: real > real,A2: real,G: real > real,F5: real > real,G2: real > real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_right_at_top_at_top
% 5.82/6.21 thf(fact_10135_lhopital__at__top__at__bot,axiom,
% 5.82/6.21 ! [F: real > real,A2: real,G: real > real,F5: real > real,G2: real > real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_at_top_at_bot
% 5.82/6.21 thf(fact_10136_lhopital__left__at__top__at__top,axiom,
% 5.82/6.21 ! [F: real > real,A2: real,G: real > real,F5: real > real,G2: real > real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ at_top_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_left_at_top_at_top
% 5.82/6.21 thf(fact_10137_lhopital__at__top,axiom,
% 5.82/6.21 ! [G: real > real,X2: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 5.82/6.21 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_at_top
% 5.82/6.21 thf(fact_10138_lhospital__at__top__at__top,axiom,
% 5.82/6.21 ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X2: real] :
% 5.82/6.21 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ at_top_real )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ at_top_real )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ at_top_real )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ X2 )
% 5.82/6.21 @ at_top_real )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ X2 )
% 5.82/6.21 @ at_top_real ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhospital_at_top_at_top
% 5.82/6.21 thf(fact_10139_lhopital__right,axiom,
% 5.82/6.21 ! [F: real > real,X2: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_right
% 5.82/6.21 thf(fact_10140_lhopital__right__0,axiom,
% 5.82/6.21 ! [F0: real > real,G0: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.82/6.21 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G0 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F0 @ X3 ) @ ( G0 @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_right_0
% 5.82/6.21 thf(fact_10141_lhopital__left,axiom,
% 5.82/6.21 ! [F: real > real,X2: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ F3
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_left
% 5.82/6.21 thf(fact_10142_lhopital__right__at__top__at__bot,axiom,
% 5.82/6.21 ! [F: real > real,A2: real,G: real > real,F5: real > real,G2: real > real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_right_at_top_at_bot
% 5.82/6.21 thf(fact_10143_lhopital__left__at__top__at__bot,axiom,
% 5.82/6.21 ! [F: real > real,A2: real,G: real > real,F5: real > real,G2: real > real] :
% 5.82/6.21 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ at_bot_real
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_left_at_top_at_bot
% 5.82/6.21 thf(fact_10144_lhopital__right__at__top,axiom,
% 5.82/6.21 ! [G: real > real,X2: real,G2: real > real,F: real > real,F5: real > real,Y3: real] :
% 5.82/6.21 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_right_at_top
% 5.82/6.21 thf(fact_10145_lhopital__right__0__at__top,axiom,
% 5.82/6.21 ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X2: real] :
% 5.82/6.21 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] :
% 5.82/6.21 ( ( G2 @ X3 )
% 5.82/6.21 != zero_zero_real )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( eventually_real
% 5.82/6.21 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ X2 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.82/6.21 => ( filterlim_real_real
% 5.82/6.21 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.82/6.21 @ ( topolo2815343760600316023s_real @ X2 )
% 5.82/6.21 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % lhopital_right_0_at_top
% 5.82/6.21 thf(fact_10146_Bseq__eq__bounded,axiom,
% 5.82/6.21 ! [F: nat > real,A2: real,B2: real] :
% 5.82/6.21 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A2 @ B2 ) )
% 5.82/6.21 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % Bseq_eq_bounded
% 5.82/6.21 thf(fact_10147_Bseq__realpow,axiom,
% 5.82/6.21 ! [X2: real] :
% 5.82/6.21 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.82/6.21 => ( bfun_nat_real @ ( power_power_real @ X2 ) @ at_top_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Bseq_realpow
% 5.82/6.21 thf(fact_10148_GreatestI__ex__nat,axiom,
% 5.82/6.21 ! [P: nat > $o,B2: nat] :
% 5.82/6.21 ( ? [X_12: nat] : ( P @ X_12 )
% 5.82/6.21 => ( ! [Y4: nat] :
% 5.82/6.21 ( ( P @ Y4 )
% 5.82/6.21 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.82/6.21 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % GreatestI_ex_nat
% 5.82/6.21 thf(fact_10149_Greatest__le__nat,axiom,
% 5.82/6.21 ! [P: nat > $o,K: nat,B2: nat] :
% 5.82/6.21 ( ( P @ K )
% 5.82/6.21 => ( ! [Y4: nat] :
% 5.82/6.21 ( ( P @ Y4 )
% 5.82/6.21 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.82/6.21 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % Greatest_le_nat
% 5.82/6.21 thf(fact_10150_GreatestI__nat,axiom,
% 5.82/6.21 ! [P: nat > $o,K: nat,B2: nat] :
% 5.82/6.21 ( ( P @ K )
% 5.82/6.21 => ( ! [Y4: nat] :
% 5.82/6.21 ( ( P @ Y4 )
% 5.82/6.21 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.82/6.21 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % GreatestI_nat
% 5.82/6.21 thf(fact_10151_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.82/6.21 ! [L: nat,U: nat] :
% 5.82/6.21 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.82/6.21 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeastSucAtMost_greaterThanAtMost
% 5.82/6.21 thf(fact_10152_suminf__eq__SUP__real,axiom,
% 5.82/6.21 ! [X: nat > real] :
% 5.82/6.21 ( ( summable_real @ X )
% 5.82/6.21 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X @ I2 ) )
% 5.82/6.21 => ( ( suminf_real @ X )
% 5.82/6.21 = ( comple1385675409528146559p_real
% 5.82/6.21 @ ( image_nat_real
% 5.82/6.21 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X @ ( set_ord_lessThan_nat @ I4 ) )
% 5.82/6.21 @ top_top_set_nat ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % suminf_eq_SUP_real
% 5.82/6.21 thf(fact_10153_finite__greaterThanAtMost__integer,axiom,
% 5.82/6.21 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % finite_greaterThanAtMost_integer
% 5.82/6.21 thf(fact_10154_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.82/6.21 ! [L: int,U: int] :
% 5.82/6.21 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.82/6.21 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.82/6.21 thf(fact_10155_decseq__bounded,axiom,
% 5.82/6.21 ! [X: nat > real,B: real] :
% 5.82/6.21 ( ( order_9091379641038594480t_real @ X )
% 5.82/6.21 => ( ! [I2: nat] : ( ord_less_eq_real @ B @ ( X @ I2 ) )
% 5.82/6.21 => ( bfun_nat_real @ X @ at_top_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % decseq_bounded
% 5.82/6.21 thf(fact_10156_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 5.82/6.21 ! [L: code_integer,U: code_integer] :
% 5.82/6.21 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 5.82/6.21 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 5.82/6.21 thf(fact_10157_decseq__convergent,axiom,
% 5.82/6.21 ! [X: nat > real,B: real] :
% 5.82/6.21 ( ( order_9091379641038594480t_real @ X )
% 5.82/6.21 => ( ! [I2: nat] : ( ord_less_eq_real @ B @ ( X @ I2 ) )
% 5.82/6.21 => ~ ! [L6: real] :
% 5.82/6.21 ( ( filterlim_nat_real @ X @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.82/6.21 => ~ ! [I5: nat] : ( ord_less_eq_real @ L6 @ ( X @ I5 ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % decseq_convergent
% 5.82/6.21 thf(fact_10158_UN__lessThan__UNIV,axiom,
% 5.82/6.21 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.82/6.21 = top_top_set_nat ) ).
% 5.82/6.21
% 5.82/6.21 % UN_lessThan_UNIV
% 5.82/6.21 thf(fact_10159_UN__atMost__UNIV,axiom,
% 5.82/6.21 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.82/6.21 = top_top_set_nat ) ).
% 5.82/6.21
% 5.82/6.21 % UN_atMost_UNIV
% 5.82/6.21 thf(fact_10160_atLeast__Suc__greaterThan,axiom,
% 5.82/6.21 ! [K: nat] :
% 5.82/6.21 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.82/6.21 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeast_Suc_greaterThan
% 5.82/6.21 thf(fact_10161_atLeast__Suc,axiom,
% 5.82/6.21 ! [K: nat] :
% 5.82/6.21 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.82/6.21 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % atLeast_Suc
% 5.82/6.21 thf(fact_10162_UN__atLeast__UNIV,axiom,
% 5.82/6.21 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.82/6.21 = top_top_set_nat ) ).
% 5.82/6.21
% 5.82/6.21 % UN_atLeast_UNIV
% 5.82/6.21 thf(fact_10163_GMVT,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real,G: real > real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.21 & ( ord_less_eq_real @ X4 @ B2 ) )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ( ord_less_real @ A2 @ X4 )
% 5.82/6.21 & ( ord_less_real @ X4 @ B2 ) )
% 5.82/6.21 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ( ord_less_eq_real @ A2 @ X4 )
% 5.82/6.21 & ( ord_less_eq_real @ X4 @ B2 ) )
% 5.82/6.21 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ( ord_less_real @ A2 @ X4 )
% 5.82/6.21 & ( ord_less_real @ X4 @ B2 ) )
% 5.82/6.21 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.82/6.21 => ? [G_c: real,F_c: real,C3: real] :
% 5.82/6.21 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.82/6.21 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.82/6.21 & ( ord_less_real @ A2 @ C3 )
% 5.82/6.21 & ( ord_less_real @ C3 @ B2 )
% 5.82/6.21 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) ) @ G_c )
% 5.82/6.21 = ( times_times_real @ ( minus_minus_real @ ( G @ B2 ) @ ( G @ A2 ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % GMVT
% 5.82/6.21 thf(fact_10164_MVT,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.21 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ F )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ X4 )
% 5.82/6.21 => ( ( ord_less_real @ X4 @ B2 )
% 5.82/6.21 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.82/6.21 => ? [L2: real,Z2: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ Z2 )
% 5.82/6.21 & ( ord_less_real @ Z2 @ B2 )
% 5.82/6.21 & ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.82/6.21 & ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) )
% 5.82/6.21 = ( times_times_real @ ( minus_minus_real @ B2 @ A2 ) @ L2 ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % MVT
% 5.82/6.21 thf(fact_10165_card__UNIV__unit,axiom,
% 5.82/6.21 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.82/6.21 = one_one_nat ) ).
% 5.82/6.21
% 5.82/6.21 % card_UNIV_unit
% 5.82/6.21 thf(fact_10166_card__Collect__less__nat,axiom,
% 5.82/6.21 ! [N: nat] :
% 5.82/6.21 ( ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.82/6.21 = N ) ).
% 5.82/6.21
% 5.82/6.21 % card_Collect_less_nat
% 5.82/6.21 thf(fact_10167_card__atMost,axiom,
% 5.82/6.21 ! [U: nat] :
% 5.82/6.21 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.82/6.21 = ( suc @ U ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_atMost
% 5.82/6.21 thf(fact_10168_card__atLeastLessThan,axiom,
% 5.82/6.21 ! [L: nat,U: nat] :
% 5.82/6.21 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.82/6.21 = ( minus_minus_nat @ U @ L ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_atLeastLessThan
% 5.82/6.21 thf(fact_10169_card__Collect__le__nat,axiom,
% 5.82/6.21 ! [N: nat] :
% 5.82/6.21 ( ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.82/6.21 = ( suc @ N ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_Collect_le_nat
% 5.82/6.21 thf(fact_10170_card__greaterThanAtMost,axiom,
% 5.82/6.21 ! [L: nat,U: nat] :
% 5.82/6.21 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.82/6.21 = ( minus_minus_nat @ U @ L ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_greaterThanAtMost
% 5.82/6.21 thf(fact_10171_card__UNIV__bool,axiom,
% 5.82/6.21 ( ( finite_card_o @ top_top_set_o )
% 5.82/6.21 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_UNIV_bool
% 5.82/6.21 thf(fact_10172_card__atLeastAtMost,axiom,
% 5.82/6.21 ! [L: nat,U: nat] :
% 5.82/6.21 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.82/6.21 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_atLeastAtMost
% 5.82/6.21 thf(fact_10173_card__atLeastLessThan__int,axiom,
% 5.82/6.21 ! [L: int,U: int] :
% 5.82/6.21 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.82/6.21 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_atLeastLessThan_int
% 5.82/6.21 thf(fact_10174_card__greaterThanLessThan,axiom,
% 5.82/6.21 ! [L: nat,U: nat] :
% 5.82/6.21 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.82/6.21 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_greaterThanLessThan
% 5.82/6.21 thf(fact_10175_card__greaterThanAtMost__int,axiom,
% 5.82/6.21 ! [L: int,U: int] :
% 5.82/6.21 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.82/6.21 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_greaterThanAtMost_int
% 5.82/6.21 thf(fact_10176_card__atLeastAtMost__int,axiom,
% 5.82/6.21 ! [L: int,U: int] :
% 5.82/6.21 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.82/6.21 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_atLeastAtMost_int
% 5.82/6.21 thf(fact_10177_card__greaterThanLessThan__int,axiom,
% 5.82/6.21 ! [L: int,U: int] :
% 5.82/6.21 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.82/6.21 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_greaterThanLessThan_int
% 5.82/6.21 thf(fact_10178_continuous__image__closed__interval,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real] :
% 5.82/6.21 ( ( ord_less_eq_real @ A2 @ B2 )
% 5.82/6.21 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ F )
% 5.82/6.21 => ? [C3: real,D4: real] :
% 5.82/6.21 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A2 @ B2 ) )
% 5.82/6.21 = ( set_or1222579329274155063t_real @ C3 @ D4 ) )
% 5.82/6.21 & ( ord_less_eq_real @ C3 @ D4 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % continuous_image_closed_interval
% 5.82/6.21 thf(fact_10179_continuous__on__arsinh_H,axiom,
% 5.82/6.21 ! [A: set_real,F: real > real] :
% 5.82/6.21 ( ( topolo5044208981011980120l_real @ A @ F )
% 5.82/6.21 => ( topolo5044208981011980120l_real @ A
% 5.82/6.21 @ ^ [X3: real] : ( arsinh_real @ ( F @ X3 ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_arsinh'
% 5.82/6.21 thf(fact_10180_card__less__Suc2,axiom,
% 5.82/6.21 ! [M8: set_nat,I: nat] :
% 5.82/6.21 ( ~ ( member_nat @ zero_zero_nat @ M8 )
% 5.82/6.21 => ( ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [K3: nat] :
% 5.82/6.21 ( ( member_nat @ ( suc @ K3 ) @ M8 )
% 5.82/6.21 & ( ord_less_nat @ K3 @ I ) ) ) )
% 5.82/6.21 = ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [K3: nat] :
% 5.82/6.21 ( ( member_nat @ K3 @ M8 )
% 5.82/6.21 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_less_Suc2
% 5.82/6.21 thf(fact_10181_card__less__Suc,axiom,
% 5.82/6.21 ! [M8: set_nat,I: nat] :
% 5.82/6.21 ( ( member_nat @ zero_zero_nat @ M8 )
% 5.82/6.21 => ( ( suc
% 5.82/6.21 @ ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [K3: nat] :
% 5.82/6.21 ( ( member_nat @ ( suc @ K3 ) @ M8 )
% 5.82/6.21 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 5.82/6.21 = ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [K3: nat] :
% 5.82/6.21 ( ( member_nat @ K3 @ M8 )
% 5.82/6.21 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_less_Suc
% 5.82/6.21 thf(fact_10182_card__less,axiom,
% 5.82/6.21 ! [M8: set_nat,I: nat] :
% 5.82/6.21 ( ( member_nat @ zero_zero_nat @ M8 )
% 5.82/6.21 => ( ( finite_card_nat
% 5.82/6.21 @ ( collect_nat
% 5.82/6.21 @ ^ [K3: nat] :
% 5.82/6.21 ( ( member_nat @ K3 @ M8 )
% 5.82/6.21 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 5.82/6.21 != zero_zero_nat ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_less
% 5.82/6.21 thf(fact_10183_subset__card__intvl__is__intvl,axiom,
% 5.82/6.21 ! [A: set_nat,K: nat] :
% 5.82/6.21 ( ( ord_less_eq_set_nat @ A @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A ) ) ) )
% 5.82/6.21 => ( A
% 5.82/6.21 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % subset_card_intvl_is_intvl
% 5.82/6.21 thf(fact_10184_continuous__on__arcosh_H,axiom,
% 5.82/6.21 ! [A: set_real,F: real > real] :
% 5.82/6.21 ( ( topolo5044208981011980120l_real @ A @ F )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( member_real @ X4 @ A )
% 5.82/6.21 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.82/6.21 => ( topolo5044208981011980120l_real @ A
% 5.82/6.21 @ ^ [X3: real] : ( arcosh_real @ ( F @ X3 ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_arcosh'
% 5.82/6.21 thf(fact_10185_continuous__on__arcosh,axiom,
% 5.82/6.21 ! [A: set_real] :
% 5.82/6.21 ( ( ord_less_eq_set_real @ A @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.82/6.21 => ( topolo5044208981011980120l_real @ A @ arcosh_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_arcosh
% 5.82/6.21 thf(fact_10186_continuous__on__arccos_H,axiom,
% 5.82/6.21 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_arccos'
% 5.82/6.21 thf(fact_10187_continuous__on__arcsin_H,axiom,
% 5.82/6.21 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_arcsin'
% 5.82/6.21 thf(fact_10188_subset__eq__atLeast0__lessThan__card,axiom,
% 5.82/6.21 ! [N7: set_nat,N: nat] :
% 5.82/6.21 ( ( ord_less_eq_set_nat @ N7 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.82/6.21 => ( ord_less_eq_nat @ ( finite_card_nat @ N7 ) @ N ) ) ).
% 5.82/6.21
% 5.82/6.21 % subset_eq_atLeast0_lessThan_card
% 5.82/6.21 thf(fact_10189_card__le__Suc__Max,axiom,
% 5.82/6.21 ! [S: set_nat] :
% 5.82/6.21 ( ( finite_finite_nat @ S )
% 5.82/6.21 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_le_Suc_Max
% 5.82/6.21 thf(fact_10190_card__sum__le__nat__sum,axiom,
% 5.82/6.21 ! [S: set_nat] :
% 5.82/6.21 ( ord_less_eq_nat
% 5.82/6.21 @ ( groups3542108847815614940at_nat
% 5.82/6.21 @ ^ [X3: nat] : X3
% 5.82/6.21 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 5.82/6.21 @ ( groups3542108847815614940at_nat
% 5.82/6.21 @ ^ [X3: nat] : X3
% 5.82/6.21 @ S ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_sum_le_nat_sum
% 5.82/6.21 thf(fact_10191_continuous__on__artanh_H,axiom,
% 5.82/6.21 ! [A: set_real,F: real > real] :
% 5.82/6.21 ( ( topolo5044208981011980120l_real @ A @ F )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( member_real @ X4 @ A )
% 5.82/6.21 => ( member_real @ ( F @ X4 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.82/6.21 => ( topolo5044208981011980120l_real @ A
% 5.82/6.21 @ ^ [X3: real] : ( artanh_real @ ( F @ X3 ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_artanh'
% 5.82/6.21 thf(fact_10192_card__nth__roots,axiom,
% 5.82/6.21 ! [C2: complex,N: nat] :
% 5.82/6.21 ( ( C2 != zero_zero_complex )
% 5.82/6.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( finite_card_complex
% 5.82/6.21 @ ( collect_complex
% 5.82/6.21 @ ^ [Z4: complex] :
% 5.82/6.21 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.21 = C2 ) ) )
% 5.82/6.21 = N ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_nth_roots
% 5.82/6.21 thf(fact_10193_card__roots__unity__eq,axiom,
% 5.82/6.21 ! [N: nat] :
% 5.82/6.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.82/6.21 => ( ( finite_card_complex
% 5.82/6.21 @ ( collect_complex
% 5.82/6.21 @ ^ [Z4: complex] :
% 5.82/6.21 ( ( power_power_complex @ Z4 @ N )
% 5.82/6.21 = one_one_complex ) ) )
% 5.82/6.21 = N ) ) ).
% 5.82/6.21
% 5.82/6.21 % card_roots_unity_eq
% 5.82/6.21 thf(fact_10194_mvt,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real,F5: real > real > real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.21 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ F )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ X4 )
% 5.82/6.21 => ( ( ord_less_real @ X4 @ B2 )
% 5.82/6.21 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.82/6.21 => ~ ! [Xi3: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ Xi3 )
% 5.82/6.21 => ( ( ord_less_real @ Xi3 @ B2 )
% 5.82/6.21 => ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A2 ) )
% 5.82/6.21 != ( F5 @ Xi3 @ ( minus_minus_real @ B2 @ A2 ) ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % mvt
% 5.82/6.21 thf(fact_10195_continuous__on__artanh,axiom,
% 5.82/6.21 ! [A: set_real] :
% 5.82/6.21 ( ( ord_less_eq_set_real @ A @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.82/6.21 => ( topolo5044208981011980120l_real @ A @ artanh_real ) ) ).
% 5.82/6.21
% 5.82/6.21 % continuous_on_artanh
% 5.82/6.21 thf(fact_10196_DERIV__isconst2,axiom,
% 5.82/6.21 ! [A2: real,B2: real,F: real > real,X2: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ B2 )
% 5.82/6.21 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B2 ) @ F )
% 5.82/6.21 => ( ! [X4: real] :
% 5.82/6.21 ( ( ord_less_real @ A2 @ X4 )
% 5.82/6.21 => ( ( ord_less_real @ X4 @ B2 )
% 5.82/6.21 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.82/6.21 => ( ( ord_less_eq_real @ A2 @ X2 )
% 5.82/6.21 => ( ( ord_less_eq_real @ X2 @ B2 )
% 5.82/6.21 => ( ( F @ X2 )
% 5.82/6.21 = ( F @ A2 ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 % DERIV_isconst2
% 5.82/6.21 thf(fact_10197_card__num1,axiom,
% 5.82/6.21 ( ( finite6454714172617411597l_num1 @ top_to3689904429138878997l_num1 )
% 5.82/6.21 = one_one_nat ) ).
% 5.82/6.21
% 5.82/6.21 % card_num1
% 5.82/6.21
% 5.82/6.21 % Helper facts (42)
% 5.82/6.21 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.82/6.21 ! [X2: int,Y3: int] :
% 5.82/6.21 ( ( if_int @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.82/6.21 ! [X2: int,Y3: int] :
% 5.82/6.21 ( ( if_int @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.82/6.21 ! [X2: nat,Y3: nat] :
% 5.82/6.21 ( ( if_nat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.82/6.21 ! [X2: nat,Y3: nat] :
% 5.82/6.21 ( ( if_nat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.82/6.21 ! [X2: num,Y3: num] :
% 5.82/6.21 ( ( if_num @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.82/6.21 ! [X2: num,Y3: num] :
% 5.82/6.21 ( ( if_num @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.82/6.21 ! [X2: rat,Y3: rat] :
% 5.82/6.21 ( ( if_rat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.82/6.21 ! [X2: rat,Y3: rat] :
% 5.82/6.21 ( ( if_rat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.82/6.21 ! [X2: real,Y3: real] :
% 5.82/6.21 ( ( if_real @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.82/6.21 ! [X2: real,Y3: real] :
% 5.82/6.21 ( ( if_real @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.82/6.21 ! [P: real > $o] :
% 5.82/6.21 ( ( P @ ( fChoice_real @ P ) )
% 5.82/6.21 = ( ? [X7: real] : ( P @ X7 ) ) ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 5.82/6.21 ! [X2: assn,Y3: assn] :
% 5.82/6.21 ( ( if_assn @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 5.82/6.21 ! [X2: assn,Y3: assn] :
% 5.82/6.21 ( ( if_assn @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.82/6.21 ! [X2: complex,Y3: complex] :
% 5.82/6.21 ( ( if_complex @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.82/6.21 ! [X2: complex,Y3: complex] :
% 5.82/6.21 ( ( if_complex @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.82/6.21 ! [X2: extended_enat,Y3: extended_enat] :
% 5.82/6.21 ( ( if_Extended_enat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.82/6.21 ! [X2: extended_enat,Y3: extended_enat] :
% 5.82/6.21 ( ( if_Extended_enat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.82/6.21 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.21 ( ( if_Code_integer @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.82/6.21 ! [X2: code_integer,Y3: code_integer] :
% 5.82/6.21 ( ( if_Code_integer @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.82/6.21 ! [X2: set_int,Y3: set_int] :
% 5.82/6.21 ( ( if_set_int @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.82/6.21 ! [X2: set_int,Y3: set_int] :
% 5.82/6.21 ( ( if_set_int @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.82/6.21 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.82/6.21 ( ( if_VEBT_VEBT @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.82/6.21 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.82/6.21 ( ( if_VEBT_VEBT @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.82/6.21 ! [X2: list_int,Y3: list_int] :
% 5.82/6.21 ( ( if_list_int @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.82/6.21 ! [X2: list_int,Y3: list_int] :
% 5.82/6.21 ( ( if_list_int @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.82/6.21 ! [X2: option_nat,Y3: option_nat] :
% 5.82/6.21 ( ( if_option_nat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.82/6.21 ! [X2: option_nat,Y3: option_nat] :
% 5.82/6.21 ( ( if_option_nat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_I_Eo_J_T,axiom,
% 5.82/6.21 ! [X2: heap_Time_Heap_o,Y3: heap_Time_Heap_o] :
% 5.82/6.21 ( ( if_Heap_Time_Heap_o @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_I_Eo_J_T,axiom,
% 5.82/6.21 ! [X2: heap_Time_Heap_o,Y3: heap_Time_Heap_o] :
% 5.82/6.21 ( ( if_Heap_Time_Heap_o @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Nat__Onat_J_T,axiom,
% 5.82/6.21 ! [X2: heap_Time_Heap_nat,Y3: heap_Time_Heap_nat] :
% 5.82/6.21 ( ( if_Hea2662716070787841314ap_nat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Nat__Onat_J_T,axiom,
% 5.82/6.21 ! [X2: heap_Time_Heap_nat,Y3: heap_Time_Heap_nat] :
% 5.82/6.21 ( ( if_Hea2662716070787841314ap_nat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.82/6.21 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 5.82/6.21 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.82/6.21 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 5.82/6.21 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.82/6.21 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.82/6.21 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.82/6.21 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.82/6.21 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__VEBT____BuildupMemImp__OVEBTi_J_T,axiom,
% 5.82/6.21 ! [X2: heap_T8145700208782473153_VEBTi,Y3: heap_T8145700208782473153_VEBTi] :
% 5.82/6.21 ( ( if_Hea8453224502484754311_VEBTi @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__VEBT____BuildupMemImp__OVEBTi_J_T,axiom,
% 5.82/6.21 ! [X2: heap_T8145700208782473153_VEBTi,Y3: heap_T8145700208782473153_VEBTi] :
% 5.82/6.21 ( ( if_Hea8453224502484754311_VEBTi @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Option__Ooption_It__Nat__Onat_J_J_T,axiom,
% 5.82/6.21 ! [X2: heap_T2636463487746394924on_nat,Y3: heap_T2636463487746394924on_nat] :
% 5.82/6.21 ( ( if_Hea5867803462524415986on_nat @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Option__Ooption_It__Nat__Onat_J_J_T,axiom,
% 5.82/6.21 ! [X2: heap_T2636463487746394924on_nat,Y3: heap_T2636463487746394924on_nat] :
% 5.82/6.21 ( ( if_Hea5867803462524415986on_nat @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.82/6.21 ! [P: $o] :
% 5.82/6.21 ( ( P = $true )
% 5.82/6.21 | ( P = $false ) ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.82/6.21 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 5.82/6.21 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y3 )
% 5.82/6.21 = Y3 ) ).
% 5.82/6.21
% 5.82/6.21 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.82/6.21 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 5.82/6.21 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y3 )
% 5.82/6.21 = X2 ) ).
% 5.82/6.21
% 5.82/6.21 % Conjectures (10)
% 5.82/6.21 thf(conj_0,hypothesis,
% 5.82/6.21 ( tia
% 5.82/6.21 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ x13 @ x14 ) ) ).
% 5.82/6.21
% 5.82/6.21 thf(conj_1,hypothesis,
% 5.82/6.21 ( ( size_s7982070591426661849_VEBTi @ tree_is )
% 5.82/6.21 = ( size_s6755466524823107622T_VEBT @ treeList ) ) ).
% 5.82/6.21
% 5.82/6.21 thf(conj_2,hypothesis,
% 5.82/6.21 xa != mi ).
% 5.82/6.21
% 5.82/6.21 thf(conj_3,hypothesis,
% 5.82/6.21 ~ ( ord_less_nat @ xa @ mi ) ).
% 5.82/6.21
% 5.82/6.21 thf(conj_4,hypothesis,
% 5.82/6.21 ~ ( ord_less_nat @ ma @ xa ) ).
% 5.82/6.21
% 5.82/6.21 thf(conj_5,hypothesis,
% 5.82/6.21 ( xaa
% 5.82/6.21 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.82/6.21
% 5.82/6.21 thf(conj_6,hypothesis,
% 5.82/6.21 ( ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.82/6.21 = none_nat ) ).
% 5.82/6.21
% 5.82/6.21 thf(conj_7,hypothesis,
% 5.82/6.21 xba = none_nat ).
% 5.82/6.21
% 5.82/6.21 thf(conj_8,hypothesis,
% 5.82/6.21 xa != ma ).
% 5.82/6.21
% 5.82/6.21 thf(conj_9,conjecture,
% 5.82/6.21 entails @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ xc ) @ ( snga_assn_VEBT_VEBTi @ x13 @ ( list_u6098035379799741383_VEBTi @ tree_is @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ xb ) ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( list_u6098035379799741383_VEBTi @ tree_is @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ xb ) ) ) @ ( vEBT_vebt_assn_raw @ ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ summary ) ) @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ treeList @ summary ) ) @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ va ) ) @ x13 @ xc ) ) ).
% 7.27/7.58
% 7.27/7.58 %------------------------------------------------------------------------------
% 7.27/7.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.bRwJb1q8AS/cvc5---1.0.5_5389.p...
% 7.27/7.58 (declare-sort $$unsorted 0)
% 7.27/7.58 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 7.27/7.58 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 7.27/7.58 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 7.27/7.58 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 7.27/7.58 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 7.27/7.58 (declare-sort tptp.itself8794530163899892676l_num1 0)
% 7.27/7.58 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 7.27/7.58 (declare-sort tptp.option936205604648967762et_nat 0)
% 7.27/7.58 (declare-sort tptp.set_Pr3948176798113811640et_nat 0)
% 7.27/7.58 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 7.27/7.58 (declare-sort tptp.list_P735349106241217576_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.option2651255830984564193nteger 0)
% 7.27/7.58 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 7.27/7.58 (declare-sort tptp.list_P5578671422887162913nteger 0)
% 7.27/7.58 (declare-sort tptp.set_Pr4811707699266497531nteger 0)
% 7.27/7.58 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 7.27/7.58 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 7.27/7.58 (declare-sort tptp.list_P2340519324556330824_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.produc3625547720036274456_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.list_P2623026923184700063T_real 0)
% 7.27/7.58 (declare-sort tptp.list_P877281246627933069T_VEBT 0)
% 7.27/7.58 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 7.27/7.58 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 7.27/7.58 (declare-sort tptp.produc8923325533196201883nteger 0)
% 7.27/7.58 (declare-sort tptp.heap_T5317711798761887292on_nat 0)
% 7.27/7.58 (declare-sort tptp.heap_T8822477325091257596_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.heap_T4980287057938770641_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 7.27/7.58 (declare-sort tptp.option2661157926820139483um_num 0)
% 7.27/7.58 (declare-sort tptp.option4927543243414619207at_nat 0)
% 7.27/7.58 (declare-sort tptp.option4624381673175914239nt_int 0)
% 7.27/7.58 (declare-sort tptp.list_P8689742595348180415l_real 0)
% 7.27/7.58 (declare-sort tptp.list_P6834414599653733731al_nat 0)
% 7.27/7.58 (declare-sort tptp.produc5170161368751668367T_real 0)
% 7.27/7.58 (declare-sort tptp.produc3757001726724277373T_VEBT 0)
% 7.27/7.58 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 7.27/7.58 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 7.27/7.58 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 7.27/7.58 (declare-sort tptp.set_Pr8218934625190621173um_num 0)
% 7.27/7.58 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 7.27/7.58 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 7.27/7.58 (declare-sort tptp.heap_T2636463487746394924on_nat 0)
% 7.27/7.58 (declare-sort tptp.heap_T8145700208782473153_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.set_op687863988967635939nteger 0)
% 7.27/7.58 (declare-sort tptp.set_list_VEBT_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.list_P3595434254542482545real_o 0)
% 7.27/7.58 (declare-sort tptp.heap_T3836121109492952855ay_nat 0)
% 7.27/7.58 (declare-sort tptp.heap_T290393402774840812st_nat 0)
% 7.27/7.58 (declare-sort tptp.set_op3165557761946182707t_unit 0)
% 7.27/7.58 (declare-sort tptp.set_op4903093089046678027l_num1 0)
% 7.27/7.58 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 7.27/7.58 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 7.27/7.58 (declare-sort tptp.option8137458692691377843t_unit 0)
% 7.27/7.58 (declare-sort tptp.option651621982937097355l_num1 0)
% 7.27/7.58 (declare-sort tptp.set_li6976499617229504675nteger 0)
% 7.27/7.58 (declare-sort tptp.set_set_Code_integer 0)
% 7.27/7.58 (declare-sort tptp.produc2422161461964618553l_real 0)
% 7.27/7.58 (declare-sort tptp.set_option_complex 0)
% 7.27/7.58 (declare-sort tptp.heap_T5660665574680485309rray_o 0)
% 7.27/7.58 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 7.27/7.58 (declare-sort tptp.heap_T844314716496656296list_o 0)
% 7.27/7.58 (declare-sort tptp.product_prod_num_num 0)
% 7.27/7.58 (declare-sort tptp.product_prod_nat_nat 0)
% 7.27/7.58 (declare-sort tptp.product_prod_int_int 0)
% 7.27/7.58 (declare-sort tptp.set_list_complex 0)
% 7.27/7.58 (declare-sort tptp.array_option_nat 0)
% 7.27/7.58 (declare-sort tptp.set_set_complex 0)
% 7.27/7.58 (declare-sort tptp.set_option_real 0)
% 7.27/7.58 (declare-sort tptp.option_set_real 0)
% 7.27/7.58 (declare-sort tptp.list_option_nat 0)
% 7.27/7.58 (declare-sort tptp.array_VEBT_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.set_option_nat 0)
% 7.27/7.58 (declare-sort tptp.set_option_int 0)
% 7.27/7.58 (declare-sort tptp.option_set_nat 0)
% 7.27/7.58 (declare-sort tptp.option_set_int 0)
% 7.27/7.58 (declare-sort tptp.list_VEBT_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.set_VEBT_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.set_list_real 0)
% 7.27/7.58 (declare-sort tptp.list_VEBT_VEBT 0)
% 7.27/7.58 (declare-sort tptp.heap_Time_Heap_nat 0)
% 7.27/7.58 (declare-sort tptp.set_list_nat 0)
% 7.27/7.58 (declare-sort tptp.set_list_int 0)
% 7.27/7.58 (declare-sort tptp.list_Code_integer 0)
% 7.27/7.58 (declare-sort tptp.set_VEBT_VEBT 0)
% 7.27/7.58 (declare-sort tptp.set_set_nat 0)
% 7.27/7.58 (declare-sort tptp.set_set_int 0)
% 7.27/7.58 (declare-sort tptp.set_Code_integer 0)
% 7.27/7.58 (declare-sort tptp.set_Product_unit 0)
% 7.27/7.58 (declare-sort tptp.set_option_o 0)
% 7.27/7.58 (declare-sort tptp.set_Numeral_num1 0)
% 7.27/7.58 (declare-sort tptp.option_set_o 0)
% 7.27/7.58 (declare-sort tptp.itself_Numeral_num1 0)
% 7.27/7.58 (declare-sort tptp.list_complex 0)
% 7.27/7.58 (declare-sort tptp.heap_Time_Heap_o 0)
% 7.27/7.58 (declare-sort tptp.set_list_o 0)
% 7.27/7.58 (declare-sort tptp.set_complex 0)
% 7.27/7.58 (declare-sort tptp.option_real 0)
% 7.27/7.58 (declare-sort tptp.filter_real 0)
% 7.27/7.58 (declare-sort tptp.itself_finite_3 0)
% 7.27/7.58 (declare-sort tptp.itself_finite_2 0)
% 7.27/7.58 (declare-sort tptp.itself_finite_1 0)
% 7.27/7.58 (declare-sort tptp.option_rat 0)
% 7.27/7.58 (declare-sort tptp.option_num 0)
% 7.27/7.58 (declare-sort tptp.option_nat 0)
% 7.27/7.58 (declare-sort tptp.option_int 0)
% 7.27/7.58 (declare-sort tptp.filter_nat 0)
% 7.27/7.58 (declare-sort tptp.vEBT_VEBTi 0)
% 7.27/7.58 (declare-sort tptp.list_real 0)
% 7.27/7.58 (declare-sort tptp.array_nat 0)
% 7.27/7.58 (declare-sort tptp.set_real 0)
% 7.27/7.58 (declare-sort tptp.list_num 0)
% 7.27/7.58 (declare-sort tptp.list_nat 0)
% 7.27/7.58 (declare-sort tptp.list_int 0)
% 7.27/7.58 (declare-sort tptp.vEBT_VEBT 0)
% 7.27/7.58 (declare-sort tptp.set_rat 0)
% 7.27/7.58 (declare-sort tptp.set_num 0)
% 7.27/7.58 (declare-sort tptp.set_nat 0)
% 7.27/7.58 (declare-sort tptp.set_int 0)
% 7.27/7.58 (declare-sort tptp.code_integer 0)
% 7.27/7.58 (declare-sort tptp.product_unit 0)
% 7.27/7.58 (declare-sort tptp.numeral_num1 0)
% 7.27/7.58 (declare-sort tptp.extended_enat 0)
% 7.27/7.58 (declare-sort tptp.array_o 0)
% 7.27/7.58 (declare-sort tptp.list_o 0)
% 7.27/7.58 (declare-sort tptp.complex 0)
% 7.27/7.58 (declare-sort tptp.assn 0)
% 7.27/7.58 (declare-sort tptp.set_o 0)
% 7.27/7.58 (declare-sort tptp.uint32 0)
% 7.27/7.58 (declare-sort tptp.real 0)
% 7.27/7.58 (declare-sort tptp.rat 0)
% 7.27/7.58 (declare-sort tptp.num 0)
% 7.27/7.58 (declare-sort tptp.nat 0)
% 7.27/7.58 (declare-sort tptp.int 0)
% 7.27/7.58 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 7.27/7.58 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 7.27/7.58 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 7.27/7.58 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 7.27/7.58 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 7.27/7.58 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 7.27/7.58 (declare-fun tptp.array_8141364883501958055_VEBTi (tptp.array_VEBT_VEBTi) tptp.heap_T4980287057938770641_VEBTi)
% 7.27/7.58 (declare-fun tptp.array_len_o (tptp.array_o) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.array_len_nat (tptp.array_nat) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.array_len_VEBT_VEBTi (tptp.array_VEBT_VEBTi) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.array_nth_o (tptp.array_o tptp.nat) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.array_nth_nat (tptp.array_nat tptp.nat) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.array_nth_option_nat (tptp.array_option_nat tptp.nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.array_nth_VEBT_VEBTi (tptp.array_VEBT_VEBTi tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.array_upd_o (tptp.nat Bool tptp.array_o) tptp.heap_T5660665574680485309rray_o)
% 7.27/7.58 (declare-fun tptp.array_upd_nat (tptp.nat tptp.nat tptp.array_nat) tptp.heap_T3836121109492952855ay_nat)
% 7.27/7.58 (declare-fun tptp.array_upd_VEBT_VEBTi (tptp.nat tptp.vEBT_VEBTi tptp.array_VEBT_VEBTi) tptp.heap_T8822477325091257596_VEBTi)
% 7.27/7.58 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 7.27/7.58 (declare-fun tptp.entails (tptp.assn tptp.assn) Bool)
% 7.27/7.58 (declare-fun tptp.ex_ass463751140784270563_VEBTi ((-> tptp.list_VEBT_VEBTi tptp.assn)) tptp.assn)
% 7.27/7.58 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 7.27/7.58 (declare-fun tptp.snga_assn_o (tptp.array_o tptp.list_o) tptp.assn)
% 7.27/7.58 (declare-fun tptp.snga_assn_nat (tptp.array_nat tptp.list_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.snga_assn_option_nat (tptp.array_option_nat tptp.list_option_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.snga_assn_VEBT_VEBTi (tptp.array_VEBT_VEBTi tptp.list_VEBT_VEBTi) tptp.assn)
% 7.27/7.58 (declare-fun tptp.fI_QUERY (tptp.assn tptp.assn tptp.assn) Bool)
% 7.27/7.58 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 7.27/7.58 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se3928097537394005634nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.bit_Sh3965577149348748681tl_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bit_Sh2154871086232339855tr_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.bits_Bit_integer (tptp.code_integer Bool) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.bits_b8758750999018896077nteger (tptp.code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.bits_b2549910563261871055nteger (tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 7.27/7.58 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 7.27/7.58 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 7.27/7.58 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 7.27/7.58 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.imaginary_unit () tptp.complex)
% 7.27/7.58 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 7.27/7.58 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 7.27/7.58 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 7.27/7.58 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 7.27/7.58 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 7.27/7.58 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 7.27/7.58 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 7.27/7.58 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.27/7.58 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 7.27/7.58 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 7.27/7.58 (declare-fun tptp.at_top_real () tptp.filter_real)
% 7.27/7.58 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 7.27/7.58 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 7.27/7.58 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 7.27/7.58 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 7.27/7.58 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 7.27/7.58 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 7.27/7.58 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 7.27/7.58 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 7.27/7.58 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.finite6454714172617411597l_num1 (tptp.set_Numeral_num1) tptp.nat)
% 7.27/7.58 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 7.27/7.58 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 7.27/7.58 (declare-fun tptp.finite6017078050557962740nteger (tptp.set_Code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 7.27/7.58 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 7.27/7.58 (declare-fun tptp.finite1283093830868386564nteger (tptp.set_li6976499617229504675nteger) Bool)
% 7.27/7.58 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 7.27/7.58 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 7.27/7.58 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 7.27/7.58 (declare-fun tptp.finite306553202115118035t_real (tptp.set_list_real) Bool)
% 7.27/7.58 (declare-fun tptp.finite5722435864697464412_VEBTi (tptp.set_list_VEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 7.27/7.58 (declare-fun tptp.finite1111429032697314574l_num1 (tptp.set_Numeral_num1) Bool)
% 7.27/7.58 (declare-fun tptp.finite4093902646404507527tion_o (tptp.set_option_o) Bool)
% 7.27/7.58 (declare-fun tptp.finite6785661671136154180nteger (tptp.set_op687863988967635939nteger) Bool)
% 7.27/7.58 (declare-fun tptp.finite2569390945932476949omplex (tptp.set_option_complex) Bool)
% 7.27/7.58 (declare-fun tptp.finite1345302120164226195on_int (tptp.set_option_int) Bool)
% 7.27/7.58 (declare-fun tptp.finite5523153139673422903on_nat (tptp.set_option_nat) Bool)
% 7.27/7.58 (declare-fun tptp.finite3139260975159805780l_num1 (tptp.set_op4903093089046678027l_num1) Bool)
% 7.27/7.58 (declare-fun tptp.finite1445617369574913404t_unit (tptp.set_op3165557761946182707t_unit) Bool)
% 7.27/7.58 (declare-fun tptp.finite5731380839103853331n_real (tptp.set_option_real) Bool)
% 7.27/7.58 (declare-fun tptp.finite2998713641127702882nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 7.27/7.58 (declare-fun tptp.finite4290736615968046902t_unit (tptp.set_Product_unit) Bool)
% 7.27/7.58 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 7.27/7.58 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 7.27/7.58 (declare-fun tptp.finite6931041176100689706nteger (tptp.set_set_Code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 7.27/7.58 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.finite6580341952239402572_VEBTi (tptp.set_VEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 7.27/7.58 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.generi2397576812484419408nteger (tptp.code_integer tptp.nat Bool) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.generi8991105624351003935it_int (tptp.int tptp.nat Bool) tptp.int)
% 7.27/7.58 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 7.27/7.58 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 7.27/7.58 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.minus_711738161318947805_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 7.27/7.58 (declare-fun tptp.minus_2794559001203777698VEBT_o ((-> tptp.vEBT_VEBT Bool) (-> tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 7.27/7.58 (declare-fun tptp.minus_2355218937544613996nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 7.27/7.58 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.minus_minus_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.minus_8146479932129876780l_num1 (tptp.set_Numeral_num1 tptp.set_Numeral_num1) tptp.set_Numeral_num1)
% 7.27/7.58 (declare-fun tptp.minus_1052850069191792384nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.minus_6452836326544984404t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 7.27/7.58 (declare-fun tptp.minus_minus_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.one_one_assn () tptp.assn)
% 7.27/7.58 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.one_one_complex () tptp.complex)
% 7.27/7.58 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.one_one_int () tptp.int)
% 7.27/7.58 (declare-fun tptp.one_one_nat () tptp.nat)
% 7.27/7.58 (declare-fun tptp.one_one_rat () tptp.rat)
% 7.27/7.58 (declare-fun tptp.one_one_real () tptp.real)
% 7.27/7.58 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 7.27/7.58 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 7.27/7.58 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.zero_zero_int () tptp.int)
% 7.27/7.58 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 7.27/7.58 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 7.27/7.58 (declare-fun tptp.zero_zero_real () tptp.real)
% 7.27/7.58 (declare-fun tptp.groups8024822376189712711omplex ((-> tptp.code_integer tptp.complex) tptp.set_Code_integer) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups7234854612051535045er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups7237345082560585321er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups6602215022474089585er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups1270011288395367621r_real ((-> tptp.code_integer tptp.real) tptp.set_Code_integer) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups1794756597179926696omplex ((-> tptp.vEBT_VEBT tptp.complex) tptp.set_VEBT_VEBT) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups769130701875090982BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups136491112297645522BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups2240296850493347238T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups1304777262505850412r_assn ((-> tptp.code_integer tptp.assn) tptp.set_Code_integer) tptp.assn)
% 7.27/7.58 (declare-fun tptp.groups862514429393162674omplex ((-> tptp.code_integer tptp.complex) tptp.set_Code_integer) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups3188404863801439024er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups3190895334310489300er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups2555765274223993564er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups9004974159866482096r_real ((-> tptp.code_integer tptp.real) tptp.set_Code_integer) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups4150731942483176573x_assn ((-> tptp.complex tptp.assn) tptp.set_complex) tptp.assn)
% 7.27/7.58 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups7882442080178216443t_assn ((-> tptp.int tptp.assn) tptp.set_int) tptp.assn)
% 7.27/7.58 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups6906906614972039071t_assn ((-> tptp.nat tptp.assn) tptp.set_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups1155561341820557179l_assn ((-> tptp.real tptp.assn) tptp.set_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups569574905686396791T_assn ((-> tptp.vEBT_VEBT tptp.assn) tptp.set_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.groups127312072573709053omplex ((-> tptp.vEBT_VEBT tptp.complex) tptp.set_VEBT_VEBT) tptp.complex)
% 7.27/7.58 (declare-fun tptp.groups6359315924273963643BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 7.27/7.58 (declare-fun tptp.groups6361806394783013919BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.groups5726676334696518183BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 7.27/7.58 (declare-fun tptp.groups2703838992350267259T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 7.27/7.58 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 7.27/7.58 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 7.27/7.58 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 7.27/7.58 (declare-fun tptp.size_a6397454172108246045_VEBTi ((-> tptp.vEBT_VEBTi tptp.nat) tptp.array_VEBT_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.heap_Time_return_o (Bool) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.heap_Time_return_nat (tptp.nat) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.heap_T3487192422709364219on_nat (tptp.option_nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.heap_T3630416162098727440_VEBTi (tptp.vEBT_VEBTi) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.hoare_hoare_triple_o (tptp.assn tptp.heap_Time_Heap_o (-> Bool tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_6478655245392655262rray_o (tptp.assn tptp.heap_T5660665574680485309rray_o (-> tptp.array_o tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_6807272225193264096ay_nat (tptp.assn tptp.heap_T3836121109492952855ay_nat (-> tptp.array_nat tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_3353465787467722821_VEBTi (tptp.assn tptp.heap_T8822477325091257596_VEBTi (-> tptp.array_VEBT_VEBTi tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_9089481587091695345list_o (tptp.assn tptp.heap_T844314716496656296list_o (-> tptp.list_o tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_7964568885773372237st_nat (tptp.assn tptp.heap_T290393402774840812st_nat (-> tptp.list_nat tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_6480275734082232733on_nat (tptp.assn tptp.heap_T5317711798761887292on_nat (-> tptp.list_option_nat tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_3904069481286416050_VEBTi (tptp.assn tptp.heap_T4980287057938770641_VEBTi (-> tptp.list_VEBT_VEBTi tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_3067605981109127869le_nat (tptp.assn tptp.heap_Time_Heap_nat (-> tptp.nat tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_7629718768684598413on_nat (tptp.assn tptp.heap_T2636463487746394924on_nat (-> tptp.option_nat tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.hoare_1429296392585015714_VEBTi (tptp.assn tptp.heap_T8145700208782473153_VEBTi (-> tptp.vEBT_VEBTi tptp.assn)) Bool)
% 7.27/7.58 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 7.27/7.58 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.if_Heap_Time_Heap_o (Bool tptp.heap_Time_Heap_o tptp.heap_Time_Heap_o) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.if_Hea2662716070787841314ap_nat (Bool tptp.heap_Time_Heap_nat tptp.heap_Time_Heap_nat) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.if_Hea5867803462524415986on_nat (Bool tptp.heap_T2636463487746394924on_nat tptp.heap_T2636463487746394924on_nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.if_Hea8453224502484754311_VEBTi (Bool tptp.heap_T8145700208782473153_VEBTi tptp.heap_T8145700208782473153_VEBTi) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 7.27/7.58 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.27/7.58 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 7.27/7.58 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 7.27/7.58 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 7.27/7.58 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 7.27/7.58 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 7.27/7.58 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 7.27/7.58 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.least_4859182151741483524sb_int (tptp.int) Bool)
% 7.27/7.58 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 7.27/7.58 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 7.27/7.58 (declare-fun tptp.foldr_o_nat ((-> Bool tptp.nat tptp.nat) tptp.list_o tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.foldr_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.foldr_real_nat ((-> tptp.real tptp.nat tptp.nat) tptp.list_real tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.foldr_real_real ((-> tptp.real tptp.real tptp.real) tptp.list_real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.foldr_VEBT_VEBTi_nat ((-> tptp.vEBT_VEBTi tptp.nat tptp.nat) tptp.list_VEBT_VEBTi tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.foldr_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat tptp.nat) tptp.list_VEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 7.27/7.58 (declare-fun tptp.map_o_nat ((-> Bool tptp.nat) tptp.list_o) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.map_o_real ((-> Bool tptp.real) tptp.list_o) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.map_o_VEBT_VEBT ((-> Bool tptp.vEBT_VEBT) tptp.list_o) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.map_int_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 7.27/7.58 (declare-fun tptp.map_int_real ((-> tptp.int tptp.real) tptp.list_int) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.map_nat_real ((-> tptp.nat tptp.real) tptp.list_nat) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.map_nat_VEBT_VEBT ((-> tptp.nat tptp.vEBT_VEBT) tptp.list_nat) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.map_real_o ((-> tptp.real Bool) tptp.list_real) tptp.list_o)
% 7.27/7.58 (declare-fun tptp.map_real_nat ((-> tptp.real tptp.nat) tptp.list_real) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.map_real_real ((-> tptp.real tptp.real) tptp.list_real) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.map_real_VEBT_VEBTi ((-> tptp.real tptp.vEBT_VEBTi) tptp.list_real) tptp.list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.map_real_VEBT_VEBT ((-> tptp.real tptp.vEBT_VEBT) tptp.list_real) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.map_VEBT_VEBTi_o ((-> tptp.vEBT_VEBTi Bool) tptp.list_VEBT_VEBTi) tptp.list_o)
% 7.27/7.58 (declare-fun tptp.map_VEBT_VEBTi_nat ((-> tptp.vEBT_VEBTi tptp.nat) tptp.list_VEBT_VEBTi) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.map_VEBT_VEBTi_real ((-> tptp.vEBT_VEBTi tptp.real) tptp.list_VEBT_VEBTi) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.map_VE483055756984248624_VEBTi ((-> tptp.vEBT_VEBTi tptp.vEBT_VEBTi) tptp.list_VEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.map_VE7998069337340375161T_VEBT ((-> tptp.vEBT_VEBTi tptp.vEBT_VEBT) tptp.list_VEBT_VEBTi) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.map_VEBT_VEBT_o ((-> tptp.vEBT_VEBT Bool) tptp.list_VEBT_VEBT) tptp.list_o)
% 7.27/7.58 (declare-fun tptp.map_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.map_VEBT_VEBT_real ((-> tptp.vEBT_VEBT tptp.real) tptp.list_VEBT_VEBT) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.map_VE7029150624388687525_VEBTi ((-> tptp.vEBT_VEBT tptp.vEBT_VEBTi) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 7.27/7.58 (declare-fun tptp.set_Code_integer2 (tptp.list_Code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 7.27/7.58 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_VEBT_VEBTi2 (tptp.list_VEBT_VEBTi) tptp.set_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 7.27/7.58 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 7.27/7.58 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.list_u6098035379799741383_VEBTi (tptp.list_VEBT_VEBTi tptp.nat tptp.vEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 7.27/7.58 (declare-fun tptp.nth_option_nat (tptp.list_option_nat tptp.nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.nth_Pr2304437835452373666nteger (tptp.list_P5578671422887162913nteger tptp.nat) tptp.produc8923325533196201883nteger)
% 7.27/7.58 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 7.27/7.58 (declare-fun tptp.nth_Pr7489471911767062336l_real (tptp.list_P8689742595348180415l_real tptp.nat) tptp.produc2422161461964618553l_real)
% 7.27/7.58 (declare-fun tptp.nth_Pr5429231388385915574T_VEBT (tptp.list_P877281246627933069T_VEBT tptp.nat) tptp.produc3757001726724277373T_VEBT)
% 7.27/7.58 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 7.27/7.58 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 7.27/7.58 (declare-fun tptp.nth_Pr6842391030413306568T_real (tptp.list_P2623026923184700063T_real tptp.nat) tptp.produc5170161368751668367T_real)
% 7.27/7.58 (declare-fun tptp.nth_Pr316670251186196177_VEBTi (tptp.list_P735349106241217576_VEBTi tptp.nat) tptp.produc3625547720036274456_VEBTi)
% 7.27/7.58 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 7.27/7.58 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.nth_VEBT_VEBTi (tptp.list_VEBT_VEBTi tptp.nat) tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.produc8792966785426426881nteger (tptp.list_Code_integer tptp.list_Code_integer) tptp.list_P5578671422887162913nteger)
% 7.27/7.58 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 7.27/7.58 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 7.27/7.58 (declare-fun tptp.product_real_o (tptp.list_real tptp.list_o) tptp.list_P3595434254542482545real_o)
% 7.27/7.58 (declare-fun tptp.product_real_nat (tptp.list_real tptp.list_nat) tptp.list_P6834414599653733731al_nat)
% 7.27/7.58 (declare-fun tptp.product_real_real (tptp.list_real tptp.list_real) tptp.list_P8689742595348180415l_real)
% 7.27/7.58 (declare-fun tptp.produc5599769701989005224_VEBTi (tptp.list_real tptp.list_VEBT_VEBTi) tptp.list_P2340519324556330824_VEBTi)
% 7.27/7.58 (declare-fun tptp.produc3722688996059531265T_VEBT (tptp.list_real tptp.list_VEBT_VEBT) tptp.list_P877281246627933069T_VEBT)
% 7.27/7.58 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 7.27/7.58 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 7.27/7.58 (declare-fun tptp.produc4908677263432625371T_real (tptp.list_VEBT_VEBT tptp.list_real) tptp.list_P2623026923184700063T_real)
% 7.27/7.58 (declare-fun tptp.produc316462671093861988_VEBTi (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBTi) tptp.list_P735349106241217576_VEBTi)
% 7.27/7.58 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 7.27/7.58 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 7.27/7.58 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 7.27/7.58 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 7.27/7.58 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 7.27/7.58 (declare-fun tptp.replicate_VEBT_VEBTi (tptp.nat tptp.vEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 7.27/7.58 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s6086282163384603972on_nat (tptp.list_option_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s987546567493390085real_o (tptp.list_P3595434254542482545real_o) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s1877336372972134351al_nat (tptp.list_P6834414599653733731al_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s3932428310213730859l_real (tptp.list_P8689742595348180415l_real) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s6963394564282275252_VEBTi (tptp.list_P2340519324556330824_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s3289364478449617953T_VEBT (tptp.list_P877281246627933069T_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s5035110155006384947T_real (tptp.list_P2623026923184700063T_real) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s3387956428969716412_VEBTi (tptp.list_P735349106241217576_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s7982070591426661849_VEBTi (tptp.list_VEBT_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_uint32 (tptp.uint32) tptp.nat)
% 7.27/7.58 (declare-fun tptp.size_size_VEBT_VEBTi (tptp.vEBT_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.inc (tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.one () tptp.num)
% 7.27/7.58 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 7.27/7.58 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 7.27/7.58 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 7.27/7.58 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 7.27/7.58 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 7.27/7.58 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 7.27/7.58 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 7.27/7.58 (declare-fun tptp.none_nat () tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.none_P4506660739021792380nteger () tptp.option2651255830984564193nteger)
% 7.27/7.58 (declare-fun tptp.none_P533106815845188193et_nat () tptp.option936205604648967762et_nat)
% 7.27/7.58 (declare-fun tptp.none_P2377608414092835994nt_int () tptp.option4624381673175914239nt_int)
% 7.27/7.58 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 7.27/7.58 (declare-fun tptp.none_P4394680061957285238um_num () tptp.option2661157926820139483um_num)
% 7.27/7.58 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 7.27/7.58 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 7.27/7.58 (declare-fun tptp.some_P6772290148444788224nteger (tptp.produc8923325533196201883nteger) tptp.option2651255830984564193nteger)
% 7.27/7.58 (declare-fun tptp.some_P624177172695371229et_nat (tptp.produc3658429121746597890et_nat) tptp.option936205604648967762et_nat)
% 7.27/7.58 (declare-fun tptp.some_P4184893108420464158nt_int (tptp.product_prod_int_int) tptp.option4624381673175914239nt_int)
% 7.27/7.58 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 7.27/7.58 (declare-fun tptp.some_P6201964756284913402um_num (tptp.product_prod_num_num) tptp.option2661157926820139483um_num)
% 7.27/7.58 (declare-fun tptp.some_rat (tptp.rat) tptp.option_rat)
% 7.27/7.58 (declare-fun tptp.some_real (tptp.real) tptp.option_real)
% 7.27/7.58 (declare-fun tptp.some_set_o (tptp.set_o) tptp.option_set_o)
% 7.27/7.58 (declare-fun tptp.some_set_int (tptp.set_int) tptp.option_set_int)
% 7.27/7.58 (declare-fun tptp.some_set_nat (tptp.set_nat) tptp.option_set_nat)
% 7.27/7.58 (declare-fun tptp.some_s513430669971965098l_num1 (tptp.set_Numeral_num1) tptp.option651621982937097355l_num1)
% 7.27/7.58 (declare-fun tptp.some_s8043159101241848530t_unit (tptp.set_Product_unit) tptp.option8137458692691377843t_unit)
% 7.27/7.58 (declare-fun tptp.some_set_real (tptp.set_real) tptp.option_set_real)
% 7.27/7.58 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 7.27/7.58 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 7.27/7.58 (declare-fun tptp.bot_bot_option_nat () tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 7.27/7.58 (declare-fun tptp.bot_bo3990330152332043303nteger () tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 7.27/7.58 (declare-fun tptp.bot_bo5651135754355059505l_num1 () tptp.set_Numeral_num1)
% 7.27/7.58 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.bot_bo3957492148770167129t_unit () tptp.set_Product_unit)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 7.27/7.58 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 7.27/7.58 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.ord_less_assn (tptp.assn tptp.assn) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_option_int (tptp.option_int tptp.option_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_option_nat (tptp.option_nat tptp.option_nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_option_num (tptp.option_num tptp.option_num) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_option_rat (tptp.option_rat tptp.option_rat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_option_real (tptp.option_real tptp.option_real) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le526730876122248049l_num1 (tptp.set_Numeral_num1 tptp.set_Numeral_num1) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le8056459307392131481t_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le3480810397992357184T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le418104280809901481VEBT_o ((-> tptp.vEBT_VEBT Bool) (-> tptp.vEBT_VEBT Bool)) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_assn (tptp.assn tptp.assn) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le1736525451366464988on_int (tptp.option_int tptp.option_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le5914376470875661696on_nat (tptp.option_nat tptp.option_nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le6622620407824499402on_num (tptp.option_num tptp.option_num) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le2406147912482264968on_rat (tptp.option_rat tptp.option_rat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le353528952715127954et_int (tptp.option_set_int tptp.option_set_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le5200684355995106405l_num1 (tptp.set_Numeral_num1 tptp.set_Numeral_num1) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le3507040750410214029t_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 7.27/7.58 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le6592769550269828683_VEBTi (tptp.set_VEBT_VEBTi tptp.set_VEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.ord_max_assn (tptp.assn tptp.assn) tptp.assn)
% 7.27/7.58 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 7.27/7.58 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.ord_max_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 7.27/7.58 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.ord_ma2202181864719522458l_num1 (tptp.set_Numeral_num1 tptp.set_Numeral_num1) tptp.set_Numeral_num1)
% 7.27/7.58 (declare-fun tptp.ord_ma508538259134630082t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 7.27/7.58 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 7.27/7.58 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 7.27/7.58 (declare-fun tptp.top_top_assn () tptp.assn)
% 7.27/7.58 (declare-fun tptp.top_to3028658606643905974d_enat () tptp.extended_enat)
% 7.27/7.58 (declare-fun tptp.top_top_option_set_o () tptp.option_set_o)
% 7.27/7.58 (declare-fun tptp.top_to4826455019444611206et_nat () tptp.option_set_nat)
% 7.27/7.58 (declare-fun tptp.top_to176924430543178203l_num1 () tptp.option651621982937097355l_num1)
% 7.27/7.58 (declare-fun tptp.top_to7662761140297458691t_unit () tptp.option8137458692691377843t_unit)
% 7.27/7.58 (declare-fun tptp.top_to1083748111577038690t_real () tptp.option_set_real)
% 7.27/7.58 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 7.27/7.58 (declare-fun tptp.top_to4645266643341252675nteger () tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.top_top_set_complex () tptp.set_complex)
% 7.27/7.58 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 7.27/7.58 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.top_to3689904429138878997l_num1 () tptp.set_Numeral_num1)
% 7.27/7.58 (declare-fun tptp.top_top_set_option_o () tptp.set_option_o)
% 7.27/7.58 (declare-fun tptp.top_to5929521628599800467nteger () tptp.set_op687863988967635939nteger)
% 7.27/7.58 (declare-fun tptp.top_to6180147692022559204omplex () tptp.set_option_complex)
% 7.27/7.58 (declare-fun tptp.top_to6430115241214627170on_int () tptp.set_option_int)
% 7.27/7.58 (declare-fun tptp.top_to8920198386146353926on_nat () tptp.set_option_nat)
% 7.27/7.58 (declare-fun tptp.top_to4428395536652758875l_num1 () tptp.set_op4903093089046678027l_num1)
% 7.27/7.58 (declare-fun tptp.top_to2690860209552263555t_unit () tptp.set_op3165557761946182707t_unit)
% 7.27/7.58 (declare-fun tptp.top_to853713521313446370n_real () tptp.set_option_real)
% 7.27/7.58 (declare-fun tptp.top_to4366644338036079209nt_int () tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 7.27/7.58 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 7.27/7.58 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 7.27/7.58 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 7.27/7.58 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 7.27/7.58 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 7.27/7.58 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 7.27/7.58 (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)
% 7.27/7.58 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.27/7.58 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 7.27/7.58 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 7.27/7.58 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 7.27/7.58 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 7.27/7.58 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 7.27/7.58 (declare-fun tptp.produc4511245868158468465l_real (tptp.real tptp.real) tptp.produc2422161461964618553l_real)
% 7.27/7.58 (declare-fun tptp.produc6931449550656315951T_VEBT (tptp.real tptp.vEBT_VEBT) tptp.produc3757001726724277373T_VEBT)
% 7.27/7.58 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 7.27/7.58 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 7.27/7.58 (declare-fun tptp.produc8117437818029410057T_real (tptp.vEBT_VEBT tptp.real) tptp.produc5170161368751668367T_real)
% 7.27/7.58 (declare-fun tptp.produc6084888613844515218_VEBTi (tptp.vEBT_VEBT tptp.vEBT_VEBTi) tptp.produc3625547720036274456_VEBTi)
% 7.27/7.58 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 7.27/7.58 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.27/7.58 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 7.27/7.58 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.27/7.58 (declare-fun tptp.type_N8448461349408098053l_num1 () tptp.itself8794530163899892676l_num1)
% 7.27/7.58 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 7.27/7.58 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 7.27/7.58 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 7.27/7.58 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 7.27/7.58 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 7.27/7.58 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 7.27/7.58 (declare-fun tptp.refine_Imp_refines_o (tptp.heap_Time_Heap_o tptp.heap_Time_Heap_o) Bool)
% 7.27/7.58 (declare-fun tptp.refine5896690332125372649list_o (tptp.heap_T844314716496656296list_o tptp.heap_T844314716496656296list_o) Bool)
% 7.27/7.58 (declare-fun tptp.refine1935026298455697829on_nat (tptp.heap_T5317711798761887292on_nat tptp.heap_T5317711798761887292on_nat) Bool)
% 7.27/7.58 (declare-fun tptp.refine3700189196150522554_VEBTi (tptp.heap_T4980287057938770641_VEBTi tptp.heap_T4980287057938770641_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.refine7594492741263601813on_nat (tptp.heap_T2636463487746394924on_nat tptp.heap_T2636463487746394924on_nat) Bool)
% 7.27/7.58 (declare-fun tptp.refine5565527176597971370_VEBTi (tptp.heap_T8145700208782473153_VEBTi tptp.heap_T8145700208782473153_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_assn (tptp.assn tptp.assn) Bool)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 7.27/7.58 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 7.27/7.58 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 7.27/7.58 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 7.27/7.58 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 7.27/7.58 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 7.27/7.58 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 7.27/7.58 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 7.27/7.58 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 7.27/7.58 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 7.27/7.58 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 7.27/7.58 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 7.27/7.58 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 7.27/7.58 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 7.27/7.58 (declare-fun tptp.collec3483841146883906114nteger ((-> tptp.list_Code_integer Bool)) tptp.set_li6976499617229504675nteger)
% 7.27/7.58 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 7.27/7.58 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 7.27/7.58 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 7.27/7.58 (declare-fun tptp.collect_list_real ((-> tptp.list_real Bool)) tptp.set_list_real)
% 7.27/7.58 (declare-fun tptp.collec1288327022334394266_VEBTi ((-> tptp.list_VEBT_VEBTi Bool)) tptp.set_list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.collect_Numeral_num1 ((-> tptp.numeral_num1 Bool)) tptp.set_Numeral_num1)
% 7.27/7.58 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.collect_Product_unit ((-> tptp.product_unit Bool)) tptp.set_Product_unit)
% 7.27/7.58 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.collec574505750873337192nteger ((-> tptp.set_Code_integer Bool)) tptp.set_set_Code_integer)
% 7.27/7.58 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 7.27/7.58 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 7.27/7.58 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 7.27/7.58 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.image_4470545334726330049nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 7.27/7.58 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.image_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 7.27/7.58 (declare-fun tptp.insert_Code_integer (tptp.code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 7.27/7.58 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.insert5033312907999012233nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 7.27/7.58 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.insert_VEBT_VEBTi (tptp.vEBT_VEBTi tptp.set_VEBT_VEBTi) tptp.set_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.set_fo1959793692361082170t_assn ((-> tptp.nat tptp.assn tptp.assn) tptp.nat tptp.nat tptp.assn) tptp.assn)
% 7.27/7.58 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 7.27/7.58 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 7.27/7.58 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_or1222409239386451017an_num (tptp.num tptp.num) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.set_or4029947393144176647an_rat (tptp.rat tptp.rat) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.set_or66887138388493659n_real (tptp.real tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_or8585797421378605585et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 7.27/7.58 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_or9101266186257409494nteger (tptp.code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 7.27/7.58 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.set_or5754767410780653050nteger (tptp.code_integer) tptp.set_Code_integer)
% 7.27/7.58 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 7.27/7.58 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 7.27/7.58 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 7.27/7.58 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 7.27/7.58 (declare-fun tptp.signed6714573509424544716de_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.signed6292675348222524329lo_int (tptp.int tptp.int) tptp.int)
% 7.27/7.58 (declare-fun tptp.time_TBOUND_o (tptp.heap_Time_Heap_o tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_TBOUND_list_o (tptp.heap_T844314716496656296list_o tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_TBOUND_list_nat (tptp.heap_T290393402774840812st_nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_T3808005469503390304on_nat (tptp.heap_T5317711798761887292on_nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_T8149879359713347829_VEBTi (tptp.heap_T4980287057938770641_VEBTi tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_TBOUND_nat (tptp.heap_Time_Heap_nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_T8353473612707095248on_nat (tptp.heap_T2636463487746394924on_nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_T5737551269749752165_VEBTi (tptp.heap_T8145700208782473153_VEBTi tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_htt_o (tptp.assn tptp.heap_Time_Heap_o (-> Bool tptp.assn) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_htt_nat (tptp.assn tptp.heap_Time_Heap_nat (-> tptp.nat tptp.assn) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_htt_option_nat (tptp.assn tptp.heap_T2636463487746394924on_nat (-> tptp.option_nat tptp.assn) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_htt_VEBT_VEBTi (tptp.assn tptp.heap_T8145700208782473153_VEBTi (-> tptp.vEBT_VEBTi tptp.assn) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.time_time_o (tptp.heap_Time_Heap_o tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 7.27/7.58 (declare-fun tptp.time_t3534373299052942712_VEBTi (tptp.heap_T4980287057938770641_VEBTi tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 7.27/7.58 (declare-fun tptp.time_time_nat (tptp.heap_Time_Heap_nat tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 7.27/7.58 (declare-fun tptp.time_time_option_nat (tptp.heap_T2636463487746394924on_nat tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 7.27/7.58 (declare-fun tptp.time_time_VEBT_VEBTi (tptp.heap_T8145700208782473153_VEBTi tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 7.27/7.58 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 7.27/7.58 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 7.27/7.58 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 7.27/7.58 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 7.27/7.58 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 7.27/7.58 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 7.27/7.58 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 7.27/7.58 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.pi () tptp.real)
% 7.27/7.58 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 7.27/7.58 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 7.27/7.58 (declare-fun tptp.type_l31302759751748491nite_1 (tptp.itself_finite_1) tptp.nat)
% 7.27/7.58 (declare-fun tptp.type_l31302759751748492nite_2 (tptp.itself_finite_2) tptp.nat)
% 7.27/7.58 (declare-fun tptp.type_l31302759751748493nite_3 (tptp.itself_finite_3) tptp.nat)
% 7.27/7.58 (declare-fun tptp.type_l796852477590012082l_num1 (tptp.itself8794530163899892676l_num1) tptp.nat)
% 7.27/7.58 (declare-fun tptp.type_l4264026598287037465l_num1 (tptp.itself_Numeral_num1) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_i_n_s_e_r_t (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_i_n_s_e_r_t2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T5076183648494686801_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T9217963907923527482_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_a_x_t (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_a_x_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_e_m_b_e_r (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_e_m_b_e_r2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T8099345112685741742_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T5837161174952499735_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_i_n_N_u_l_l (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T5462971552011256508_l_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_i_n_t (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_m_i_n_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_p_r_e_d (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_p_r_e_d2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_p_r_e_d_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_p_r_e_d_rel2 (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_s_u_c_c (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_s_u_c_c2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T_s_u_c_c_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_T_s_u_c_c_rel2 (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V441764108873111860ildupi (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V9176841429113362141ildupi (tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.vEBT_V3352910403632780892pi_rel (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V2957053500504383685pi_rel (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_Tb (tptp.nat) tptp.int)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_Tb2 (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_Tb_rel (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_Tb_rel2 (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_highi (tptp.nat tptp.nat) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_lowi (tptp.nat tptp.nat) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_minNulli (tptp.vEBT_VEBTi) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.vEBT_V5740978063120863272li_rel (tptp.vEBT_VEBTi tptp.vEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V2326993469660664182atei_o (tptp.nat tptp.heap_Time_Heap_o) tptp.heap_T844314716496656296list_o)
% 7.27/7.58 (declare-fun tptp.vEBT_V7726092123322077554ei_nat (tptp.nat tptp.heap_Time_Heap_nat) tptp.heap_T290393402774840812st_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V792416675989592002on_nat (tptp.nat tptp.heap_T2636463487746394924on_nat) tptp.heap_T5317711798761887292on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V1859673955506687831_VEBTi (tptp.nat tptp.heap_T8145700208782473153_VEBTi) tptp.heap_T4980287057938770641_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_V739175172307565963ildupi (tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_V3964819847710782039nserti (tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_V854960066525838166emberi (tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.nat) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.vEBT_Leafi (Bool Bool) tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_Nodei (tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi) tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_c6104975476656191286Heap_o ((-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_Time_Heap_o) (-> Bool Bool tptp.heap_Time_Heap_o) tptp.vEBT_VEBTi) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.vEBT_c1335663792808957512ap_nat ((-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_Time_Heap_nat) (-> Bool Bool tptp.heap_Time_Heap_nat) tptp.vEBT_VEBTi) tptp.heap_Time_Heap_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_c6250501799366334488on_nat ((-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T2636463487746394924on_nat) (-> Bool Bool tptp.heap_T2636463487746394924on_nat) tptp.vEBT_VEBTi) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_c6028912655521741485_VEBTi ((-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T8145700208782473153_VEBTi) (-> Bool Bool tptp.heap_T8145700208782473153_VEBTi) tptp.vEBT_VEBTi) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_case_VEBTi_nat ((-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.nat) (-> Bool Bool tptp.nat) tptp.vEBT_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_size_VEBTi (tptp.vEBT_VEBTi) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_assn_raw (tptp.vEBT_VEBT tptp.vEBT_VEBTi) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_v8524038756793281170aw_rel (tptp.produc3625547720036274456_VEBTi tptp.produc3625547720036274456_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_buildupi (tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_inserti (tptp.vEBT_VEBTi tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_maxti (tptp.vEBT_VEBTi) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_maxti_rel (tptp.vEBT_VEBTi tptp.vEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_memberi (tptp.vEBT_VEBTi tptp.nat) tptp.heap_Time_Heap_o)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_minti (tptp.vEBT_VEBTi) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_minti_rel (tptp.vEBT_VEBTi tptp.vEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V1365221501068881998eletei (tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 7.27/7.58 (declare-fun tptp.vEBT_T_d_e_l_e_t_e (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_T8441311223069195367_e_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V1232361888498592333_e_t_e (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V6368547301243506412_e_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_height (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_height_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_L6286945158656146733_VEBTi (tptp.set_nat (-> Bool tptp.vEBT_VEBTi tptp.assn) tptp.list_o tptp.list_VEBT_VEBTi) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1319876754960170684T_VEBT (tptp.set_nat (-> Bool tptp.vEBT_VEBT tptp.assn) tptp.list_o tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L7980206306069228746real_o (tptp.set_nat (-> tptp.real Bool tptp.assn) tptp.list_real tptp.list_o) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L234762979517870878al_nat (tptp.set_nat (-> tptp.real tptp.nat tptp.assn) tptp.list_real tptp.list_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L5184575500739366650l_real (tptp.set_nat (-> tptp.real tptp.real tptp.assn) tptp.list_real tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L7851252805511451907_VEBTi (tptp.set_nat (-> tptp.real tptp.vEBT_VEBTi tptp.assn) tptp.list_real tptp.list_VEBT_VEBTi) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L3095048238742455910T_VEBT (tptp.set_nat (-> tptp.real tptp.vEBT_VEBT tptp.assn) tptp.list_real tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L7058566406413635588VEBT_o (tptp.set_nat (-> tptp.vEBT_VEBT Bool tptp.assn) tptp.list_VEBT_VEBT tptp.list_o) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8650695023172932196BT_nat (tptp.set_nat (-> tptp.vEBT_VEBT tptp.nat tptp.assn) tptp.list_VEBT_VEBT tptp.list_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L4281036506115550016T_real (tptp.set_nat (-> tptp.vEBT_VEBT tptp.real tptp.assn) tptp.list_VEBT_VEBT tptp.list_real) tptp.assn)
% 7.27/7.58 (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)
% 7.27/7.58 (declare-fun tptp.vEBT_L3204528365124325536T_VEBT (tptp.set_nat (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn) tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L4725278957065240257o_real ((-> Bool tptp.real tptp.assn) tptp.list_o tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1750719106661372127T_VEBT ((-> Bool tptp.vEBT_VEBT tptp.assn) tptp.list_o tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L74593716426352029nt_int ((-> tptp.int tptp.int tptp.assn) tptp.list_int tptp.list_int) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L77084186935402305nt_nat ((-> tptp.int tptp.nat tptp.assn) tptp.list_int tptp.list_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8288995350762215837t_real ((-> tptp.int tptp.real tptp.assn) tptp.list_int tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1664421287176695555T_VEBT ((-> tptp.int tptp.vEBT_VEBT tptp.assn) tptp.list_int tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L6102073776069194049t_real ((-> tptp.nat tptp.real tptp.assn) tptp.list_nat tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8158188754432654943T_VEBT ((-> tptp.nat tptp.vEBT_VEBT tptp.assn) tptp.list_nat tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L6234343332106409831real_o ((-> tptp.real Bool tptp.assn) tptp.list_real tptp.list_o) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1443519841834266653al_int ((-> tptp.real tptp.int tptp.assn) tptp.list_real tptp.list_int) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1446010312343316929al_nat ((-> tptp.real tptp.nat tptp.assn) tptp.list_real tptp.list_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1930518968523514909l_real ((-> tptp.real tptp.real tptp.assn) tptp.list_real tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L9060850011106065574_VEBTi ((-> tptp.real tptp.vEBT_VEBTi tptp.assn) tptp.list_real tptp.list_VEBT_VEBTi) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L4595930785310033027T_VEBT ((-> tptp.real tptp.vEBT_VEBT tptp.assn) tptp.list_real tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8937798142398754470i_real ((-> tptp.vEBT_VEBTi tptp.real tptp.assn) tptp.list_VEBT_VEBTi tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L7265847600308530106T_VEBT ((-> tptp.vEBT_VEBTi tptp.vEBT_VEBT tptp.assn) tptp.list_VEBT_VEBTi tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L7489408758114837031VEBT_o ((-> tptp.vEBT_VEBT Bool tptp.assn) tptp.list_VEBT_VEBT tptp.list_o) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8294436054247626077BT_int ((-> tptp.vEBT_VEBT tptp.int tptp.assn) tptp.list_VEBT_VEBT tptp.list_int) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8296926524756676353BT_nat ((-> tptp.vEBT_VEBT tptp.nat tptp.assn) tptp.list_VEBT_VEBT tptp.list_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L8010285020845282001on_nat ((-> tptp.vEBT_VEBT tptp.option_nat tptp.assn) tptp.list_VEBT_VEBT tptp.list_option_nat) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L5781919052683127133T_real ((-> tptp.vEBT_VEBT tptp.real tptp.assn) tptp.list_VEBT_VEBT tptp.list_real) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L6296928887356842470_VEBTi ((-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn) tptp.list_VEBT_VEBT tptp.list_VEBT_VEBTi) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_L1279224858307276611T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn) tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.assn)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.27/7.58 (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)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V8646137997579335489_i_l_d (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V8346862874174094_d_u_p (tptp.nat) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_V1247956027447740395_p_rel (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_V5144397997797733112_d_rel (tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_cnt (tptp.vEBT_VEBT) tptp.real)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_cnt2 (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_cnt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_cnt_rel2 (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_space (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_space2 (tptp.vEBT_VEBT) tptp.nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_space_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_space_rel2 (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_vebt_predi (tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_VEBT_vebt_succi (tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_predi (tptp.vEBT_VEBTi tptp.nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_succi (tptp.vEBT_VEBTi tptp.nat) tptp.heap_T2636463487746394924on_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 7.27/7.58 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 7.27/7.58 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 7.27/7.58 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 7.27/7.58 (declare-fun tptp.accp_P7675410724331315407_VEBTi ((-> tptp.produc3625547720036274456_VEBTi tptp.produc3625547720036274456_VEBTi Bool) tptp.produc3625547720036274456_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.accp_VEBT_VEBTi ((-> tptp.vEBT_VEBTi tptp.vEBT_VEBTi Bool) tptp.vEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 7.27/7.58 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 7.27/7.58 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 7.27/7.58 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 7.27/7.58 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 7.27/7.58 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 7.27/7.58 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 7.27/7.58 (declare-fun tptp.member_list_real (tptp.list_real tptp.set_list_real) Bool)
% 7.27/7.58 (declare-fun tptp.member8117914210271334748_VEBTi (tptp.list_VEBT_VEBTi tptp.set_list_VEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 7.27/7.58 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 7.27/7.58 (declare-fun tptp.member157494554546826820nteger (tptp.produc8923325533196201883nteger tptp.set_Pr4811707699266497531nteger) Bool)
% 7.27/7.58 (declare-fun tptp.member6260224972018164377et_nat (tptp.produc3658429121746597890et_nat tptp.set_Pr3948176798113811640et_nat) Bool)
% 7.27/7.58 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 7.27/7.58 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.27/7.58 (declare-fun tptp.member7279096912039735102um_num (tptp.product_prod_num_num tptp.set_Pr8218934625190621173um_num) Bool)
% 7.27/7.58 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 7.27/7.58 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 7.27/7.58 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 7.27/7.58 (declare-fun tptp.member_VEBT_VEBTi (tptp.vEBT_VEBTi tptp.set_VEBT_VEBTi) Bool)
% 7.27/7.58 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.27/7.58 (declare-fun tptp.aktnode () tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.ma () tptp.nat)
% 7.27/7.58 (declare-fun tptp.mi () tptp.nat)
% 7.27/7.58 (declare-fun tptp.minew () tptp.nat)
% 7.27/7.58 (declare-fun tptp.na () tptp.nat)
% 7.27/7.58 (declare-fun tptp.newnode () tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.tia () tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.tree_is () tptp.list_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.va () tptp.nat)
% 7.27/7.58 (declare-fun tptp.x13 () tptp.array_VEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.x14 () tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.xa () tptp.nat)
% 7.27/7.58 (declare-fun tptp.xaa () tptp.vEBT_VEBT)
% 7.27/7.58 (declare-fun tptp.xb () tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.xba () tptp.option_nat)
% 7.27/7.58 (declare-fun tptp.xc () tptp.vEBT_VEBTi)
% 7.27/7.58 (declare-fun tptp.xnew () tptp.nat)
% 7.27/7.58 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D tptp.assn) (X tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) B)))) (=> (@ (@ tptp.entails (@ _let_1 (@ (@ tptp.times_times_assn C) D))) X) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ _let_1 C)) D)) X)))))
% 7.27/7.58 (assert (forall ((P tptp.assn) (Q tptp.assn) (Q2 tptp.assn) (R tptp.assn) (X tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P))) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 Q)) Q2)) R)) X) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 R)) Q)) Q2)) X)))))
% 7.27/7.58 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn B) A)) C)) X) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) B)) C)) X))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (D2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X2) D2)) (@ (@ tptp.vEBT_VEBT_low X2) D2)) D2) X2)))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2)) I) X2))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) I) X2))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real Xs) I) X2)) I) X2))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I) X2)) I) X2))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X2)) I) X2))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (J tptp.nat) (X2 tptp.vEBT_VEBTi)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L))) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) J) X2)) I) (@ (@ tptp.nth_VEBT_VEBTi L) I)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (J tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) J) X2)) I) (@ (@ tptp.nth_VEBT_VEBT L) I)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_real) (J tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L))) (= (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real L) J) X2)) I) (@ (@ tptp.nth_real L) I)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_o) (J tptp.nat) (X2 Bool)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L))) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o L) J) X2)) I) (@ (@ tptp.nth_o L) I)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_nat) (J tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) J) X2)) I) (@ (@ tptp.nth_nat L) I)))))
% 7.27/7.58 (assert (forall ((B2 tptp.real) (W tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A2) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.27/7.58 (assert (forall ((B2 tptp.rat) (W tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) _let_1)) A2) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) _let_1)) B2)))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B2) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) _let_1)) B2)))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (@ (@ tptp.ord_less_nat X2) Mi) (@ (@ tptp.ord_less_nat Ma) X2)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X2) _let_1))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (I tptp.nat)) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) (@ (@ tptp.nth_VEBT_VEBTi Xs) I)) Xs)))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ (@ tptp.nth_VEBT_VEBT Xs) I)) Xs)))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I) (@ (@ tptp.nth_nat Xs) I)) Xs)))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_o Xs) I) (@ (@ tptp.nth_o Xs) I)) Xs)))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_real Xs) I) (@ (@ tptp.nth_real Xs) I)) Xs)))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2)) J) (@ (@ tptp.nth_VEBT_VEBTi Xs) J)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) J) (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X2)) J) (@ (@ tptp.nth_nat Xs) J)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (not (= I J)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I) X2)) J) (@ (@ tptp.nth_o Xs) J)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_real) (X2 tptp.real)) (=> (not (= I J)) (= (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real Xs) I) X2)) J) (@ (@ tptp.nth_real Xs) J)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (I tptp.nat) (X2 tptp.real)) (= (@ tptp.size_size_list_real (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ tptp.size_size_list_real Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs) I) X2)) (@ tptp.size_size_list_o Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I) X2)) (@ tptp.size_size_list_nat Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (I tptp.nat) (X2 tptp.vEBT_VEBTi)) (= (@ tptp.size_s7982070591426661849_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2)) (@ tptp.size_s7982070591426661849_VEBTi Xs))))
% 7.27/7.58 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (not (= X2 tptp.none_P5556105721700978146at_nat)) (exists ((Y tptp.product_prod_nat_nat)) (= X2 (@ tptp.some_P7363390416028606310at_nat Y))))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (= (not (= X2 tptp.none_nat)) (exists ((Y tptp.nat)) (= X2 (@ tptp.some_nat Y))))))
% 7.27/7.58 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (forall ((Y tptp.product_prod_nat_nat)) (not (= X2 (@ tptp.some_P7363390416028606310at_nat Y)))) (= X2 tptp.none_P5556105721700978146at_nat))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X2 (@ tptp.some_nat Y)))) (= X2 tptp.none_nat))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 7.27/7.58 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_eq_nat Y) X3)))))))
% 7.27/7.58 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_eq_nat X3) Y)))))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 7.27/7.58 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 7.27/7.58 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 7.27/7.58 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y2)) (= X22 Y2))))
% 7.27/7.58 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y2)) (= X22 Y2))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (I tptp.nat) (X2 tptp.vEBT_VEBTi) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I))) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ _let_1 X2)) I) Y3) (@ _let_1 Y3)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X2)) I) Y3) (@ _let_1 Y3)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.list_update_nat Xs) I))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 X2)) I) Y3) (@ _let_1 Y3)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X2 Bool) (Y3 Bool)) (let ((_let_1 (@ (@ tptp.list_update_o Xs) I))) (= (@ (@ (@ tptp.list_update_o (@ _let_1 X2)) I) Y3) (@ _let_1 Y3)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (I tptp.nat) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.list_update_real Xs) I))) (= (@ (@ (@ tptp.list_update_real (@ _let_1 X2)) I) Y3) (@ _let_1 Y3)))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X2 Mi) (= X2 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 Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((V tptp.option2651255830984564193nteger)) (= (forall ((X3 tptp.code_integer) (Y tptp.code_integer)) (not (= V (@ tptp.some_P6772290148444788224nteger (@ (@ tptp.produc1086072967326762835nteger X3) Y))))) (= V tptp.none_P4506660739021792380nteger))))
% 7.27/7.58 (assert (forall ((V tptp.option936205604648967762et_nat)) (= (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (not (= V (@ tptp.some_P624177172695371229et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y))))) (= V tptp.none_P533106815845188193et_nat))))
% 7.27/7.58 (assert (forall ((V tptp.option2661157926820139483um_num)) (= (forall ((X3 tptp.num) (Y tptp.num)) (not (= V (@ tptp.some_P6201964756284913402um_num (@ (@ tptp.product_Pair_num_num X3) Y))))) (= V tptp.none_P4394680061957285238um_num))))
% 7.27/7.58 (assert (forall ((V tptp.option4624381673175914239nt_int)) (= (forall ((X3 tptp.int) (Y tptp.int)) (not (= V (@ tptp.some_P4184893108420464158nt_int (@ (@ tptp.product_Pair_int_int X3) Y))))) (= V tptp.none_P2377608414092835994nt_int))))
% 7.27/7.58 (assert (forall ((V tptp.option4927543243414619207at_nat)) (= (forall ((X3 tptp.nat) (Y tptp.nat)) (not (= V (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y))))) (= V tptp.none_P5556105721700978146at_nat))))
% 7.27/7.58 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X3)) (@ tptp.some_nat Y)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2) Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (I tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_real Xs)) I) (= (@ (@ (@ tptp.list_update_real Xs) I) X2) Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X2 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) I) (= (@ (@ (@ tptp.list_update_o Xs) I) X2) Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I) (= (@ (@ (@ tptp.list_update_nat Xs) I) X2) Xs))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (I tptp.nat) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s7982070591426661849_VEBTi Xs)) I) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2) Xs))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) _let_1)) B2)))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B2) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) _let_1)) B2)))))
% 7.27/7.58 (assert (forall ((B2 tptp.real) (W tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A2) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.27/7.58 (assert (forall ((B2 tptp.rat) (W tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) _let_1)) A2) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N))))))
% 7.27/7.58 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 7.27/7.58 (assert (forall ((A2 tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (@ (@ tptp.member_VEBT_VEBT A2) (@ tptp.collect_VEBT_VEBT P)) (@ P A2))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A2) (@ tptp.collect_real P)) (@ P A2))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A2) (@ tptp.collect_int P)) (@ P A2))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A2) (@ tptp.collect_complex P)) (@ P A2))))
% 7.27/7.58 (assert (forall ((A2 tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.member5262025264175285858nt_int A2) (@ tptp.collec213857154873943460nt_int P)) (@ P A2))))
% 7.27/7.58 (assert (forall ((A tptp.set_VEBT_VEBT)) (= (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X3) A))) A)))
% 7.27/7.58 (assert (forall ((A tptp.set_real)) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A))) A)))
% 7.27/7.58 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A))) A)))
% 7.27/7.58 (assert (forall ((A tptp.set_int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A))) A)))
% 7.27/7.58 (assert (forall ((A tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A))) A)))
% 7.27/7.58 (assert (forall ((A tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X3) A))) A)))
% 7.27/7.58 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 7.27/7.58 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 7.27/7.58 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 7.27/7.58 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X4 tptp.product_prod_int_int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collec213857154873943460nt_int P) (@ tptp.collec213857154873943460nt_int Q)))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.27/7.58 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((M tptp.set_int) (X2 tptp.option_set_int)) (=> (@ (@ tptp.ord_le353528952715127954et_int (@ tptp.some_set_int M)) X2) (not (forall ((M2 tptp.set_int)) (=> (= X2 (@ tptp.some_set_int M2)) (not (@ (@ tptp.ord_less_eq_set_int M) M2))))))))
% 7.27/7.58 (assert (forall ((M tptp.rat) (X2 tptp.option_rat)) (=> (@ (@ tptp.ord_le2406147912482264968on_rat (@ tptp.some_rat M)) X2) (not (forall ((M2 tptp.rat)) (=> (= X2 (@ tptp.some_rat M2)) (not (@ (@ tptp.ord_less_eq_rat M) M2))))))))
% 7.27/7.58 (assert (forall ((M tptp.num) (X2 tptp.option_num)) (=> (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num M)) X2) (not (forall ((M2 tptp.num)) (=> (= X2 (@ tptp.some_num M2)) (not (@ (@ tptp.ord_less_eq_num M) M2))))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (X2 tptp.option_nat)) (=> (@ (@ tptp.ord_le5914376470875661696on_nat (@ tptp.some_nat M)) X2) (not (forall ((M2 tptp.nat)) (=> (= X2 (@ tptp.some_nat M2)) (not (@ (@ tptp.ord_less_eq_nat M) M2))))))))
% 7.27/7.58 (assert (forall ((M tptp.int) (X2 tptp.option_int)) (=> (@ (@ tptp.ord_le1736525451366464988on_int (@ tptp.some_int M)) X2) (not (forall ((M2 tptp.int)) (=> (= X2 (@ tptp.some_int M2)) (not (@ (@ tptp.ord_less_eq_int M) M2))))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 7.27/7.58 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_set_int A2) D2))))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_rat A2) D2))))))
% 7.27/7.58 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_num A2) D2))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_nat A2) D2))))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_int A2) D2))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4)))))))))
% 7.27/7.58 (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)))
% 7.27/7.58 (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)))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z2) (@ _let_1 Z2))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 7.27/7.58 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N3) (@ P M3))) (@ P N3))) (@ P N))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.27/7.58 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N4) (= M6 N4)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.27/7.58 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (not (= M6 N4))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) N) (not (@ P N5)))) (@ P N)) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N6) N) (@ P N6))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 7.27/7.58 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (= (and (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) _let_1)) (= B2 _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat B2) (@ tptp.suc A2))) (= B2 A2))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (S tptp.set_Pr4811707699266497531nteger) (P (-> tptp.code_integer tptp.code_integer Bool))) (let ((_let_1 (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger A3) B3)) S) (@ (@ P A3) B3))))))))
% 7.27/7.58 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat) (S tptp.set_Pr3948176798113811640et_nat) (P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (let ((_let_1 (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A3 tptp.heap_e7401611519738050253t_unit) (B3 tptp.set_nat)) (and (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A3) B3)) S) (@ (@ P A3) B3))))))))
% 7.27/7.58 (assert (forall ((A2 tptp.num) (B2 tptp.num) (S tptp.set_Pr8218934625190621173um_num) (P (-> tptp.num tptp.num Bool))) (let ((_let_1 (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num A3) B3)) S) (@ (@ P A3) B3))))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A3) B3)) S) (@ (@ P A3) B3))))))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (B2 tptp.int) (S tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int tptp.int Bool))) (let ((_let_1 (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A3) B3)) S) (@ (@ P A3) B3))))))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y3)) (= X2 Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.58 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3)))))) (@ P N))))
% 7.27/7.58 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P M3))) (@ P N3))) (@ P N))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 7.27/7.58 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 7.27/7.58 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Y3 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X2) (@ tptp.size_s6755466524823107622T_VEBT Y3))) (not (= X2 Y3)))))
% 7.27/7.58 (assert (forall ((X2 tptp.list_real) (Y3 tptp.list_real)) (=> (not (= (@ tptp.size_size_list_real X2) (@ tptp.size_size_list_real Y3))) (not (= X2 Y3)))))
% 7.27/7.58 (assert (forall ((X2 tptp.list_o) (Y3 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X2) (@ tptp.size_size_list_o Y3))) (not (= X2 Y3)))))
% 7.27/7.58 (assert (forall ((X2 tptp.list_nat) (Y3 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y3))) (not (= X2 Y3)))))
% 7.27/7.58 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y3))) (not (= X2 Y3)))))
% 7.27/7.58 (assert (forall ((X2 tptp.list_VEBT_VEBTi) (Y3 tptp.list_VEBT_VEBTi)) (=> (not (= (@ tptp.size_s7982070591426661849_VEBTi X2) (@ tptp.size_s7982070591426661849_VEBTi Y3))) (not (= X2 Y3)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_real)) (=> (not (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Ys))) (not (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (Ys tptp.list_VEBT_VEBTi)) (=> (not (= (@ tptp.size_s7982070591426661849_VEBTi Xs) (@ tptp.size_s7982070591426661849_VEBTi Ys))) (not (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_real)) (= (@ tptp.size_size_list_real Xs3) N))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 7.27/7.58 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBTi)) (= (@ tptp.size_s7982070591426661849_VEBTi Xs3) N))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (I3 tptp.nat) (Xs tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi) (X5 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.list_u6098035379799741383_VEBTi Xs))) (=> (not (= I I3)) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ (@ _let_1 I) X2)) I3) X5) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ (@ _let_1 I3) X5)) I) X2))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (I3 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (X5 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I I3)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X2)) I3) X5) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I3) X5)) I) X2))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat) (X5 tptp.nat)) (let ((_let_1 (@ tptp.list_update_nat Xs))) (=> (not (= I I3)) (= (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I) X2)) I3) X5) (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I3) X5)) I) X2))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (I3 tptp.nat) (Xs tptp.list_o) (X2 Bool) (X5 Bool)) (let ((_let_1 (@ tptp.list_update_o Xs))) (=> (not (= I I3)) (= (@ (@ (@ tptp.list_update_o (@ (@ _let_1 I) X2)) I3) X5) (@ (@ (@ tptp.list_update_o (@ (@ _let_1 I3) X5)) I) X2))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (I3 tptp.nat) (Xs tptp.list_real) (X2 tptp.real) (X5 tptp.real)) (let ((_let_1 (@ tptp.list_update_real Xs))) (=> (not (= I I3)) (= (@ (@ (@ tptp.list_update_real (@ (@ _let_1 I) X2)) I3) X5) (@ (@ (@ tptp.list_update_real (@ (@ _let_1 I3) X5)) I) X2))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M7 tptp.nat)) (and (= M (@ tptp.suc M7)) (@ (@ tptp.ord_less_nat N) M7))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 7.27/7.58 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs))))
% 7.27/7.58 (assert (forall ((P (-> tptp.list_real Bool)) (Xs 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 Xs))))
% 7.27/7.58 (assert (forall ((P (-> tptp.list_o Bool)) (Xs 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 Xs))))
% 7.27/7.58 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs 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 Xs))))
% 7.27/7.58 (assert (forall ((P (-> tptp.list_VEBT_VEBTi Bool)) (Xs tptp.list_VEBT_VEBTi)) (=> (forall ((Xs3 tptp.list_VEBT_VEBTi)) (=> (forall ((Ys2 tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s7982070591426661849_VEBTi Ys2)) (@ tptp.size_s7982070591426661849_VEBTi Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs))))
% 7.27/7.58 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y3 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y3 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y3 (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.27/7.58 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y3 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y3 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y3 (@ tptp.some_nat B3)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y3 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y3 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_nat A3)) (=> (= Y3 (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y3 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y3 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= X2 (@ tptp.some_nat A3)) (=> (= Y3 (@ tptp.some_nat B3)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.27/7.58 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X3 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X3)))))))
% 7.27/7.58 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X3 tptp.nat)) (@ P3 (@ tptp.some_nat X3)))))))
% 7.27/7.58 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X3 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X3)))))))
% 7.27/7.58 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X3 tptp.nat)) (@ P3 (@ tptp.some_nat X3)))))))
% 7.27/7.58 (assert (forall ((Y3 tptp.option4927543243414619207at_nat)) (=> (not (= Y3 tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y3 (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 7.27/7.58 (assert (forall ((Y3 tptp.option_nat)) (=> (not (= Y3 tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y3 (@ tptp.some_nat X23))))))))
% 7.27/7.58 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 7.27/7.58 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 7.27/7.58 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 7.27/7.58 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex A2) (@ tptp.numera6690914467698888265omplex tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) (@ tptp.numeral_numeral_real tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) (@ tptp.numeral_numeral_rat tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) (@ tptp.numeral_numeral_nat tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) (@ tptp.numeral_numeral_int tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A2) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A2) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A2) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A2) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A2) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) (@ tptp.numera6690914467698888265omplex tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) (@ tptp.numeral_numeral_real tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) (@ tptp.numeral_numeral_rat tptp.one)) A2)))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_real (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_num (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N2) (@ (@ tptp.ord_less_int (@ F N)) (@ F N2))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.vEBT_VEBT tptp.nat Bool))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (exists ((Li tptp.vEBT_VEBT)) (@ (@ P Li) I2)))) (not (forall ((L2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT L2) N) (not (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ P (@ (@ tptp.nth_VEBT_VEBT L2) I5)) I5))))))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.real tptp.nat Bool))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (exists ((Li tptp.real)) (@ (@ P Li) I2)))) (not (forall ((L2 tptp.list_real)) (=> (= (@ tptp.size_size_list_real L2) N) (not (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ P (@ (@ tptp.nth_real L2) I5)) I5))))))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> Bool tptp.nat Bool))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (exists ((Li Bool)) (@ (@ P Li) I2)))) (not (forall ((L2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o L2) N) (not (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ P (@ (@ tptp.nth_o L2) I5)) I5))))))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (exists ((Li tptp.nat)) (@ (@ P Li) I2)))) (not (forall ((L2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat L2) N) (not (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ P (@ (@ tptp.nth_nat L2) I5)) I5))))))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (P (-> tptp.vEBT_VEBTi tptp.nat Bool))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (exists ((Li tptp.vEBT_VEBTi)) (@ (@ P Li) I2)))) (not (forall ((L2 tptp.list_VEBT_VEBTi)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi L2) N) (not (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ P (@ (@ tptp.nth_VEBT_VEBTi L2) I5)) I5))))))))))
% 7.27/7.58 (assert (= (lambda ((Y6 tptp.list_VEBT_VEBT) (Z3 tptp.list_VEBT_VEBT)) (= Y6 Z3)) (lambda ((Xs2 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) (@ (@ tptp.nth_VEBT_VEBT Ys3) I4))))))))
% 7.27/7.58 (assert (= (lambda ((Y6 tptp.list_real) (Z3 tptp.list_real)) (= Y6 Z3)) (lambda ((Xs2 tptp.list_real) (Ys3 tptp.list_real)) (and (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_real Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I4) (@ (@ tptp.nth_real Ys3) I4))))))))
% 7.27/7.58 (assert (= (lambda ((Y6 tptp.list_o) (Z3 tptp.list_o)) (= Y6 Z3)) (lambda ((Xs2 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) (@ (@ tptp.nth_o Ys3) I4))))))))
% 7.27/7.58 (assert (= (lambda ((Y6 tptp.list_nat) (Z3 tptp.list_nat)) (= Y6 Z3)) (lambda ((Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 7.27/7.58 (assert (= (lambda ((Y6 tptp.list_VEBT_VEBTi) (Z3 tptp.list_VEBT_VEBTi)) (= Y6 Z3)) (lambda ((Xs2 tptp.list_VEBT_VEBTi) (Ys3 tptp.list_VEBT_VEBTi)) (and (= (@ tptp.size_s7982070591426661849_VEBTi Xs2) (@ tptp.size_s7982070591426661849_VEBTi Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_VEBT_VEBTi Xs2) I4) (@ (@ tptp.nth_VEBT_VEBTi Ys3) I4))))))))
% 7.27/7.58 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 tptp.vEBT_VEBT)) (@ (@ P I4) X7)))) (exists ((Xs2 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))))))))
% 7.27/7.58 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.real Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 tptp.real)) (@ (@ P I4) X7)))) (exists ((Xs2 tptp.list_real)) (and (= (@ tptp.size_size_list_real Xs2) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_real Xs2) I4)))))))))
% 7.27/7.58 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 Bool)) (@ (@ P I4) X7)))) (exists ((Xs2 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs2) I4)))))))))
% 7.27/7.58 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 tptp.nat)) (@ (@ P I4) X7)))) (exists ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs2) I4)))))))))
% 7.27/7.58 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBTi Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X7 tptp.vEBT_VEBTi)) (@ (@ P I4) X7)))) (exists ((Xs2 tptp.list_VEBT_VEBTi)) (and (= (@ tptp.size_s7982070591426661849_VEBTi Xs2) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBTi Xs2) I4)))))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Ys) I2)))) (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_real)) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Ys) I2)))) (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I2) (@ (@ tptp.nth_o Ys) I2)))) (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) (@ (@ tptp.nth_nat Ys) I2)))) (= Xs Ys)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (Ys tptp.list_VEBT_VEBTi)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi Xs) (@ tptp.size_s7982070591426661849_VEBTi Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (= (@ (@ tptp.nth_VEBT_VEBTi Xs) I2) (@ (@ tptp.nth_VEBT_VEBTi Ys) I2)))) (= Xs Ys)))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2) Xs) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I) X2)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (= (@ (@ (@ tptp.list_update_real Xs) I) X2) Xs) (= (@ (@ tptp.nth_real Xs) I) X2)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ (@ tptp.list_update_o Xs) I) X2) Xs) (= (@ (@ tptp.nth_o Xs) I) X2)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I) X2) Xs) (= (@ (@ tptp.nth_nat Xs) I) X2)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (= (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2) Xs) (= (@ (@ tptp.nth_VEBT_VEBTi Xs) I) X2)))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X2)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L))))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT L) J))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real L) I) X2)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L))))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_real L) J))))))))
% 7.27/7.58 (assert (forall ((L tptp.list_o) (I tptp.nat) (X2 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) X2)) J) (and (=> _let_1 X2) (=> (not _let_1) (@ (@ tptp.nth_o L) J)))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) I) X2)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat L) J))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) X2)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L))))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBTi L) J))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_real) (J tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real Xs) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_real Xs) J)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (X2 Bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I) X2)) J) (and (=> _let_1 X2) (=> (not _let_1) (@ (@ tptp.nth_o Xs) J))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBTi) (J tptp.nat) (X2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBTi Xs) J)))))))))
% 7.27/7.58 (assert (=> (not (= tptp.ma tptp.mi)) (=> (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.na) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))))
% 7.27/7.58 (assert (=> (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.xa) (=> (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.na) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X2 Mi) (= X2 Ma) (and (@ (@ tptp.ord_less_nat X2) Ma) (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))))))))))
% 7.27/7.58 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 7.27/7.58 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X2 Mi) (= X2 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))))
% 7.27/7.58 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X2) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Mi))))))
% 7.27/7.58 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Ma))))))
% 7.27/7.58 (assert (=> (not (= tptp.ma tptp.mi)) (=> (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xnew) (@ (@ tptp.divide_divide_nat tptp.na) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_option_nat tptp.none_nat) (@ tptp.some_nat X2))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_option_real (@ tptp.some_real X2)) (@ tptp.some_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_option_rat (@ tptp.some_rat X2)) (@ tptp.some_rat Y3)) (@ (@ tptp.ord_less_rat X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.ord_less_option_num (@ tptp.some_num X2)) (@ tptp.some_num Y3)) (@ (@ tptp.ord_less_num X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.ord_less_option_nat (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_option_int (@ tptp.some_int X2)) (@ tptp.some_int Y3)) (@ (@ tptp.ord_less_int X2) Y3))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (@ (@ tptp.ord_le5914376470875661696on_nat tptp.none_nat) X2)))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (not (@ (@ tptp.ord_less_option_nat X2) tptp.none_nat))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ tptp.ord_le353528952715127954et_int (@ tptp.some_set_int X2)) (@ tptp.some_set_int Y3)) (@ (@ tptp.ord_less_eq_set_int X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_le2406147912482264968on_rat (@ tptp.some_rat X2)) (@ tptp.some_rat Y3)) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num X2)) (@ tptp.some_num Y3)) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.ord_le5914376470875661696on_nat (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_le1736525451366464988on_int (@ tptp.some_int X2)) (@ tptp.some_int Y3)) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_le5914376470875661696on_nat (@ tptp.some_nat X2)) tptp.none_nat))))
% 7.27/7.58 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) (@ tptp.suc (@ tptp.suc tptp.va))) tptp.treeList) tptp.summary)) tptp.na))
% 7.27/7.58 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M3) N3) (@ P M3))) (@ P N3))) (@ P N))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (@ (@ tptp.ord_le5914376470875661696on_nat tptp.none_nat) X2)))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (=> (@ (@ tptp.ord_le5914376470875661696on_nat X2) tptp.none_nat) (= X2 tptp.none_nat))))
% 7.27/7.58 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_option_nat tptp.none_nat) (@ tptp.some_nat X2))))
% 7.27/7.58 (assert (forall ((X2 tptp.option_nat)) (=> (@ (@ tptp.ord_less_option_nat tptp.none_nat) X2) (exists ((Z2 tptp.nat)) (= X2 (@ tptp.some_nat Z2))))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X2) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (=> (not (= X2 Mi)) (=> (not (= X2 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))))))))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X2) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X2) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 7.27/7.58 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 7.27/7.58 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 7.27/7.58 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (@ (@ tptp.ord_less_eq_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))))
% 7.27/7.58 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2))) _let_1) TreeList) Summary)))))
% 7.27/7.58 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 7.27/7.58 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete T) X2)) N))))
% 7.27/7.58 (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) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList2) S3))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_delete T) X2)) Y3) (and (not (= X2 Y3)) (@ (@ tptp.vEBT_vebt_member T) Y3))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X2) Y3) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)) (@ tptp.some_nat Z)))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat Mini) X2))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Va) _let_1))))) (= (@ (@ tptp.times_times_nat I) _let_2) (@ (@ tptp.times_times_nat _let_2) I))))))
% 7.27/7.58 (assert (= tptp.vEBT_VEBT_high (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 7.27/7.58 (assert (forall ((Tree tptp.vEBT_VEBT) (X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X2) tptp.none_nat))))))
% 7.27/7.58 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 7.27/7.58 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Y3)) (@ (@ tptp.ord_less_nat Y3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Y3)) (@ (@ tptp.ord_less_nat Y3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y3) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X2)) Y3) (or (@ (@ tptp.vEBT_vebt_member T) Y3) (= X2 Y3)))))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 7.27/7.58 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.member_nat X2) (@ tptp.vEBT_set_vebt T))))))
% 7.27/7.58 (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)))))))))
% 7.27/7.58 (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)))))))))
% 7.27/7.58 (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)))))))))
% 7.27/7.58 (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)))))))))
% 7.27/7.58 (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)))))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X2) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X2) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2))))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M5) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.code_integer) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ (@ 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)))))))
% 7.27/7.58 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat tptp.na) (@ (@ tptp.divide_divide_nat tptp.na) _let_1))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) (@ (@ tptp.minus_minus_nat tptp.na) (@ (@ tptp.divide_divide_nat tptp.na) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A2))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A2) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_3573771949741848930nteger A2) (@ (@ tptp.power_8256067586552552935nteger (@ _let_2 N)) _let_1)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A2))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A2) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A2))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_rat A2) (@ (@ tptp.power_power_rat (@ _let_2 N)) _let_1)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A2))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A2) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A2))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A2) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT T) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt T) (@ (@ tptp.divide_divide_nat tptp.na) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 7.27/7.58 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X2)) Y3) (and (not (= X2 Y3)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y3))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X4) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs) N))))))
% 7.27/7.58 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X8) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 7.27/7.58 (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))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X2)) X2)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y3) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y3)) X2))))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A2) B2)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A2) _let_1)) (@ (@ tptp.times_times_complex B2) _let_1))))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B2)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A2) _let_1)) (@ (@ tptp.times_times_real B2) _let_1))))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A2) _let_1)) (@ (@ tptp.times_times_rat B2) _let_1))))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A2) _let_1)) (@ (@ tptp.times_times_int B2) _let_1))))))
% 7.27/7.58 (assert (forall ((V tptp.num) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B2) C2)) (@ (@ tptp.minus_minus_complex (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.58 (assert (forall ((V tptp.num) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.58 (assert (forall ((V tptp.num) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.58 (assert (forall ((V tptp.num) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_real) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_real Xs))) (let ((_let_2 (@ tptp.size_size_list_real Xs))) (=> (@ (@ 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 Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_real2 Xs))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (let ((_let_2 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_o2 Xs))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBTi) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBTi Xs))) (let ((_let_2 (@ tptp.size_s7982070591426661849_VEBTi Xs))) (=> (@ (@ 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 Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBTi2 Xs))))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y3) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat X2) Y3) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat X2) Z4)) (@ (@ tptp.ord_less_eq_nat Y3) Z4)))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y3) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat Y3) X2) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat Z4) X2)) (@ (@ tptp.ord_less_eq_nat Z4) Y3)))))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Px)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Sx)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 7.27/7.58 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 7.27/7.58 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X3))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (B tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B)))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 7.27/7.58 (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))))))))
% 7.27/7.58 (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))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (let ((_let_2 (@ tptp.minus_minus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A2) C2) (=> (@ _let_1 C2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A2)) (@ _let_2 B2)) (@ _let_1 A2))))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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))))))))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (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)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (A tptp.set_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi) (I tptp.nat)) (=> (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 Xs)) A) (=> (@ (@ tptp.member_VEBT_VEBTi X2) A) (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2))) A)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A) (=> (@ (@ tptp.member_VEBT_VEBT X2) A) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2))) A)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (A tptp.set_nat) (X2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X2))) A)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (A tptp.set_o) (X2 Bool) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X2))) A)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (A tptp.set_real) (X2 tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A) (=> (@ (@ tptp.member_real X2) A) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X2))) A)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_int) (A tptp.set_int) (X2 tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X2))) A)))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 7.27/7.58 (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))))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C2) A2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A2) C2)) (@ (@ tptp.minus_minus_nat B2) C2))))))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y3)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y3) X2)) _let_1)))))
% 7.27/7.58 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger X2) Y3)) _let_1) (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger Y3) X2)) _let_1)))))
% 7.27/7.58 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y3)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y3) X2)) _let_1)))))
% 7.27/7.58 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y3)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y3) X2)) _let_1)))))
% 7.27/7.58 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y3)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y3) X2)) _let_1)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N)) (@ tptp.set_real2 Xs)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N)) (@ tptp.set_o2 Xs)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ (@ tptp.member_VEBT_VEBTi (@ (@ tptp.nth_VEBT_VEBTi Xs) N)) (@ tptp.set_VEBT_VEBTi2 Xs)))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (=> (forall ((X4 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X4) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs) N))))))
% 7.27/7.58 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) X2))))))
% 7.27/7.58 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) X2))))))
% 7.27/7.58 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I4) X2))))))
% 7.27/7.58 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) X2))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) X2))))))
% 7.27/7.58 (assert (forall ((X2 tptp.vEBT_VEBTi) (Xs tptp.list_VEBT_VEBTi)) (= (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (= (@ (@ tptp.nth_VEBT_VEBTi Xs) I4) X2))))))
% 7.27/7.58 (assert (forall ((L tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 L)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT L)) (@ P (@ (@ tptp.nth_VEBT_VEBT L) I4)))))))
% 7.27/7.58 (assert (forall ((L tptp.list_real) (P (-> tptp.real Bool))) (= (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 L)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real L)) (@ P (@ (@ tptp.nth_real L) I4)))))))
% 7.27/7.58 (assert (forall ((L tptp.list_o) (P (-> Bool Bool))) (= (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 L)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o L)) (@ P (@ (@ tptp.nth_o L) I4)))))))
% 7.27/7.58 (assert (forall ((L tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 L)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat L)) (@ P (@ (@ tptp.nth_nat L) I4)))))))
% 7.27/7.58 (assert (forall ((L tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool))) (= (forall ((X3 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X3) (@ tptp.set_VEBT_VEBTi2 L)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s7982070591426661849_VEBTi L)) (@ P (@ (@ tptp.nth_VEBT_VEBTi L) I4)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I2)))) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X2)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I2)))) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ P X2)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X2 Bool)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I2)))) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ P X2)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I2)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool)) (X2 tptp.vEBT_VEBTi)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs) I2)))) (=> (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ P X2)))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool))) (= (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I4)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I4)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))))))
% 7.27/7.58 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool))) (= (forall ((X3 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X3) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs) I4)))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_int) (X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y3))) (or (= X2 Y3) (and (@ _let_1 (@ tptp.set_int2 L)) (forall ((Y tptp.int)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y)))))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y3))) (or (= X2 Y3) (and (@ _let_1 (@ tptp.set_VEBT_VEBT2 L)) (forall ((Y tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y)))))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (= (@ _let_1 (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y3))) (or (= X2 Y3) (and (@ _let_1 (@ tptp.set_real2 L)) (forall ((Y tptp.real)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y)))))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_o) (X2 Bool) (Y3 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ _let_1 (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y3))) (or (= X2 Y3) (and (@ _let_1 (@ tptp.set_o2 L)) (forall ((Y Bool)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y)))))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y3))) (or (= X2 Y3) (and (@ _let_1 (@ tptp.set_nat2 L)) (forall ((Y tptp.nat)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y)))))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.member_VEBT_VEBTi X2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (= (@ _let_1 (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y3))) (or (= X2 Y3) (and (@ _let_1 (@ tptp.set_VEBT_VEBTi2 L)) (forall ((Y tptp.vEBT_VEBTi)) (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y)))))))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X2))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) X2))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) N) X2))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X2))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X2))))))
% 7.27/7.58 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) N) X2))))))
% 7.27/7.58 (assert (forall ((X2 tptp.int) (L tptp.list_int) (I tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y3))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (not (= X2 Y3))) (@ _let_1 (@ tptp.set_int2 L)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.vEBT_VEBT) (L tptp.list_VEBT_VEBT) (I tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y3))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (not (= X2 Y3))) (@ _let_1 (@ tptp.set_VEBT_VEBT2 L)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.real) (L tptp.list_real) (I tptp.nat) (Y3 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y3))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (not (= X2 Y3))) (@ _let_1 (@ tptp.set_real2 L)))))))
% 7.27/7.58 (assert (forall ((X2 Bool) (L tptp.list_o) (I tptp.nat) (Y3 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ _let_1 (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y3))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= X2 (not Y3))) (@ _let_1 (@ tptp.set_o2 L)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (L tptp.list_nat) (I tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y3))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (not (= X2 Y3))) (@ _let_1 (@ tptp.set_nat2 L)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.vEBT_VEBTi) (L tptp.list_VEBT_VEBTi) (I tptp.nat) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.member_VEBT_VEBTi X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y3))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (not (= X2 Y3))) (@ _let_1 (@ tptp.set_VEBT_VEBTi2 L)))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_int) (X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y3))) (or (= X2 Y3) (forall ((Y tptp.int)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y3))) (or (= X2 Y3) (forall ((Y tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y3))) (or (= X2 Y3) (forall ((Y tptp.real)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_o) (X2 Bool) (Y3 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y3))) (or (= X2 Y3) (forall ((Y Bool)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y3))) (or (= X2 Y3) (forall ((Y tptp.nat)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y)))))))))
% 7.27/7.58 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi) (Y3 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (= (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y3))) (or (= X2 Y3) (forall ((Y tptp.vEBT_VEBTi)) (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y)))))))))
% 7.27/7.58 (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)))))))
% 7.27/7.58 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A2) B2)) (@ (@ tptp.divide_divide_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat X2))) (=> (@ _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)))))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat X2))) (=> (@ _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)))))))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A2) N))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) A2) (@ (@ tptp.times_3573771949741848930nteger A2) _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A2) N))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N))) (= (@ (@ tptp.times_times_rat _let_1) A2) (@ (@ tptp.times_times_rat A2) _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N))) (= (@ (@ tptp.times_times_nat _let_1) A2) (@ (@ tptp.times_times_nat A2) _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N))) (= (@ (@ tptp.times_times_int _let_1) A2) (@ (@ tptp.times_times_int A2) _let_1)))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A2) B2)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A2) N)) (@ (@ tptp.power_power_complex B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A2) B2)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A2) B2)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A2) B2)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A2) B2)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)))))
% 7.27/7.58 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) N))) (let ((_let_2 (@ tptp.times_times_complex Y3))) (=> (= (@ (@ tptp.times_times_complex X2) Y3) (@ _let_2 X2)) (= (@ (@ tptp.times_times_complex _let_1) Y3) (@ _let_2 _let_1)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger X2) N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger Y3))) (=> (= (@ (@ tptp.times_3573771949741848930nteger X2) Y3) (@ _let_2 X2)) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y3) (@ _let_2 _let_1)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) N))) (let ((_let_2 (@ tptp.times_times_real Y3))) (=> (= (@ (@ tptp.times_times_real X2) Y3) (@ _let_2 X2)) (= (@ (@ tptp.times_times_real _let_1) Y3) (@ _let_2 _let_1)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) N))) (let ((_let_2 (@ tptp.times_times_rat Y3))) (=> (= (@ (@ tptp.times_times_rat X2) Y3) (@ _let_2 X2)) (= (@ (@ tptp.times_times_rat _let_1) Y3) (@ _let_2 _let_1)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X2) N))) (let ((_let_2 (@ tptp.times_times_nat Y3))) (=> (= (@ (@ tptp.times_times_nat X2) Y3) (@ _let_2 X2)) (= (@ (@ tptp.times_times_nat _let_1) Y3) (@ _let_2 _let_1)))))))
% 7.27/7.58 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X2) N))) (let ((_let_2 (@ tptp.times_times_int Y3))) (=> (= (@ (@ tptp.times_times_int X2) Y3) (@ _let_2 X2)) (= (@ (@ tptp.times_times_int _let_1) Y3) (@ _let_2 _let_1)))))))
% 7.27/7.58 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A2) B2)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A2) N)) (@ (@ tptp.power_power_complex B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A2) B2)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A2) B2)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)))))
% 7.27/7.58 (assert (forall ((A2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_8256067586552552935nteger (@ _let_1 M)) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2)) A2)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X2) X2)) X2)) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger X2) X2)) X2)) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X2) X2)) X2)) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X2) X2)) X2)) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.power_power_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X2) X2)) X2)) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X2) X2)) X2)) X2))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A2))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A2))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A2))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A2))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_8256067586552552935nteger (@ _let_2 N)) _let_1))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X3) N4))) (@ (@ tptp.vEBT_VEBT_low X3) N4)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2))))))))
% 7.27/7.59 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (let ((_let_1 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= tptp.xnew (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_2) (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.va))) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))))))))
% 7.27/7.59 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L3 tptp.nat) (D3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D3))) L3))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y3) _let_1)) X2)) N) X2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y3) _let_1)) X2)) N) Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 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 A2) B2))) (@ _let_1 A2)) (@ _let_1 B2)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_assn tptp.one_one_assn) N) tptp.one_one_assn)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) N) tptp.one_one_Code_integer)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (let ((_let_1 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= tptp.minew (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_2) (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.va))) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A2) B2)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A2) _let_1)) (@ (@ tptp.times_times_complex B2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A2) B2)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) _let_1)) (@ (@ tptp.times_times_real B2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) _let_1)) (@ (@ tptp.times_times_rat B2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) _let_1)) (@ (@ tptp.times_times_nat B2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) _let_1)) (@ (@ tptp.times_times_int B2) _let_1))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C2)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 7.27/7.59 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 7.27/7.59 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.va))) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_3))))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.divide_divide_nat tptp.va) _let_1))) (= tptp.newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) (@ _let_6 _let_7))) _let_3)) _let_5)) (@ tptp.suc _let_7)))) (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ _let_6 _let_2))) _let_5)) _let_2)))))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (=> (not (= tptp.ma tptp.mi)) (=> (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma) (= tptp.aktnode (@ _let_4 (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2))) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_3))))) (@ tptp.suc _let_2)))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.code_integer) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_rat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_nat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_int (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))))))))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (forall ((B2 tptp.code_integer) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 7.27/7.59 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 7.27/7.59 (assert (not (forall ((Aktnode tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (not (=> (not (= tptp.ma tptp.mi)) (=> (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma) (= Aktnode (@ _let_4 (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2))) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_3))))) (@ tptp.suc _let_2))))))))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2))))))
% 7.27/7.59 (assert (forall ((S tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.collect_nat P)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ P X3))))))
% 7.27/7.59 (assert (forall ((S tptp.set_complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex S) (@ tptp.collect_complex P)) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (@ P X3))))))
% 7.27/7.59 (assert (forall ((S tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le2843351958646193337nt_int S) (@ tptp.collec213857154873943460nt_int P)) (forall ((X3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int X3) S) (@ P X3))))))
% 7.27/7.59 (assert (forall ((S tptp.set_int) (P (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int S) (@ tptp.collect_int P)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ P X3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X2))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 7.27/7.59 (assert (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))
% 7.27/7.59 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 7.27/7.59 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 7.27/7.59 (assert (forall ((A tptp.nat) (K tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A (@ _let_1 A2)) (= (@ tptp.suc A) (@ _let_1 (@ tptp.suc A2)))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 7.27/7.59 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 7.27/7.59 (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))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 7.27/7.59 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 7.27/7.59 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 7.27/7.59 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 7.27/7.59 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q4 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q4)))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 7.27/7.59 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N3) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 7.27/7.59 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_real A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A) (=> (@ (@ tptp.ord_less_nat B2) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.times_times_nat A) N7))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (A4 tptp.nat) (B2 tptp.nat) (N7 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A4) (=> (@ (@ tptp.ord_less_nat B2) N7) (=> (@ (@ tptp.ord_less_nat B4) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A4) N7)) B4)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (A4 tptp.nat) (B2 tptp.nat) (B4 tptp.nat) (N7 tptp.nat)) (=> (= A2 A4) (=> (@ (@ tptp.ord_less_nat B2) B4) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A4) N7)) B4))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((X2 tptp.assn) (Y3 tptp.assn) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X2) Y3) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X2) N)) (@ (@ tptp.power_power_assn Y3) N)) tptp.one_one_assn))))
% 7.27/7.59 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X2) Y3) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y3) N)) tptp.one_one_complex))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X2) Y3) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y3) N)) tptp.one_one_Code_integer))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X2) Y3) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y3) N)) tptp.one_one_real))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X2) Y3) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y3) N)) tptp.one_one_rat))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X2) Y3) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y3) N)) tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X2) Y3) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y3) N)) tptp.one_one_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (A4 tptp.nat) (B2 tptp.nat) (B4 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) A4) (=> (@ (@ tptp.ord_less_eq_nat B2) B4) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A4) N7)) B4))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A2)) N) (@ _let_1 (@ (@ tptp.power_power_complex A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A2)) N) (@ _let_1 (@ (@ tptp.power_power_real A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A2)) N) (@ _let_1 (@ (@ tptp.power_power_rat A2) N))))))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 7.27/7.59 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 7.27/7.59 (assert (forall ((N2 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 N2)))) (=> (@ (@ tptp.ord_less_eq_nat N2) 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))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B2) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A2) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A2) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) (@ (@ tptp.power_8256067586552552935nteger A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_real A2) (@ (@ tptp.power_power_real A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_rat A2) (@ (@ tptp.power_power_rat A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_nat A2) (@ (@ tptp.power_power_nat A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_int A2) (@ (@ tptp.power_power_int A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_real A2) (@ tptp.suc N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) (@ tptp.suc N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) (@ tptp.suc N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) (@ tptp.suc N)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N7)))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A2))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A2)) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A2)) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A2)) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A2)) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A2)) B2)))))
% 7.27/7.59 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 7.27/7.59 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 7.27/7.59 (assert (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (N tptp.nat) (X2 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 Y3) _let_2) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 M)) (=> (= Sz (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat X2) _let_2)) Y3)) (@ _let_1 Sz)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 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 X2) Y3)) _let_2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y3)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y3) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y3)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y3)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y3) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X2) Y3)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y3) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X2)) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X2) Y3)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y3) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y3)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 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 X2) Y3)) _let_2) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y3)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y3) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y3)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y3)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y3) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y3)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y3) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y3)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 7.27/7.59 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 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 Mi) Mi))) Deg) TreeList) Summary)) X2)) tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 7.27/7.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete T) X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e T) X2)) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (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 (= X2 Mi) (@ (@ tptp.ord_less_nat X2) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X2) (@ (@ (@ 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)))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi 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 (= X2 Mi) (@ (@ tptp.ord_less_nat X2) Ma)) (=> (not (= Mi 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 Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ 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)))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi 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 Mi) Ma))) Deg) TreeList) Summary)) X2))) (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 (= X2 Mi) (@ (@ tptp.ord_less_nat X2) Ma)) (=> (not (= Mi 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)))))))))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi 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 (= X2 Mi) (@ (@ tptp.ord_less_nat X2) Ma)) (=> (not (= Mi 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 Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ 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))))))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (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 (= X2 Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X2))) (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) (= X2 Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi))) (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 Mi) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X2) (@ (@ (@ 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)))))))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (X2 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 (= X2 Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi))) (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 X2) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X2) _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)) X2) (@ (@ (@ 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)) Mi) (@ (@ 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)))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat X2) Maxi))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.27/7.59 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ (@ 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)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ (@ 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)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ (@ 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)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ (@ 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)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ (@ 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)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (M tptp.num) (N tptp.num) (B2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A2))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (M tptp.num) (N tptp.num) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat N))) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (M tptp.num) (N tptp.num) (B2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (M tptp.num) (N tptp.num) (B2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B2)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (M tptp.num) (N tptp.num) (B2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B2)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (M tptp.num) (N tptp.num) (B2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B2)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (X2 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 Mi))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X2) _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)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X2 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)))))))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi 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 (= X2 Mi) (@ (@ tptp.ord_less_nat X2) Ma)) (=> (not (= Mi 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 Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ 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))))))))))))))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (X2 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 (= X2 Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList) Summary)) X2))) (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 X2) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X2) _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)) Mi) (@ (@ 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))))))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (X2 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 Mi))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X2) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X2) _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)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X2 Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi) (@ (@ 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))))))))))))))))))))
% 7.27/7.59 (assert (forall ((B2 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) B2)) tptp.one_one_int)) _let_1) B2))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 7.27/7.59 (assert (forall ((Z tptp.extended_enat) (Y3 tptp.extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y3) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y3) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y3)) Z))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 7.27/7.59 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 7.27/7.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 7.27/7.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) 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 (= X2 Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X2))) (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 (= X2 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) Mi))) (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) X2))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X2) Mi) (@ (@ tptp.ord_less_nat Ma) X2)))) (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)))))))))))))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (= X2 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))))) X2))) (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 Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (and _let_6 (= X2 Ma)))) (let ((_let_13 (= _let_11 tptp.one_one_nat))) (let ((_let_14 (or (@ (@ tptp.ord_less_nat X2) Mi) (@ (@ tptp.ord_less_nat Ma) X2)))) (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))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y3)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y3) _let_2)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Xd tptp.nat) (Xe tptp.vEBT_VEBT) (Xf tptp.list_VEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.va))) _let_2))) (let ((_let_4 (= tptp.xa tptp.mi))) (let ((_let_5 (not _let_4))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (=> (not (or (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi) (@ (@ tptp.ord_less_nat tptp.ma) tptp.xa))) (=> (not (and _let_4 (= tptp.xa tptp.ma))) (=> (and (=> _let_4 (= Xa (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) (@ (@ tptp.power_power_nat _let_2) _let_3))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_6)))))) (=> _let_5 (= Xa tptp.xa))) (=> (and (=> _let_4 (= Xb Xa)) (=> _let_5 (= Xb tptp.mi))) (=> (= Xc (@ (@ tptp.vEBT_VEBT_low Xa) _let_3)) (=> (= Xd (@ (@ tptp.vEBT_VEBT_high Xa) _let_3)) (=> (@ (@ tptp.ord_less_nat Xd) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)) (=> (= Xe (@ (@ tptp.vEBT_vebt_delete (@ _let_1 Xd)) Xc)) (=> (= Xf (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) Xd) Xe)) (=> (@ tptp.vEBT_VEBT_minNull Xe) (=> (@ (@ tptp.vEBT_invar_vebt tptp.summary) N) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.vEBT_vebt_assn_raw tptp.summary) Ti)) (@ (@ (@ tptp.vEBT_V1365221501068881998eletei tptp.summary) Ti) Xd)) (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_vebt_delete tptp.summary) Xd))))))))))))))))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height _let_1))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Xd tptp.nat) (N tptp.nat) (Ti tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_2 (@ _let_1 Xd))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.va))) _let_3))) (let ((_let_5 (= tptp.xa tptp.mi))) (let ((_let_6 (not _let_5))) (let ((_let_7 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (=> (not (or (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi) (@ (@ tptp.ord_less_nat tptp.ma) tptp.xa))) (=> (not (and _let_5 (= tptp.xa tptp.ma))) (=> (and (=> _let_5 (= Xa (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_7)))))) (=> _let_6 (= Xa tptp.xa))) (=> (and (=> _let_5 (= Xb Xa)) (=> _let_6 (= Xb tptp.mi))) (=> (= Xc (@ (@ tptp.vEBT_VEBT_low Xa) _let_4)) (=> (= Xd (@ (@ tptp.vEBT_VEBT_high Xa) _let_4)) (=> (@ (@ tptp.ord_less_nat Xd) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)) (=> (@ (@ tptp.vEBT_invar_vebt _let_2) N) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.vEBT_vebt_assn_raw _let_2) Ti)) (@ (@ (@ tptp.vEBT_V1365221501068881998eletei _let_2) Ti) Xc)) (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_vebt_delete _let_2) Xc))))))))))))))))))))
% 7.27/7.59 (assert (forall ((A2 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 A2))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.27/7.59 (assert (forall ((A2 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 A2))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.27/7.59 (assert (forall ((A2 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 A2))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int A2) tptp.one_one_int) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) tptp.one_one_complex) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) tptp.one_one_real) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) tptp.one_one_rat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat A2) tptp.one_one_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int A2) tptp.one_one_int) A2)))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ (@ tptp.vEBT_V3964819847710782039nserti T) Ti) X2)) (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_vebt_insert T) X2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A2) B2)) E)) C2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) E)) C2))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (E tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) E)) C2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) E)) C2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) E)) C2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A2) B2)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A2) B2)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A2) B2)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) C2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (C2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) C2)) A2) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B2) A2)) (@ (@ tptp.times_times_real C2) A2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) C2)) A2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B2) A2)) (@ (@ tptp.times_times_rat C2) A2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B2) C2)) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B2) A2)) (@ (@ tptp.times_times_nat C2) A2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) C2)) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B2) A2)) (@ (@ tptp.times_times_int C2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B2)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)))))
% 7.27/7.59 (assert (= (lambda ((X3 tptp.assn)) X3) (@ tptp.times_times_assn tptp.one_one_assn)))
% 7.27/7.59 (assert (= (lambda ((X3 tptp.real)) X3) (@ tptp.times_times_real tptp.one_one_real)))
% 7.27/7.59 (assert (= (lambda ((X3 tptp.rat)) X3) (@ tptp.times_times_rat tptp.one_one_rat)))
% 7.27/7.59 (assert (= (lambda ((X3 tptp.nat)) X3) (@ tptp.times_times_nat tptp.one_one_nat)))
% 7.27/7.59 (assert (= (lambda ((X3 tptp.int)) X3) (@ tptp.times_times_int tptp.one_one_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real A2) tptp.one_one_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) tptp.one_one_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B2) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B2) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B2) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real A2) B2)) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A2) B2)) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A2) B2)) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A2) B2)) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A2) B2)) A2))))
% 7.27/7.59 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) _let_2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 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 A2) C2))) (@ (@ tptp.times_times_real B2) D2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A2) _let_2)) (@ (@ tptp.power_power_real D2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B2) _let_2)) (@ (@ tptp.power_power_real C2) _let_2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D2)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B2)) E)) C2) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C2) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C2) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D2)) (= C2 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (= C2 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (= C2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) Y3)) (@ (@ tptp.minus_minus_real X2) Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y3) Y3)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) Y3)) (@ (@ tptp.minus_minus_rat X2) Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y3) Y3)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) Y3)) (@ (@ tptp.minus_minus_int X2) Y3)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B2)) E)) C2)) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C2)) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C2)) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D2)) (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D2)) (@ (@ tptp.ord_less_real C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (E tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E)) C2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B2)) E)) C2)) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C2)) D2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (E tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C2)) D2))))
% 7.27/7.59 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)))))
% 7.27/7.59 (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)))
% 7.27/7.59 (assert (forall ((X21 Bool) (X222 Bool)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) (@ tptp.suc (@ tptp.suc tptp.va))) tptp.treeList) tptp.summary))) (=> (= tptp.tia (@ (@ tptp.vEBT_Leafi X21) X222)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.vEBT_vebt_assn_raw _let_1) tptp.tia)) (@ (@ (@ tptp.vEBT_V1365221501068881998eletei _let_1) tptp.tia) tptp.xa)) (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_vebt_delete _let_1) tptp.xa)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 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 A2) B2)) _let_1)) A2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B2) A2)) _let_1)))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 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 B2) A2)) _let_1)) A2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B2) A2)) _let_1)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 7.27/7.59 (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))))))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) Mi) X2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X2) Y)))) tptp.bot_bot_set_nat)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 7.27/7.59 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X2)))) tptp.bot_bot_set_nat)))))
% 7.27/7.59 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 7.27/7.59 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 7.27/7.59 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 7.27/7.59 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.27/7.59 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 7.27/7.59 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 7.27/7.59 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((S tptp.set_VEBT_VEBT)) (=> (not (= S tptp.bot_bo8194388402131092736T_VEBT)) (not (forall ((X4 tptp.vEBT_VEBT)) (not (@ (@ tptp.member_VEBT_VEBT X4) S)))))))
% 7.27/7.59 (assert (forall ((S tptp.set_real)) (=> (not (= S tptp.bot_bot_set_real)) (not (forall ((X4 tptp.real)) (not (@ (@ tptp.member_real X4) S)))))))
% 7.27/7.59 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (not (forall ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) S)))))))
% 7.27/7.59 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (not (forall ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) S)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.vEBT_VEBT) (S tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) S) (not (= S tptp.bot_bo8194388402131092736T_VEBT)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (S tptp.set_real)) (=> (@ (@ tptp.member_real X2) S) (not (= S tptp.bot_bot_set_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) S) (not (= S tptp.bot_bot_set_nat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X2) S) (not (= S tptp.bot_bot_set_int)))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.minus_minus_set_nat A) B) tptp.bot_bot_set_nat))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= (@ (@ tptp.minus_minus_set_int A) B) tptp.bot_bot_set_int))))
% 7.27/7.59 (assert (forall ((Y3 tptp.num)) (=> (not (= Y3 tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y3 (@ tptp.bit0 X23)))) (not (forall ((X32 tptp.num)) (not (= Y3 (@ tptp.bit1 X32)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.product_prod_num_num)) (=> (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N3))))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N3))))) (not (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N3))))))))))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y) (= X3 Y)))))
% 7.27/7.59 (assert (forall ((S tptp.set_real)) (=> (exists ((X8 tptp.real)) (@ (@ tptp.member_real X8) S)) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z5)))) (exists ((Y4 tptp.real)) (and (forall ((X8 tptp.real)) (=> (@ (@ tptp.member_real X8) S) (@ (@ tptp.ord_less_eq_real X8) Y4))) (forall ((Z5 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z5))) (@ (@ tptp.ord_less_eq_real Y4) Z5)))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A2) A2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger A2) A2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A2) A2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A2) A2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A2) A2)) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A2) A2)) A2))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 7.27/7.59 (assert (forall ((C2 tptp.real)) (= (lambda ((X3 tptp.real)) (@ (@ tptp.times_times_real X3) C2)) (@ tptp.times_times_real C2))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat)) (= (lambda ((X3 tptp.rat)) (@ (@ tptp.times_times_rat X3) C2)) (@ tptp.times_times_rat C2))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat)) (= (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C2)) (@ tptp.times_times_nat C2))))
% 7.27/7.59 (assert (forall ((C2 tptp.int)) (= (lambda ((X3 tptp.int)) (@ (@ tptp.times_times_int X3) C2)) (@ tptp.times_times_int C2))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y3 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) Y3)) tptp.one_one_nat)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B2)) (@ (@ tptp.minus_minus_real C2) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) D2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.minus_minus_rat C2) D2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) D2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.minus_minus_int C2) D2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.power_power_real X2) N3))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) X2) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat X2) tptp.one_one_nat))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y3)) (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y3) B2))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) A2)) B2))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y3)) (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y3) B2))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) A2)) B2))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y3)) (@ (@ tptp.times_times_int A2) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y3) B2))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) A2)) B2))))))
% 7.27/7.59 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) __flatten_var_0))))
% 7.27/7.59 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A5) tptp.one_one_int)) __flatten_var_0))))
% 7.27/7.59 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X2))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_d_e_l_e_t_e T) X2)) (@ (@ 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))))))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete T) X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_d_e_l_e_t_e T) X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))
% 7.27/7.59 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 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 Mi) Mi))) Deg) TreeList) Summary)) X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1))))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((U tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_V441764108873111860ildupi N)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) U))))))
% 7.27/7.59 (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))))))))))
% 7.27/7.59 (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))))))))))
% 7.27/7.59 (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))))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ (@ tptp.vEBT_V3964819847710782039nserti T) Ti) X2)) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull T)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) (@ tptp.vEBT_V739175172307565963ildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N)))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_VEBT_space T)) (@ tptp.vEBT_VEBT_space2 T))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ tptp.vEBT_V739175172307565963ildupi N)) (@ tptp.vEBT_V441764108873111860ildupi N))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ (@ tptp.vEBT_V3964819847710782039nserti T) Ti) X2)) tptp.one_one_nat))))
% 7.27/7.59 (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)))
% 7.27/7.59 (assert (forall ((X2 tptp.heap_T8145700208782473153_VEBTi) (C2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.time_T5737551269749752165_VEBTi X2) C2) (@ (@ tptp.time_T8149879359713347829_VEBTi (@ (@ tptp.vEBT_V1859673955506687831_VEBTi N) X2)) (@ _let_1 (@ (@ tptp.times_times_nat (@ _let_1 C2)) N)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.heap_Time_Heap_o) (C2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.time_TBOUND_o X2) C2) (@ (@ tptp.time_TBOUND_list_o (@ (@ tptp.vEBT_V2326993469660664182atei_o N) X2)) (@ _let_1 (@ (@ tptp.times_times_nat (@ _let_1 C2)) N)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.heap_T2636463487746394924on_nat) (C2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.time_T8353473612707095248on_nat X2) C2) (@ (@ tptp.time_T3808005469503390304on_nat (@ (@ tptp.vEBT_V792416675989592002on_nat N) X2)) (@ _let_1 (@ (@ tptp.times_times_nat (@ _let_1 C2)) N)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.heap_Time_Heap_nat) (C2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.time_TBOUND_nat X2) C2) (@ (@ tptp.time_TBOUND_list_nat (@ (@ tptp.vEBT_V7726092123322077554ei_nat N) X2)) (@ _let_1 (@ (@ tptp.times_times_nat (@ _let_1 C2)) N)))))))
% 7.27/7.59 (assert (forall ((U tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi tptp.one_one_assn) (@ tptp.vEBT_V739175172307565963ildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) U))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_V441764108873111860ildupi N)) (@ (@ tptp.minus_minus_nat (@ tptp.vEBT_VEBT_Tb2 N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) (@ tptp.vEBT_vebt_buildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi tptp.one_one_assn) (@ tptp.vEBT_V739175172307565963ildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N))) (@ tptp.vEBT_V441764108873111860ildupi N))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high X2) _let_4))) (let ((_let_6 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_3) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ _let_6 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low X2) _let_4)))) tptp.one_one_nat)))))))))))))))))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X4))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_real A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 7.27/7.59 (assert (forall ((C2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C2))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A) B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C2))) (= (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.heap_T8145700208782473153_VEBTi) (C2 tptp.nat) (N tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi X2) H3)) C2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_t3534373299052942712_VEBTi (@ (@ tptp.vEBT_V1859673955506687831_VEBTi N) X2)) H2)) (@ _let_1 (@ (@ tptp.times_times_nat (@ _let_1 C2)) N)))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi tptp.one_one_assn) (@ tptp.vEBT_vebt_buildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N))) (@ tptp.vEBT_V441764108873111860ildupi N))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 7.27/7.59 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) tptp.bot_bot_set_int) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) tptp.bot_bot_set_nat) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A) tptp.bot_bot_set_int)))
% 7.27/7.59 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A) tptp.bot_bot_set_nat)))
% 7.27/7.59 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) A) tptp.bot_bot_set_int)))
% 7.27/7.59 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) A) tptp.bot_bot_set_nat)))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_V441764108873111860ildupi N))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup N))))))
% 7.27/7.59 (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))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 7.27/7.59 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 7.27/7.59 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 7.27/7.59 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X2) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B2)) W)) (= X2 (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger X2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B2)) W)) (= X2 (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X2) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (= X2 (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X2) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (= X2 (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X2) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (= X2 (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B2)) W) (@ tptp.semiri8010041392384452111omplex X2)) (= (@ (@ tptp.power_power_nat B2) W) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B2)) W) (@ tptp.semiri4939895301339042750nteger X2)) (= (@ (@ tptp.power_power_nat B2) W) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W) (@ tptp.semiri5074537144036343181t_real X2)) (= (@ (@ tptp.power_power_nat B2) W) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W) (@ tptp.semiri1314217659103216013at_int X2)) (= (@ (@ tptp.power_power_nat B2) W) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W) (@ tptp.semiri1316708129612266289at_nat X2)) (= (@ (@ tptp.power_power_nat B2) W) X2))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger M)) N))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((U tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi tptp.one_one_assn) (@ tptp.vEBT_vebt_buildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) U))))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 7.27/7.59 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N) (@ tptp.semiri4939895301339042750nteger Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y3))))
% 7.27/7.59 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.semiri8010041392384452111omplex Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y3))))
% 7.27/7.59 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.semiri681578069525770553at_rat Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y3))))
% 7.27/7.59 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.semiri5074537144036343181t_real Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y3))))
% 7.27/7.59 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) (@ tptp.semiri1314217659103216013at_int Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y3))))
% 7.27/7.59 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y3)) (= _let_1 Y3)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger Y3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y3) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y3) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y3) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y3) _let_1) (= Y3 _let_1)))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B2)) W)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B2)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B2)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B2) W)))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B2)) W)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X2))))
% 7.27/7.59 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_nat X2) _let_1)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_eq_nat X2) _let_1)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 7.27/7.59 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (@ (@ tptp.time_TBOUND_o (@ (@ (@ tptp.vEBT_V854960066525838166emberi T) Ti) X2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ (@ tptp.vEBT_VEBT_vebt_predi T) Ti) X2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ (@ tptp.vEBT_VEBT_vebt_succi T) Ti) X2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one)))))) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ tptp.vEBT_vebt_inserti Ti) X2)) (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_vebt_insert T) X2))) (@ (@ tptp.plus_plus_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.vEBT_VEBT_height T)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y3) (@ (@ tptp.times_times_rat Y3) _let_1)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y3) (@ (@ tptp.times_times_real Y3) _let_1)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y3) (@ (@ tptp.times_times_int Y3) _let_1)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X2))) (= (@ (@ tptp.times_times_nat _let_1) Y3) (@ (@ tptp.times_times_nat Y3) _let_1)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((A2 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 A2))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 7.27/7.59 (assert (forall ((A2 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 A2))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X2) Y3)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X2)) (@ tptp.semiri4216267220026989637d_enat Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X2) Y3)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.semiri5074537144036343181t_real Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X2) Y3)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X2) Y3)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ tptp.semiri1316708129612266289at_nat Y3)))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2)))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_real) (B tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (C2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C2))) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C2 tptp.real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (not (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_eq_set_int B) A))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_int A) B) (not (@ (@ tptp.ord_less_eq_set_int B) A)))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (= tptp.ord_le4337996190870823476T_VEBT (lambda ((A6 tptp.set_VEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X3))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B5 tptp.set_real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 7.27/7.59 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B5) (not (= A6 B5))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (= tptp.ord_le4337996190870823476T_VEBT (lambda ((A6 tptp.set_VEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (forall ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B5)))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X4 tptp.product_prod_int_int)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 7.27/7.59 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B5) (@ (@ tptp.ord_less_eq_set_int B5) A6)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X3 tptp.complex)) (=> (@ P X3) (@ Q X3))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)) (forall ((X3 tptp.product_prod_int_int)) (=> (@ P X3) (@ Q X3))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 7.27/7.59 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A6))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B5) (= A6 B5)))))
% 7.27/7.59 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 7.27/7.59 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT A) B) (exists ((B3 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A))))))
% 7.27/7.59 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A) B) (exists ((B3 tptp.real)) (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B) A))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (exists ((B3 tptp.int)) (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B) A))))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (exists ((B3 tptp.nat)) (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B) A))))))
% 7.27/7.59 (assert (forall ((C2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C2))) (=> (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C2))) (=> (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) B)) (@ _let_1 A)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A) B)) (@ _let_1 A)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (@ _let_1 A)))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ _let_1 A)))))
% 7.27/7.59 (assert (forall ((C2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C2))) (=> (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) B)) (not (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A) B)) (not (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (not (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (not (@ _let_1 B))))))
% 7.27/7.59 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 7.27/7.59 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 7.27/7.59 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N4)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 7.27/7.59 (assert (= tptp.bot_bot_set_complex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) false))))
% 7.27/7.59 (assert (= tptp.bot_bo1796632182523588997nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) false))))
% 7.27/7.59 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) false))))
% 7.27/7.59 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) false))))
% 7.27/7.59 (assert (forall ((A tptp.set_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ P X3))))) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ P X3))))) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P X3))))) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ P X3))))) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X3) A) (@ P X3))))) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ P X3))))) A)))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B5))))))
% 7.27/7.59 (assert (= tptp.ord_le4337996190870823476T_VEBT (lambda ((A6 tptp.set_VEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (@ (@ tptp.ord_le418104280809901481VEBT_o (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X3) A6))) (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X3) B5))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A6))) (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) B5))))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B5))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 7.27/7.59 (assert (= tptp.minus_5127226145743854075T_VEBT (lambda ((A6 tptp.set_VEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X3))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 7.27/7.59 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 7.27/7.59 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 7.27/7.59 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B5 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 7.27/7.59 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X3))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 7.27/7.59 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B5)))))))))
% 7.27/7.59 (assert (= tptp.minus_5127226145743854075T_VEBT (lambda ((A6 tptp.set_VEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (@ (@ tptp.minus_2794559001203777698VEBT_o (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X3) A6))) (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X3) B5)))))))
% 7.27/7.59 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A6))) (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) B5)))))))
% 7.27/7.59 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B5)))))))
% 7.27/7.59 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B5 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A6))) (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) B5)))))))
% 7.27/7.59 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ (@ tptp.minus_711738161318947805_int_o (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X3) A6))) (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X3) B5)))))))
% 7.27/7.59 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B5)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2)))) tptp.one_one_real)))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (= (@ (@ tptp.minus_minus_set_nat B) (@ (@ tptp.minus_minus_set_nat C) A)) A)))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (= (@ (@ tptp.minus_minus_set_int B) (@ (@ tptp.minus_minus_set_int C) A)) A)))))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) B)) A)))
% 7.27/7.59 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (@ (@ tptp.ord_less_eq_set_nat D) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat C) D))))))
% 7.27/7.59 (assert (forall ((A tptp.set_int) (C tptp.set_int) (D tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C) (=> (@ (@ tptp.ord_less_eq_set_int D) B) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) B)) (@ (@ tptp.minus_minus_set_int C) D))))))
% 7.27/7.59 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (@ P I))))))
% 7.27/7.59 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 7.27/7.59 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 7.27/7.59 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (@ P I))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I tptp.int)) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_Tb2 N)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_cnt2 (@ tptp.vEBT_vebt_buildup N))))))
% 7.27/7.59 (assert (= tptp.vEBT_VEBT_cnt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_cnt2 T2)))))
% 7.27/7.59 (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))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ tptp.vEBT_vebt_buildupi N)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.log _let_2))) (let ((_let_4 (@ tptp.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) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_4))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_4)) (@ _let_3 (@ _let_3 U)))))))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_V8346862874174094_d_u_p N)) (@ tptp.vEBT_V8646137997579335489_i_l_d N))))
% 7.27/7.59 (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))))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (@ (@ 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) X2))) (@ (@ tptp.plus_plus_real _let_1) (@ _let_2 (@ _let_2 U))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.vEBT_VEBTi)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leafi A3) B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.array_VEBT_VEBTi) (Uw2 tptp.vEBT_VEBTi)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.array_VEBT_VEBTi) (Uz2 tptp.vEBT_VEBTi)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.vEBT_V441764108873111860ildupi N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A2) A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (C2 tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A2) C2) (@ (@ tptp.times_times_complex B2) C2)) (or (= C2 tptp.zero_zero_complex) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A2) C2) (@ (@ tptp.times_times_real B2) C2)) (or (= C2 tptp.zero_zero_real) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C2) (@ (@ tptp.times_times_rat B2) C2)) (or (= C2 tptp.zero_zero_rat) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) C2) (@ (@ tptp.times_times_nat B2) C2)) (or (= C2 tptp.zero_zero_nat) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C2) (@ (@ tptp.times_times_int B2) C2)) (or (= C2 tptp.zero_zero_int) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_complex) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_real) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_rat) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_nat) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_int) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A2) B2) tptp.zero_zero_complex) (or (= A2 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A2) B2) tptp.zero_zero_real) (or (= A2 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex A2) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A2) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A2) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A2) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A2) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 7.27/7.59 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A2) tptp.zero_zero_nat) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A2) B2)) (and (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A2) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A2) B2) tptp.zero_zero_nat) (and (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A2) B2)) (@ (@ tptp.ord_less_eq_real B2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A2) B2)) (@ (@ tptp.ord_less_real B2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_rat B2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_int B2) A2))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y3) Y3)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y3) Y3)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (B2 tptp.complex)) (= (= C2 (@ (@ tptp.times_times_complex C2) B2)) (or (= C2 tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (B2 tptp.real)) (= (= C2 (@ (@ tptp.times_times_real C2) B2)) (or (= C2 tptp.zero_zero_real) (= B2 tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (B2 tptp.rat)) (= (= C2 (@ (@ tptp.times_times_rat C2) B2)) (or (= C2 tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (B2 tptp.int)) (= (= C2 (@ (@ tptp.times_times_int C2) B2)) (or (= C2 tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex C2) A2) C2) (or (= C2 tptp.zero_zero_complex) (= A2 tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.times_times_real C2) A2) C2) (or (= C2 tptp.zero_zero_real) (= A2 tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat C2) A2) C2) (or (= C2 tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.times_times_int C2) A2) C2) (or (= C2 tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (B2 tptp.complex)) (= (= C2 (@ (@ tptp.times_times_complex B2) C2)) (or (= C2 tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (B2 tptp.real)) (= (= C2 (@ (@ tptp.times_times_real B2) C2)) (or (= C2 tptp.zero_zero_real) (= B2 tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (B2 tptp.rat)) (= (= C2 (@ (@ tptp.times_times_rat B2) C2)) (or (= C2 tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (B2 tptp.int)) (= (= C2 (@ (@ tptp.times_times_int B2) C2)) (or (= C2 tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (C2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A2) C2) C2) (or (= C2 tptp.zero_zero_complex) (= A2 tptp.one_one_complex)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.times_times_real A2) C2) C2) (or (= C2 tptp.zero_zero_real) (= A2 tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C2) C2) (or (= C2 tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C2) C2) (or (= C2 tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 7.27/7.59 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 7.27/7.59 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 7.27/7.59 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 7.27/7.59 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) A2) tptp.one_one_complex))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A2) A2) tptp.one_one_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A2) A2) tptp.one_one_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A2) A2) tptp.one_one_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A2) A2) tptp.one_one_int))))
% 7.27/7.59 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) B2)) B2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) B2)) A2) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) B2)) A2) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) B2)) A2) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) B2)) A2) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) B2)) A2) B2))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A2)) (@ _let_1 B2)))) (let ((_let_3 (= C2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A2) B2)))))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A2)) (@ _let_1 B2)))) (let ((_let_3 (= C2 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A2) B2)))))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2)) (@ (@ tptp.divide_divide_nat A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (@ (@ tptp.divide_divide_int A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (not (= C2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_int A2) B2))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) (@ tptp.suc N)) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numeral_numeral_nat K)) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 7.27/7.59 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 7.27/7.59 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 7.27/7.59 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 7.27/7.59 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 7.27/7.59 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X2) M) _let_1) (or (= M tptp.zero_zero_nat) (= X2 _let_1))))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 7.27/7.59 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 7.27/7.59 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X2) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A2) _let_1) B2)) (=> _let_2 (= A2 tptp.zero_zero_complex))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A2 (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A2) _let_1) B2)) (=> _let_2 (= A2 tptp.zero_zero_real))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A2 (@ (@ tptp.divide_divide_rat B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A2) _let_1) B2)) (=> _let_2 (= A2 tptp.zero_zero_rat))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.complex) (W tptp.num) (A2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A2) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_complex))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (W tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A2) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_real))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (W tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) _let_1) A2) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_rat A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_rat))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C2)) A2)) B2) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C2)) A2)) B2) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B2)) A2)) B2) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B2)) A2)) B2) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat B2) C2))) B2) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int B2) C2))) B2) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat C2) B2))) B2) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int C2) B2))) B2) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A2) B2))))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A2) N) tptp.zero_zero_rat) (and (= A2 tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A2) N) tptp.zero_zero_nat) (and (= A2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A2) N) tptp.zero_zero_real) (and (= A2 tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A2) N) tptp.zero_zero_int) (and (= A2 tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A2) N) tptp.zero_zero_complex) (and (= A2 tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger A2) N) tptp.zero_z3403309356797280102nteger) (and (= A2 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (= (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (= (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (= (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (= (@ (@ tptp.power_power_complex A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A2 tptp.zero_zero_complex))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.27/7.59 (assert (forall ((B2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N)) (@ (@ tptp.ord_less_eq_real A2) B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)) (@ (@ tptp.ord_less_eq_rat A2) B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)) (@ (@ tptp.ord_less_eq_nat A2) B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)) (@ (@ tptp.ord_less_eq_int A2) B2))))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.27/7.59 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.27/7.59 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.27/7.59 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y3) _let_1)) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 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 X2) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y3) _let_1)) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_nat X2) _let_1) (@ (@ tptp.power_power_nat Y3) _let_1)) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y3) _let_1)) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A2 tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A2 tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A2 tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A2 tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) tptp.zero_z3403309356797280102nteger) (and (= X2 tptp.zero_z3403309356797280102nteger) (= Y3 tptp.zero_z3403309356797280102nteger))))))
% 7.27/7.59 (assert (forall ((B2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X2)) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 7.27/7.59 (assert (forall ((Z tptp.int)) (not (forall ((M5 tptp.nat) (N3 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 7.27/7.59 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 7.27/7.59 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 7.27/7.59 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 7.27/7.59 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 7.27/7.59 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A2) C2) (@ (@ tptp.times_times_complex B2) C2)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A2) C2) (@ (@ tptp.times_times_real B2) C2)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A2) C2) (@ (@ tptp.times_times_rat B2) C2)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A2) C2) (@ (@ tptp.times_times_nat B2) C2)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A2) C2) (@ (@ tptp.times_times_int B2) C2)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (not (= C2 tptp.zero_zero_nat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (not (= C2 tptp.zero_zero_int)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (=> (not (= B2 tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A2) B2) tptp.zero_zero_complex))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A2) B2) tptp.zero_zero_real))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A2) B2) tptp.zero_zero_complex) (or (= A2 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real A2) B2) tptp.zero_zero_real) (or (= A2 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A2) B2) tptp.zero_zero_complex)) (and (not (= A2 tptp.zero_zero_complex)) (not (= B2 tptp.zero_zero_complex))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A2) B2) tptp.zero_zero_real)) (and (not (= A2 tptp.zero_zero_real)) (not (= B2 tptp.zero_zero_real))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat)) (and (not (= A2 tptp.zero_zero_rat)) (not (= B2 tptp.zero_zero_rat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat)) (and (not (= A2 tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int)) (and (not (= A2 tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (=> (not (= A2 tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A2) N) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A2) N) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (not (= A2 tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A2) N) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (=> (not (= A2 tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A2) N) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat)) (=> (not (= A2 tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A2) N) tptp.zero_zero_complex)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.power_8256067586552552935nteger A2) N) tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.59 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (@ (@ P X4) tptp.zero_zero_nat)) (=> (forall ((Y4 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y4))) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ P X4) Y4) (@ (@ P (@ tptp.suc X4)) (@ tptp.suc Y4)))) (@ (@ P M) N))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 7.27/7.59 (assert (forall ((Y3 tptp.nat)) (=> (not (= Y3 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y3 (@ tptp.suc Nat3))))))))
% 7.27/7.59 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 7.27/7.59 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3))))))) (@ P N)))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.real) (B2 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 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_real A2) N) (@ (@ tptp.power_power_real B2) N)) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_8256067586552552935nteger A2) N) (@ (@ tptp.power_8256067586552552935nteger B2) N)) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.rat) (B2 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 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_rat A2) N) (@ (@ tptp.power_power_rat B2) N)) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.nat) (B2 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 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_nat A2) N) (@ (@ tptp.power_power_nat B2) N)) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.int) (B2 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 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_int A2) N) (@ (@ tptp.power_power_int B2) N)) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A2) N) (@ (@ tptp.power_power_real B2) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (= (@ (@ tptp.power_8256067586552552935nteger A2) N) (@ (@ tptp.power_8256067586552552935nteger B2) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A2) N) (@ (@ tptp.power_power_rat B2) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A2) N) (@ (@ tptp.power_power_nat B2) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A2) N) (@ (@ tptp.power_power_int B2) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B2))))))))
% 7.27/7.59 (assert (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ tptp.vEBT_V441764108873111860ildupi _let_1) _let_1)))
% 7.27/7.59 (assert (= (@ tptp.vEBT_V441764108873111860ildupi tptp.zero_zero_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.27/7.59 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 7.27/7.59 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 7.27/7.59 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 7.27/7.59 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 7.27/7.59 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)))))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))
% 7.27/7.59 (assert (= tptp.ord_less_eq_int (lambda ((W2 tptp.int) (Z4 tptp.int)) (exists ((N4 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int N4)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A2) B2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) A2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A2) B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B2) A2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B2) A2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) A2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B2) A2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y3)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X2) Y3)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) Y3)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y3) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.27/7.59 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2)) (and (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) B2)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2)) (and (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) B2)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real B2) A2) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real B2) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat B2) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int B2) A2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B2) A2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B2) A2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B2) A2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B2) A2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) A2)) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) A2)) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) A2)) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_real A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_real A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.power_power_assn A2) tptp.zero_zero_nat) tptp.one_one_assn)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.power_power_rat A2) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.27/7.59 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) tptp.zero_zero_nat) tptp.one_one_complex)))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A2) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 7.27/7.59 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N3) (@ P Nn))) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N3) (@ P Nn))) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 7.27/7.59 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.27/7.59 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 7.27/7.59 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.27/7.59 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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 ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K2) (not (@ P I5)))) (@ P K2)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (= (@ tptp.suc N) M) (= N (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X2) (not (= X2 tptp.zero_zero_nat)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 7.27/7.59 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z4 tptp.int)) (exists ((N4 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) D2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real B2) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) B2)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) B2)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2))))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) B2)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A2) B2)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) B2)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2)))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A2) B2)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y3) Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y3) Y3)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y3) Y3))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y3) Y3))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y3) X2)) X2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y3) X2)) X2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y3) X2)) X2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Y3)) X2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Y3)) X2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Y3)) X2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B2)) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.one_one_rat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.one_one_nat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.one_one_int))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) A2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) A2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C2)) A2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) A2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (@ _let_1 (@ (@ tptp.divide_divide_nat A2) B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (@ _let_1 (@ (@ tptp.divide_divide_int A2) B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.divide_divide_nat A2) B2) tptp.zero_zero_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.divide_divide_int A2) B2) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3))) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y3) Y3))) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y3) Y3))) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y3 tptp.zero_zero_real))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y3) Y3))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y3 tptp.zero_zero_rat))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y3) Y3))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y3 tptp.zero_zero_int))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) N)) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) tptp.one_one_Code_integer)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N)) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C2) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C2) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C2) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.complex) (C2 tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C2) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (C2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C2) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) C2) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_rat _let_1) C2))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A2) _let_2) (@ (@ tptp.power_power_real B2) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_8256067586552552935nteger A2) _let_2) (@ (@ tptp.power_8256067586552552935nteger B2) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A2) _let_2) (@ (@ tptp.power_power_rat B2) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A2) _let_2) (@ (@ tptp.power_power_nat B2) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A2) _let_2) (@ (@ tptp.power_power_int B2) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger B2) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) _let_1)) (@ (@ tptp.power_power_rat B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_eq_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) _let_1)) (@ (@ tptp.power_power_nat B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat A2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) _let_1)) (@ (@ tptp.power_power_int B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int A2) B2))))))
% 7.27/7.59 (assert (= (@ tptp.vEBT_VEBT_Tb2 tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) B2)) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) B2)) tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) B2)) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) B2)) tptp.one_one_int)))))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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 ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) K2) (not (@ P I5)))) (@ P (@ tptp.suc K2))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 7.27/7.59 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B2)) (and (=> (@ (@ tptp.ord_less_nat A2) B2) (@ P tptp.zero_zero_nat)) (forall ((D3 tptp.nat)) (=> (= A2 (@ (@ tptp.plus_plus_nat B2) D3)) (@ P D3)))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B2)) (not (or (and (@ (@ tptp.ord_less_nat A2) B2) (not (@ P tptp.zero_zero_nat))) (exists ((D3 tptp.nat)) (and (= A2 (@ (@ tptp.plus_plus_nat B2) D3)) (not (@ P D3)))))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 7.27/7.59 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 7.27/7.59 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 7.27/7.59 (assert (forall ((X2 tptp.vEBT_VEBTi) (Xs tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s7982070591426661849_VEBTi Xs)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.times_times_nat B2) C2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) C2)) B2)))))
% 7.27/7.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 7.27/7.59 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2))))
% 7.27/7.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S2)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (= (@ tptp.vEBT_VEBT_Tb2 (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C2) (@ (@ tptp.times_times_real B2) C2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat B2) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int B2) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C2) A2)) C2) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C2) A2)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C2) A2)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C2) (@ (@ tptp.times_times_real C2) B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat C2) B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int C2) B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) C2) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C2)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.times_times_real B2) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat B2) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int B2) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C2) A2)) C2) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C2) A2)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C2) A2)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C2) (@ (@ tptp.times_times_real C2) B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat C2) B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int C2) B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (A2 tptp.real) (Y3 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X2) A2) (=> (@ (@ tptp.ord_less_eq_real Y3) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y3))) A2)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (Y3 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X2) A2) (=> (@ (@ tptp.ord_less_eq_rat Y3) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y3))) A2)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (A2 tptp.int) (Y3 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X2) A2) (=> (@ (@ tptp.ord_less_eq_int Y3) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y3))) A2)))))))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.real) (C2 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 C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.rat) (C2 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 C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (C2 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 C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (C2 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 C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) _let_1)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A2) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) _let_1)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) _let_1)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) _let_1)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) _let_1)) _let_1))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) (@ tptp.suc N))) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc N))) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) (@ tptp.suc N))) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) (@ tptp.suc N))) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) (@ tptp.suc N))) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc N))) tptp.one_one_Code_integer)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) (@ tptp.suc N))) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) (@ tptp.suc N))) tptp.one_one_rat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A2) (@ tptp.suc N))) tptp.one_one_nat)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) (@ tptp.suc N))) tptp.one_one_int)))))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.27/7.59 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 7.27/7.59 (assert (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (N7 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N7)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.power_power_real A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.power_8256067586552552935nteger A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.power_power_rat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.power_power_nat A2) N))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int A2) N))))))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (not (= A2 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))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A2))) (=> (not (= A2 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))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (not (= A2 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))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (not (= A2 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))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (not (= A2 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))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (not (= A2 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))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A2) N)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A2) N)))))))
% 7.27/7.59 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N4)) N4))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N4))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) C2)) A2) (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.divide_divide_nat A2) C2))))))
% 7.27/7.59 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N4))))))
% 7.27/7.59 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) (@ _let_1 N))) (@ _let_1 M)) (@ (@ tptp.ord_less_nat A2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst) Smry))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X2) _let_1))))
% 7.27/7.59 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2))))
% 7.27/7.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (A2 tptp.real) (Y3 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X2) A2) (=> (@ (@ tptp.ord_less_real Y3) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y3))) A2)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (Y3 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X2) A2) (=> (@ (@ tptp.ord_less_rat Y3) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y3))) A2)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (A2 tptp.int) (Y3 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X2) A2) (=> (@ (@ tptp.ord_less_int Y3) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y3))) A2)))))))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.real) (C2 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 C2) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.27/7.59 (assert (forall ((W tptp.num) (B2 tptp.rat) (C2 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 C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (C2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.divide_divide_real A2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.divide_divide_rat A2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y3) (@ (@ tptp.ord_le3102999989581377725nteger X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_eq_rat X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y3) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (@ (@ tptp.ord_less_eq_int X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X2) _let_2) (@ (@ tptp.power_power_real Y3) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 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 X2) _let_2) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X2) _let_2) (@ (@ tptp.power_power_rat Y3) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X2) _let_2) (@ (@ tptp.power_power_nat Y3) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X2) _let_2) (@ (@ tptp.power_power_int Y3) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= X2 Y3))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A2 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))))))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A2 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))))))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A2 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))))))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 7.27/7.59 (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))))))))
% 7.27/7.59 (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))))))))
% 7.27/7.59 (assert (= tptp.power_power_assn (lambda ((P4 tptp.assn) (M6 tptp.nat)) (@ (@ (@ tptp.if_assn (= M6 tptp.zero_zero_nat)) tptp.one_one_assn) (@ (@ tptp.times_times_assn P4) (@ (@ tptp.power_power_assn P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (= tptp.power_power_complex (lambda ((P4 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P4) (@ (@ tptp.power_power_complex P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (= tptp.power_8256067586552552935nteger (lambda ((P4 tptp.code_integer) (M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P4) (@ (@ tptp.power_8256067586552552935nteger P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (= tptp.power_power_real (lambda ((P4 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P4) (@ (@ tptp.power_power_real P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (= tptp.power_power_rat (lambda ((P4 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P4) (@ (@ tptp.power_power_rat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (= tptp.power_power_nat (lambda ((P4 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P4) (@ (@ tptp.power_power_nat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (= tptp.power_power_int (lambda ((P4 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P4) (@ (@ tptp.power_power_int P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A2) (@ _let_1 N))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A2) (@ _let_1 N))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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 ((Q5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q5)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q5))) (@ P Q5))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (M tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X2) _let_1))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TreeList) Summary)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TreeList) Summary)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y3) (@ (@ tptp.ord_le6747313008572928689nteger X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_real X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_rat X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y3) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (@ (@ tptp.ord_less_int X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1))) tptp.zero_z3403309356797280102nteger) (and (= X2 tptp.zero_z3403309356797280102nteger) (= Y3 tptp.zero_z3403309356797280102nteger))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 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 X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 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 X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1))) (or (not (= X2 tptp.zero_z3403309356797280102nteger)) (not (= Y3 tptp.zero_z3403309356797280102nteger)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y3 tptp.zero_zero_real)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y3 tptp.zero_zero_rat)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y3 tptp.zero_zero_int)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1))) tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 7.27/7.59 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) TreeList) Summary)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) TreeList) Summary)) X2) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((Y3 tptp.vEBT_VEBTi)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.array_VEBT_VEBTi) (X142 tptp.vEBT_VEBTi)) (not (= Y3 (@ (@ (@ (@ tptp.vEBT_Nodei X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y3 (@ (@ tptp.vEBT_Leafi X212) X223))))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X2) N)) (@ _let_1 M)))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X2) N)) (@ _let_1 N)))))))))
% 7.27/7.59 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((U tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X2) Y3)) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y3)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 7.27/7.59 (assert (forall ((U tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X2) Y3)) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y3)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (let ((_let_3 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_3)) (@ _let_2 (@ _let_2 U))))))))))))
% 7.27/7.59 (assert (forall ((X2 tptp.vEBT_VEBTi)) (=> (not (= X2 (@ (@ tptp.vEBT_Leafi false) false))) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leafi true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leafi Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.array_VEBT_VEBTi) (Uy2 tptp.vEBT_VEBTi)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.array_VEBT_VEBTi) (Vc2 tptp.vEBT_VEBTi)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_V441764108873111860ildupi N))) (@ (@ tptp.minus_minus_int (@ tptp.vEBT_VEBT_Tb N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A2)) (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A2)) (@ (@ tptp.ord_less_eq_real B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A2)) (@ (@ tptp.ord_less_eq_rat B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) A2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) A2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBTi)) (@ (@ tptp.time_TBOUND_o (@ tptp.vEBT_VEBT_minNulli T)) tptp.one_one_nat)))
% 7.27/7.59 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B2) (@ (@ tptp.times_times_complex A2) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B2) (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B2) (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) (@ (@ tptp.times_times_complex A2) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A2) (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A2) (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B2)))))
% 7.27/7.59 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.vEBT_VEBT_cnt T))))
% 7.27/7.59 (assert (= tptp.vEBT_VEBT_Tb (lambda ((T2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_Tb2 T2)))))
% 7.27/7.59 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 7.27/7.59 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 7.27/7.59 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B2) tptp.zero_zero_complex) (or (= A2 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) B2) tptp.zero_zero_real) (or (= A2 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_complex) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_real) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_rat) (= A2 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (C2 tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) C2) (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (or (= C2 tptp.zero_zero_complex) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) C2) (@ (@ tptp.divide_divide_real B2) C2)) (or (= C2 tptp.zero_zero_real) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) C2) (@ (@ tptp.divide_divide_rat B2) C2)) (or (= C2 tptp.zero_zero_rat) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.27/7.59 (assert (forall ((B2 tptp.complex) (C2 tptp.complex) (A2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B2) C2)) A2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B2) A2)) C2))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (C2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B2) A2)) C2))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B2) A2)) C2))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A2))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_complex B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A2))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) C2)) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) C2)) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) C2)) B2))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A2))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.divide_divide_rat (@ _let_1 B2)) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.log A2) tptp.one_one_real) tptp.zero_zero_real)))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B2) tptp.one_one_complex) (and (not (= B2 tptp.zero_zero_complex)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) B2) tptp.one_one_real) (and (not (= B2 tptp.zero_zero_real)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B2) tptp.one_one_rat) (and (not (= B2 tptp.zero_zero_rat)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A2) B2)) (and (not (= B2 tptp.zero_zero_complex)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A2) B2)) (and (not (= B2 tptp.zero_zero_real)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A2) B2)) (and (not (= B2 tptp.zero_zero_rat)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) A2) tptp.one_one_complex))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A2) A2) tptp.one_one_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A2) A2) tptp.one_one_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A2) A2))) (let ((_let_2 (= A2 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A2) A2))) (let ((_let_2 (= A2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A2) A2))) (let ((_let_2 (= A2 tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real B2) A2) tptp.one_one_real) (and (not (= A2 tptp.zero_zero_real)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B2) A2) tptp.one_one_rat) (and (not (= A2 tptp.zero_zero_rat)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B2) A2)) (and (not (= A2 tptp.zero_zero_real)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B2) A2)) (and (not (= A2 tptp.zero_zero_rat)) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)) (= A2 tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)) (= A2 tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A2)) (@ _let_1 B2)))) (let ((_let_3 (= C2 tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A2) B2)))))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A2)) (@ _let_1 B2)))) (let ((_let_3 (= C2 tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A2) B2)))))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A2)) (@ _let_1 B2)))) (let ((_let_3 (= C2 tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A2) B2)))))))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.divide1717551699836669952omplex A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_real A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_rat A2) B2))))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C2) A2)) (@ (@ tptp.times_times_complex B2) C2)) (@ (@ tptp.divide1717551699836669952omplex A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C2) A2)) (@ (@ tptp.times_times_real B2) C2)) (@ (@ tptp.divide_divide_real A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C2) A2)) (@ (@ tptp.times_times_rat B2) C2)) (@ (@ tptp.divide_divide_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) C2)) (@ (@ tptp.times_times_complex B2) C2)) (@ (@ tptp.divide1717551699836669952omplex A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (@ (@ tptp.divide_divide_real A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (@ (@ tptp.divide_divide_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) C2)) (@ (@ tptp.times_times_complex C2) B2)) (@ (@ tptp.divide1717551699836669952omplex A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real C2) B2)) (@ (@ tptp.divide_divide_real A2) B2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat C2) B2)) (@ (@ tptp.divide_divide_rat A2) B2)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (= (= (@ (@ tptp.divide_divide_int A2) B2) A2) (= B2 tptp.one_one_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (not (= A2 tptp.one_one_real)) (= (@ (@ tptp.log A2) A2) tptp.one_one_real)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log A2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_real X2) Y3)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A2) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.log A2) X2)) (@ (@ tptp.ord_less_real A2) X2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A2) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_2 X2) (= (@ _let_2 (@ (@ tptp.log A2) X2)) (@ _let_1 X2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A2)) tptp.one_one_real) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) A2)) tptp.one_one_rat) (@ _let_1 B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A2)) tptp.one_one_real) (@ (@ tptp.ord_less_real B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) A2)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A2)) (@ (@ tptp.ord_less_real B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A2)) (@ (@ tptp.ord_less_rat B2) A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A2)) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)) (@ _let_1 A2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log A2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3)))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A2) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A2) X2)) (@ (@ tptp.ord_less_eq_real A2) X2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A2) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A2) X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))))
% 7.27/7.59 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 7.27/7.59 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (not (= A2 tptp.one_one_real)) (= (@ (@ tptp.log A2) (@ (@ tptp.power_power_real A2) B2)) (@ tptp.semiri5074537144036343181t_real B2))))))
% 7.27/7.59 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.27/7.59 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 7.27/7.59 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))))
% 7.27/7.59 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 7.27/7.59 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 7.27/7.59 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 7.27/7.59 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 7.27/7.59 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 7.27/7.59 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((X8 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X8))))
% 7.27/7.59 (assert (forall ((X8 tptp.rat)) (exists ((Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X8))))
% 7.27/7.59 (assert (forall ((X8 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X8) X_1))))
% 7.27/7.59 (assert (forall ((X8 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X8) X_1))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (not (= A2 tptp.one_one_real)) (= (@ (@ tptp.log B2) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B2))))))))
% 7.27/7.59 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 7.27/7.59 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A2))))))
% 7.27/7.59 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) N3)) Y3))))))
% 7.27/7.59 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 7.27/7.59 (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))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (= (@ _let_1 (@ (@ tptp.divide_divide_int A2) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A2) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_int A2) B2)) (@ _let_1 A2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A2) B2)) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (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)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B2))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) A4) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A4) B2)) (@ (@ tptp.divide_divide_int A2) B2))))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 B2)) (@ _let_1 B4))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) A4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B2)) (@ (@ tptp.divide_divide_int A4) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B2)) A2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X2) K)) X2)))))
% 7.27/7.59 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2))))))
% 7.27/7.59 (assert (forall ((M tptp.int) (A2 tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int M) N))) M) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) M)) N)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log A2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A2) (=> (not (= A2 tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y3)) (@ (@ tptp.plus_plus_real (@ _let_1 X2)) (@ _let_1 Y3)))))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log A2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A2) (=> (not (= A2 tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.minus_minus_real (@ _let_1 X2)) (@ _let_1 Y3)))))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real X4) N) A2) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5) (= (@ (@ tptp.power_power_real Y5) N) A2)) (= Y5 X4)))))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A2)))))))
% 7.27/7.59 (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)))))
% 7.27/7.59 (assert (forall ((B4 tptp.int) (Q6 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q6)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q6)))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (Q3 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q6 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q6)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q3)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B2) (@ (@ tptp.ord_less_eq_int Q3) Q6)))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (Q3 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q6 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q6)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q3)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B2) (@ (@ tptp.ord_less_eq_int Q6) Q3))))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (Q6 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q6)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B2) (=> (@ (@ tptp.ord_less_int R2) B2) (@ (@ tptp.ord_less_eq_int Q6) Q3))))))))
% 7.27/7.59 (assert (forall ((B2 tptp.int) (Q6 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q6)) 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) Q6)))))))))
% 7.27/7.59 (assert (= (@ tptp.vEBT_VEBT_Tb tptp.zero_zero_nat) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C2) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) X2)) C2))) (= X2 tptp.zero_zero_real)))))))
% 7.27/7.59 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) R2) (= (@ (@ tptp.divide_divide_int A2) B2) Q3))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B2) (= (@ (@ tptp.divide_divide_int A2) B2) Q3))))))
% 7.27/7.59 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))))))
% 7.27/7.59 (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)))))))))
% 7.27/7.59 (assert (forall ((X2 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) X2)) X2)) _let_1) X2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) X2)) X2)) _let_1) X2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A2) B2)) C2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A2) C2)) (@ (@ tptp.divide1717551699836669952omplex B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) B2)) C2) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) B2)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2)))))
% 7.27/7.59 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex Y3) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y3) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y3) W)))))
% 7.27/7.59 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) W)) (@ (@ tptp.times_times_complex Y3) Z)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) W)) (@ (@ tptp.times_times_real Y3) Z)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) W)) (@ (@ tptp.times_times_rat Y3) Z)))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A2))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_complex C2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_real C2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A2))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_rat C2) B2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A2) B2)) C2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A2) C2)) (@ (@ tptp.divide1717551699836669952omplex B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A2) B2)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2)))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A2) B2)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2)))))
% 7.27/7.59 (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))))))
% 7.27/7.59 (assert (= (@ tptp.vEBT_VEBT_Tb (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B2))) (@ _let_1 A2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.int) (B2 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) A2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B2))) (@ _let_1 A2)) (@ (@ tptp.divide_divide_int B2) A2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.divide_divide_real A2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.divide_divide_rat A2) C2))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y3)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y3)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y3)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y3)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y3)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y3))))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y3)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y3)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y3)) tptp.zero_zero_real)))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y3)) tptp.zero_zero_rat)))))
% 7.27/7.59 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y3)))))))
% 7.27/7.59 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y3)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real A2) B2)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A2)) (not (= C2 tptp.zero_zero_real))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)) (not (= C2 tptp.zero_zero_rat))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)))))))
% 7.27/7.59 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2))))))
% 7.27/7.59 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2))))))
% 7.27/7.59 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B2) tptp.one_one_complex) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A2) B2) tptp.one_one_real) (= A2 B2)))))
% 7.27/7.59 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B2) tptp.one_one_rat) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y3) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W) Y3)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y3) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W) Y3)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y3) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W) Y3)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.complex) (C2 tptp.complex) (A2 tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C2) A2) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_complex A2) C2))) (=> _let_1 (= A2 tptp.zero_zero_complex)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (C2 tptp.real) (A2 tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C2) A2) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_real A2) C2))) (=> _let_1 (= A2 tptp.zero_zero_real)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) C2) A2) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_rat A2) C2))) (=> _let_1 (= A2 tptp.zero_zero_rat)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex)) (let ((_let_1 (= C2 tptp.zero_zero_complex))) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A2) C2) B2)) (=> _let_1 (= A2 tptp.zero_zero_complex)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (= C2 tptp.zero_zero_real))) (= (= A2 (@ (@ tptp.divide_divide_real B2) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A2) C2) B2)) (=> _let_1 (= A2 tptp.zero_zero_real)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (= C2 tptp.zero_zero_rat))) (= (= A2 (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A2) C2) B2)) (=> _let_1 (= A2 tptp.zero_zero_rat)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.complex) (B2 tptp.complex) (A2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (= B2 (@ (@ tptp.times_times_complex A2) C2)) (= (@ (@ tptp.divide1717551699836669952omplex B2) C2) A2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (=> (= B2 (@ (@ tptp.times_times_real A2) C2)) (= (@ (@ tptp.divide_divide_real B2) C2) A2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (=> (= B2 (@ (@ tptp.times_times_rat A2) C2)) (= (@ (@ tptp.divide_divide_rat B2) C2) A2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A2) C2) B2) (= A2 (@ (@ tptp.divide1717551699836669952omplex B2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A2) C2) B2) (= A2 (@ (@ tptp.divide_divide_real B2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A2) C2) B2) (= A2 (@ (@ tptp.divide_divide_rat B2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.complex) (B2 tptp.complex) (A2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C2) A2) (= B2 (@ (@ tptp.times_times_complex A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B2) C2) A2) (= B2 (@ (@ tptp.times_times_real A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B2) C2) A2) (= B2 (@ (@ tptp.times_times_rat A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (= (@ (@ tptp.times_times_complex A2) C2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (= A2 (@ (@ tptp.divide_divide_real B2) C2)) (= (@ (@ tptp.times_times_real A2) C2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C2 tptp.zero_zero_rat)) (= (= A2 (@ (@ tptp.divide_divide_rat B2) C2)) (= (@ (@ tptp.times_times_rat A2) C2) B2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y3) E2)))) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y3) E2)))) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y3) W))))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y3) W))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y3) W))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat X2) Y3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y3) W))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y3) W)))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y3) W)))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) C2)) (@ (@ tptp.divide_divide_real B2) C2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ tptp.ord_less_eq_real A2) B2)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) C2)) (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y3)) tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y3)) tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y3)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y3)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y3))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y3))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y3)) tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y3)) tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A2)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_real B2) A2)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B2)) (= A2 tptp.zero_zero_real))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) A2)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_rat B2) A2)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B2)) (= A2 tptp.zero_zero_rat))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ _let_1 B2)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ _let_1 B2)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (C2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (and (=> _let_4 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_2) (@ _let_1 A2))))))))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (and (=> _let_4 (@ (@ tptp.ord_less_rat B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B2)) (=> (not _let_2) (@ _let_1 A2))))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real Z) Y3)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.times_times_rat Z) Y3)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y3)) X2) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X2) Y3))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y3)) X2) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X2) Y3))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B2) A2) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A2) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.times_times_complex B2) Z))) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A2) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.times_times_real B2) Z))) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A2) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.times_times_rat B2) Z))) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.divide1717551699836669952omplex B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A2) Z)) B2)) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.divide_divide_real B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) Z)) B2)) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.divide_divide_rat B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) Z)) B2)) Z))))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y3))) (@ (@ tptp.times_times_complex Y3) Z)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y3))) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y3)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y3))) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y3)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y3))) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y3))) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y3))) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y3))) Y3)))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y3) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real Y3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat Y3) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Z)) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A2) (@ (@ tptp.divide1717551699836669952omplex B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A2) Z)) B2)) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A2) (@ (@ tptp.divide_divide_real B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A2) Z)) B2)) Z))))))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.divide_divide_rat B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A2) Z)) B2)) Z))))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y3))) (@ (@ tptp.times_times_complex Y3) Z)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z)))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z)))))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y3) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real Y3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat Y3) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Z)) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X2)) Y3)))) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X2)) Y3)))) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A2)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real B2) A2)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A2) B2)) (= A2 tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) A2)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat B2) A2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) B2)) (= A2 tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real A2) B2)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat A2) B2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (C2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A2) C2))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2)))))))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A2) C2))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B2) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2)))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A2))) (let ((_let_2 (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C2))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B2) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C2)) A2) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C2)) A2) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A2) C2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B2) C2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B2) C2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.times_times_real Z) Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.times_times_rat Z) Y3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y3)) Z)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y3)) X2) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X2) Y3))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y3)) X2) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X2) Y3))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C2))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z))) tptp.zero_zero_real))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z))) tptp.zero_zero_rat))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z))) tptp.zero_zero_real))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z))) tptp.zero_zero_rat))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B2) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B2) M))))))
% 7.27/7.60 (assert (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B2) _let_1)))))))
% 7.27/7.60 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S2))) V))))))
% 7.27/7.60 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B2) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B2) M))))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (assert (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.27/7.60 (assert (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.vEBT_V9176841429113362141ildupi N)) (@ (@ tptp.minus_minus_int (@ tptp.vEBT_VEBT_Tb N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ tptp.pure_assn (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (@ tptp.vEBT_vebt_buildupi N)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup N))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N))))))
% 7.27/7.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ tptp.ord_less_nat X2))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_4 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) X2) (@ _let_4 Ma))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) tptp.zero_zero_nat)) tptp.zero_zero_nat)))))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A2) B2)) (@ (@ tptp.ord_less_real B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_rat B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_int B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A2) B2)) (@ (@ tptp.ord_less_eq_real B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e X2) Xa) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa (@ tptp.suc tptp.zero_zero_nat)) _let_1)) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (exists ((N3 tptp.nat)) (= Xa (@ tptp.suc (@ tptp.suc N3)))) _let_1)) (=> (=> (exists ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (= Xa Mi2))) (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))))) Xa))) (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 (= Xa Ma2)))) (let ((_let_12 (= Y3 tptp.one_one_nat))) (let ((_let_13 (or (@ (@ tptp.ord_less_nat Xa) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_13 _let_12) (=> (not _let_13) (and (=> _let_11 _let_12) (=> (not _let_11) (= Y3 (@ (@ (@ 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)))))))))))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A2) A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B6 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B6))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3)))))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_V441764108873111860ildupi N)) (@ tptp.vEBT_V9176841429113362141ildupi N))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A2) (@ (@ tptp.plus_plus_real C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A2) (@ (@ tptp.plus_plus_nat C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q3) tptp.zero_z5237406670263579293d_enat) Q3)))
% 7.27/7.60 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q3) Q3)))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A2) tptp.zero_zero_complex) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) tptp.zero_zero_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A2) A2)) (= A2 tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A2) A2)) (= A2 tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A2) A2)) (= A2 tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B2) A2) A2) (= B2 tptp.zero_zero_complex))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A2) A2) (= B2 tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) A2) (= B2 tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A2) A2) (= B2 tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) A2) (= B2 tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A2) B2) A2) (= B2 tptp.zero_zero_complex))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A2) B2) A2) (= B2 tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B2) A2) (= B2 tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B2) A2) (= B2 tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B2) A2) (= B2 tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= A2 (@ (@ tptp.plus_plus_complex B2) A2)) (= B2 tptp.zero_zero_complex))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= A2 (@ (@ tptp.plus_plus_real B2) A2)) (= B2 tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat B2) A2)) (= B2 tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B2) A2)) (= B2 tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int B2) A2)) (= B2 tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (= A2 (@ (@ tptp.plus_plus_complex A2) B2)) (= B2 tptp.zero_zero_complex))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= A2 (@ (@ tptp.plus_plus_real A2) B2)) (= B2 tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat A2) B2)) (= B2 tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B2)) (= B2 tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int A2) B2)) (= B2 tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y3) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y3)) (and (= X2 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.ord_less_eq_real A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.ord_less_eq_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.ord_less_real A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.ord_less_int A2) B2))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A2) A2) tptp.zero_zero_complex)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) A2) tptp.zero_zero_real)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A2) tptp.zero_zero_complex) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) tptp.zero_zero_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A2) tptp.zero_zero_complex) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) tptp.zero_zero_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A2) A2) tptp.zero_zero_complex)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) A2) tptp.zero_zero_real)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) tptp.one_one_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_real A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B2)) A2) B2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) A2) B2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B2)) A2) B2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) A2) B2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.minus_minus_real A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.minus_minus_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.minus_minus_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.minus_minus_int A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) B2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A2) A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.plus_plus_real B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) B2)) B2) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B2) A2)) B2) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B2) A2)) B2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B2) A2)) B2) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B2) A2)) B2) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B2)) B2) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real B2) A2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat B2) A2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat B2) A2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int B2) A2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.vEBT_Leaf A2) B2)) X2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (Ai Bool) (Bi Bool)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_Leaf A2) B2)) (@ (@ tptp.vEBT_Leafi Ai) Bi)) (@ tptp.pure_assn (and (= Ai A2) (= Bi B2))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y3 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y3 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D4)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 7.27/7.60 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 7.27/7.60 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 7.27/7.60 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A2) B2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N))) _let_1))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B2))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ tptp.vEBT_Leaf A2) B2)) X2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X4)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3)) X4)))))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_V9176841429113362141ildupi tptp.zero_zero_nat) tptp.one_one_int))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A2))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B2)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A2) B2)) X2) (and (=> _let_2 A2) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc3625547720036274456_VEBTi)) (=> (forall ((A3 Bool) (B3 Bool) (Ai2 Bool) (Bi2 Bool)) (not (= X2 (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf A3) B3)) (@ (@ tptp.vEBT_Leafi Ai2) Bi2))))) (=> (forall ((Mmo tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (Tree_list tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Mmoi tptp.option4927543243414619207at_nat) (Degi tptp.nat) (Tree_array tptp.array_VEBT_VEBTi) (Summaryi tptp.vEBT_VEBTi)) (not (= X2 (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node Mmo) Deg2) Tree_list) Summary2)) (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi) Degi) Tree_array) Summaryi))))) (=> (forall ((V2 tptp.option4927543243414619207at_nat) (Va3 tptp.nat) (Vb3 tptp.list_VEBT_VEBT) (Vc3 tptp.vEBT_VEBT) (Vd Bool) (Ve Bool)) (not (= X2 (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node V2) Va3) Vb3) Vc3)) (@ (@ tptp.vEBT_Leafi Vd) Ve))))) (not (forall ((Vd Bool) (Ve Bool) (V2 tptp.option4927543243414619207at_nat) (Va3 tptp.nat) (Vb3 tptp.array_VEBT_VEBTi) (Vc3 tptp.vEBT_VEBTi)) (not (= X2 (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf Vd) Ve)) (@ (@ (@ (@ tptp.vEBT_Nodei V2) Va3) Vb3) Vc3)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (A2 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A2))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X2))) (let ((_let_4 (= X2 tptp.one_one_nat))) (let ((_let_5 (= X2 tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((A tptp.real) (K tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_real A) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)))))))
% 7.27/7.60 (assert (forall ((A tptp.rat) (K tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_rat A) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A tptp.nat) (K tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A tptp.int) (K tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_int A) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 7.27/7.60 (assert (forall ((B tptp.real) (K tptp.real) (B2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((B tptp.rat) (K tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((B tptp.nat) (K tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((B tptp.int) (K tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A2) (@ (@ tptp.plus_plus_real C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (= tptp.plus_plus_real (lambda ((A5 tptp.real) (B6 tptp.real)) (@ (@ tptp.plus_plus_real B6) A5))))
% 7.27/7.60 (assert (= tptp.plus_plus_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.plus_plus_rat B6) A5))))
% 7.27/7.60 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.plus_plus_nat B6) A5))))
% 7.27/7.60 (assert (= tptp.plus_plus_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ tptp.plus_plus_int B6) A5))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B2))) (let ((_let_2 (@ tptp.plus_plus_real A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B2))) (let ((_let_2 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (=> (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (=> (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B2) A2) (@ (@ tptp.plus_plus_real C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A2) (@ (@ tptp.plus_plus_nat C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C2) A2)) (= B2 C2))))
% 7.27/7.60 (assert (forall ((X2 tptp.assn)) (= (= tptp.one_one_assn X2) (= X2 tptp.one_one_assn))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 7.27/7.60 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (= tptp.times_times_real (lambda ((A5 tptp.real) (B6 tptp.real)) (@ (@ tptp.times_times_real B6) A5))))
% 7.27/7.60 (assert (= tptp.times_times_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.times_times_rat B6) A5))))
% 7.27/7.60 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.times_times_nat B6) A5))))
% 7.27/7.60 (assert (= tptp.times_times_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ tptp.times_times_int B6) A5))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_nat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A2) B2) (@ (@ tptp.minus_minus_real C2) D2)) (= (= A2 B2) (= C2 D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C2) D2)) (= (= A2 B2) (= C2 D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C2) D2)) (= (= A2 B2) (= C2 D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C2)) B2) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B2) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C2)) B2) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B2) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc (@ tptp.suc N))) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc (@ tptp.suc N))) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 Bool)) (let ((_let_1 (not Y3))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y3) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) Y3) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) Y3) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y3))))))))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_V9176841429113362141ildupi (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 7.27/7.60 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (N3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc N3)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X4)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3)) X4)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B3 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B3)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N3))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (Va3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc Va3)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X4)))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2)) X4)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2)) X4)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A2) tptp.zero_zero_complex) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) tptp.zero_zero_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) D2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (not (forall ((C3 tptp.nat)) (not (= B2 (@ (@ tptp.plus_plus_nat A2) C3))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (exists ((C4 tptp.nat)) (= B6 (@ (@ tptp.plus_plus_nat A5) C4))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.ord_less_eq_real A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.ord_less_eq_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.ord_less_real A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.ord_less_int A2) B2))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C2))) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.complex) (Z3 tptp.complex)) (= Y6 Z3)) (lambda ((A5 tptp.complex) (B6 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A5) B6) tptp.zero_zero_complex))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) (lambda ((A5 tptp.real) (B6 tptp.real)) (= (@ (@ tptp.minus_minus_real A5) B6) tptp.zero_zero_real))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A5 tptp.rat) (B6 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A5) B6) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A5 tptp.int) (B6 tptp.int)) (= (@ (@ tptp.minus_minus_int A5) B6) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (D2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real D2) C2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) C2)) (@ (@ tptp.minus_minus_real B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat D2) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C2)) (@ (@ tptp.minus_minus_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (D2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int D2) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C2)) (@ (@ tptp.minus_minus_int B2) D2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C2))) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) C2)) (@ (@ tptp.minus_minus_real B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C2)) (@ (@ tptp.minus_minus_rat B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C2)) (@ (@ tptp.minus_minus_int B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A2) B2) (@ (@ tptp.minus_minus_real C2) D2)) (= (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real C2) D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C2) D2)) (= (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat C2) D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C2) D2)) (= (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int C2) D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) C2)) (@ (@ tptp.minus_minus_real B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C2)) (@ (@ tptp.minus_minus_rat B2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C2)) (@ (@ tptp.minus_minus_int B2) C2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C2))) (=> (@ (@ tptp.ord_less_real B2) A2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_rat B2) A2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_int B2) A2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A2) B2) (@ (@ tptp.minus_minus_real C2) D2)) (= (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_real C2) D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C2) D2)) (= (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat C2) D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C2) D2)) (= (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int C2) D2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (D2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real D2) C2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) C2)) (@ (@ tptp.minus_minus_real B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat D2) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C2)) (@ (@ tptp.minus_minus_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (D2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int D2) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C2)) (@ (@ tptp.minus_minus_int B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) tptp.one_one_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 7.27/7.60 (assert (forall ((A tptp.real) (K tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_real A) B2) (@ _let_1 (@ (@ tptp.minus_minus_real A2) B2)))))))
% 7.27/7.60 (assert (forall ((A tptp.rat) (K tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_rat A) B2) (@ _let_1 (@ (@ tptp.minus_minus_rat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A tptp.int) (K tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_int A) B2) (@ _let_1 (@ (@ tptp.minus_minus_int A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (= (@ (@ tptp.minus_minus_real A2) B2) C2) (= A2 (@ (@ tptp.plus_plus_real C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A2) B2) C2) (= A2 (@ (@ tptp.plus_plus_rat C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A2) B2) C2) (= A2 (@ (@ tptp.plus_plus_int C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (= A2 (@ (@ tptp.minus_minus_real C2) B2)) (= (@ (@ tptp.plus_plus_real A2) B2) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.minus_minus_rat C2) B2)) (= (@ (@ tptp.plus_plus_rat A2) B2) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.minus_minus_int C2) B2)) (= (@ (@ tptp.plus_plus_int A2) B2) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) (@ (@ tptp.minus_minus_real B2) C2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.minus_minus_rat B2) C2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.minus_minus_int B2) C2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B2)) C2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)) (@ (@ tptp.minus_minus_real (@ _let_1 C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C2) B2) A2) (= C2 (@ (@ tptp.minus_minus_real A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C2) B2) A2) (= C2 (@ (@ tptp.minus_minus_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C2) B2) A2) (= C2 (@ (@ tptp.minus_minus_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C2) B2) A2) (= C2 (@ (@ tptp.minus_minus_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X2) Y3)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X2) Z)) (@ (@ tptp.plus_plus_real Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X2) Y3)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X2) Z)) (@ (@ tptp.plus_plus_rat Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X2) Y3)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X2) Z)) (@ (@ tptp.plus_plus_nat Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X2) Y3)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X2) Z)) (@ (@ tptp.plus_plus_int Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X2))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y3) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y3) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y3) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y3) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X2) Y3)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X2) Z)) (@ (@ tptp.minus_minus_real Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X2) Y3)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X2) Z)) (@ (@ tptp.minus_minus_rat Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X2) Y3)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X2) Z)) (@ (@ tptp.minus_minus_int Y3) Z)))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.vEBT_Leaf A2) B2)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X2) Y3) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X2) Y3) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y3) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X2) Y3) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y3) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X2) Y3) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_real X2) Y3) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_rat X2) Y3) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_nat X2) Y3) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_int X2) Y3) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C2) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C2)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C2)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C2)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C2)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C2) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (forall ((C3 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A2) C3)) (= C3 tptp.zero_zero_nat)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C2)))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real C2) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C2)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C2)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C2)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B6 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A5) B6)) tptp.zero_zero_real))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A5) B6)) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A5) B6)) tptp.zero_zero_int))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B6 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A5) B6)) tptp.zero_zero_real))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A5) B6)) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A5) B6)) tptp.zero_zero_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A2) B2))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B2) A2) C2) (= B2 (@ (@ tptp.plus_plus_nat C2) A2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.minus_minus_nat B2) A2)) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat C2) (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C2) A2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C2)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C2)) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A2) (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C2) A2)) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C2)) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.minus_minus_real C2) B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) B2)) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.minus_minus_rat C2) B2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.minus_minus_int C2) B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) B2)) C2) (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.plus_plus_real C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) B2)) C2) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) B2)) C2) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) B2)) C2) (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) B2)) C2) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) B2)) C2) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int C2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.minus_minus_real C2) B2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B2)) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.minus_minus_rat C2) B2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) C2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.minus_minus_int C2) B2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) C2))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) _let_1) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ tptp.ord_less_nat Xa))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (= Y3 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_3 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa) (@ _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 Xa) _let_1))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B2)) tptp.zero_zero_real)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real B2) C2) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.plus_plus_real A2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.plus_plus_rat A2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (@ (@ tptp.ord_less_nat B2) (@ (@ tptp.plus_plus_nat A2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (@ (@ tptp.ord_less_int B2) (@ (@ tptp.plus_plus_int A2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C2)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (=> (not (= Xa Mi2)) (=> (not (= Xa Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y3 (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y3) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y3) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y3) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (= Y3 (not (=> (not (= Xa Mi2)) (=> (not (= Xa Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (=> (not (= Xa Mi2)) (=> (not (= Xa Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (not (= Y3 _let_1)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 (@ (@ tptp.plus_plus_nat _let_1) (@ (@ (@ tptp.if_nat (= Xa tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (= Y3 (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= Xa Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (= Xa Ma2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa)) 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 Xa) _let_3)))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X2) Xa) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) Mi2) Xa))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2)) (not (= Y3 (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa Mi2) (= Xa 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)))))))))))))))))))
% 7.27/7.60 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A5 Bool) (B6 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A5) B6))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A22 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X7))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N4) _let_1)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X7)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N4)) (= A22 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N4))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))))))
% 7.27/7.60 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X8) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X8) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X8) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X8) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X8) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5)))) (=> (=> _let_1 (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X8) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X8 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X8) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low X8) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X8) (@ (@ tptp.ord_less_eq_nat X8) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X8) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5)))) (=> (=> _let_1 (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X8) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X8 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X8) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low X8) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X8) (@ (@ tptp.ord_less_eq_nat X8) Ma2)))))))))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa tptp.one_one_nat))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= X2 _let_2) (not (and (=> _let_4 (= Y3 (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y3 (@ _let_1 true))) (=> (not _let_3) (= Y3 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa) Xa))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (not (= Y3 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa Mi2) (= Xa Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X2) Xa) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (= Xa tptp.zero_zero_nat) (not (= Y3 (@ (@ tptp.vEBT_Leaf false) B3)))))) (=> (forall ((A3 Bool)) (=> (exists ((B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa (@ tptp.suc tptp.zero_zero_nat)) (not (= Y3 (@ (@ tptp.vEBT_Leaf A3) false)))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (exists ((N3 tptp.nat)) (= Xa (@ tptp.suc (@ tptp.suc N3)))) (not (= Y3 _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))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (=> (forall ((Mi2 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 Mi2) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (=> (forall ((Mi2 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 Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.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 (= Xa Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa))) (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 (= Xa 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) Mi2))) (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 Xa) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa)))) (=> (= X2 _let_2) (not (and (=> _let_24 (= Y3 _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (not _let_23) (= Y3 (@ (@ (@ 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)))))))))))))))))))))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_o (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.vEBT_VEBT_minNulli Ti)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ tptp.vEBT_VEBT_minNull T)))))) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y3 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y3 tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y3 (@ tptp.some_nat Ma2)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y3 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y3 tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y3 (@ tptp.some_nat Mi2)))))))))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (= (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ tptp.pure_assn B2)) F) Q) (=> B2 (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) F) Q)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_o (@ tptp.pure_assn B2)) F) Q) (=> B2 (@ (@ (@ tptp.hoare_hoare_triple_o tptp.one_one_assn) F) Q)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (= (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ tptp.pure_assn B2)) F) Q) (=> B2 (@ (@ (@ tptp.hoare_7629718768684598413on_nat tptp.one_one_assn) F) Q)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (= (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ tptp.pure_assn B2)) F) Q) (=> B2 (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) F) Q)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ tptp.pure_assn B2)) Q) (=> B2 (@ (@ tptp.entails tptp.one_one_assn) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (= (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) (=> B2 (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) F) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) (=> B2 (@ (@ (@ tptp.hoare_hoare_triple_o P) F) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (= (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) (=> B2 (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) F) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (= (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) (=> B2 (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) F) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) Q) (=> B2 (@ (@ tptp.entails P) Q)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (A2 Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (= _let_1 tptp.none_nat))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.vEBT_VEBT_minNulli Ti)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ tptp.vEBT_VEBT_minNull T))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ (@ tptp.vEBT_V854960066525838166emberi T) Ti) X2)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_member T) X2))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ (@ tptp.vEBT_VEBT_vebt_predi T) Ti) X2)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_pred T) X2)))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ (@ tptp.vEBT_VEBT_vebt_succi T) Ti) X2)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_succ T) X2)))))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B2)) (@ tptp.pure_assn (and A2 B2)))))
% 7.27/7.60 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 7.27/7.60 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.one_one_assn) P)))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one))))) (@ (@ (@ (@ tptp.time_htt_o (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ tptp.vEBT_vebt_memberi Ti) X2)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_member T) X2)))))) (@ (@ tptp.plus_plus_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.vEBT_VEBT_height T)))))))
% 7.27/7.60 (assert (= tptp.times_times_assn (lambda ((P3 tptp.assn) (Q7 tptp.assn)) (@ (@ tptp.times_times_assn Q7) P3))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) B) (=> (@ (@ tptp.entails B) A) (= A B)))))
% 7.27/7.60 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) P)))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B3)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B3)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X4)) (@ tptp.some_P7363390416028606310at_nat Y4)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X4 tptp.nat) (Y4 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X4)) (@ tptp.some_nat Y4)))))))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (Q tptp.assn) (Q2 tptp.assn)) (=> (@ (@ tptp.entails P) P5) (=> (@ (@ tptp.entails Q) Q2) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) Q)) (@ (@ tptp.times_times_assn P5) Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (C2 tptp.heap_T8145700208782473153_VEBTi)) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P5) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (Q (-> Bool tptp.assn)) (Q2 (-> Bool tptp.assn)) (C2 tptp.heap_Time_Heap_o)) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 Bool)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (=> (@ (@ (@ tptp.hoare_hoare_triple_o P5) C2) Q) (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (Q (-> tptp.option_nat tptp.assn)) (Q2 (-> tptp.option_nat tptp.assn)) (C2 tptp.heap_T2636463487746394924on_nat)) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 tptp.option_nat)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat P5) C2) Q) (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (Q (-> tptp.nat tptp.assn)) (Q2 (-> tptp.nat tptp.assn)) (C2 tptp.heap_Time_Heap_nat)) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat P5) C2) Q) (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (Q2 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2))) (=> (@ _let_1 Q) (=> (forall ((X4 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (@ _let_1 Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (Q2 (-> Bool tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_hoare_triple_o P) C2))) (=> (@ _let_1 Q) (=> (forall ((X4 Bool)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (@ _let_1 Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (Q2 (-> tptp.option_nat tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_7629718768684598413on_nat P) C2))) (=> (@ _let_1 Q) (=> (forall ((X4 tptp.option_nat)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (@ _let_1 Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (Q2 (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_3067605981109127869le_nat P) C2))) (=> (@ _let_1 Q) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.entails (@ Q X4)) (@ Q2 X4))) (@ _let_1 Q2))))))
% 7.27/7.60 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P) P)))
% 7.27/7.60 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A2)) (@ tptp.some_P7363390416028606310at_nat B2)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A2) B2)))))
% 7.27/7.60 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A2)) (@ tptp.some_nat B2)) (@ tptp.some_nat (@ (@ F A2) B2)))))
% 7.27/7.60 (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)))
% 7.27/7.60 (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)))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn P) R)) C2) (lambda ((X3 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ Q X3)) R))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.times_times_assn P) R)) C2) (lambda ((X3 Bool)) (@ (@ tptp.times_times_assn (@ Q X3)) R))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.times_times_assn P) R)) C2) (lambda ((X3 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ Q X3)) R))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.times_times_assn P) R)) C2) (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_assn (@ Q X3)) R))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) P5) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P5) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (=> (@ (@ tptp.entails P) P5) (=> (@ (@ (@ tptp.hoare_hoare_triple_o P5) C2) Q) (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (=> (@ (@ tptp.entails P) P5) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat P5) C2) Q) (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (P5 tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (=> (@ (@ tptp.entails P) P5) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat P5) C2) Q) (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) F) Q)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_hoare_triple_o P) F) Q)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) F) Q)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) F) Q)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) F) Q)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ tptp.pure_assn B2)) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_hoare_triple_o tptp.one_one_assn) F) Q)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ tptp.pure_assn B2)) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_7629718768684598413on_nat tptp.one_one_assn) F) Q)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ tptp.pure_assn B2)) F) Q))))
% 7.27/7.60 (assert (forall ((B2 Bool) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (=> (=> B2 (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) F) Q)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ tptp.pure_assn B2)) F) Q))))
% 7.27/7.60 (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)))
% 7.27/7.60 (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)))
% 7.27/7.60 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y3 tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y3 tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X2) Xa) Xb) Y3) (=> (=> (= Xa tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B3)) (not (= Y3 (@ tptp.some_P7363390416028606310at_nat (@ (@ X2 A3) B3)))))))))))))))
% 7.27/7.60 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.option_nat) (Xb tptp.option_nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X2) Xa) Xb) Y3) (=> (=> (= Xa tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa (@ tptp.some_nat A3)) (forall ((B3 tptp.nat)) (=> (= Xb (@ tptp.some_nat B3)) (not (= Y3 (@ tptp.some_nat (@ (@ X2 A3) B3)))))))))))))))
% 7.27/7.60 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_nat Y) X3) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs2) (=> (@ (@ tptp.ord_less_nat Z4) X3) (@ (@ tptp.ord_less_eq_nat Z4) Y))))))))
% 7.27/7.60 (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)))
% 7.27/7.60 (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)))
% 7.27/7.60 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 7.27/7.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vd3 tptp.list_VEBT_VEBT) (Ve3 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd3) Ve3)) Vf2) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A2) B2)))) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= _let_1 tptp.none_nat))))))))
% 7.27/7.60 (assert (forall ((B2 Bool) (A2 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A2) B2)))) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (= _let_1 tptp.none_nat))))))))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A2) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (= _let_1 tptp.none_nat))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) N)))))
% 7.27/7.60 (assert (forall ((I tptp.nat) (Ts tptp.list_VEBT_VEBT) (Tsi tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Ts)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Ts) Tsi)) (@ tptp.vEBT_vebt_maxti (@ (@ tptp.nth_VEBT_VEBTi Tsi) I))) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ tptp.pure_assn (= R5 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Ts) I))))) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Ts) Tsi)))))))
% 7.27/7.60 (assert (forall ((I tptp.nat) (Ts tptp.list_VEBT_VEBT) (Tsi tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Ts)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Ts) Tsi)) (@ tptp.vEBT_vebt_minti (@ (@ tptp.nth_VEBT_VEBTi Tsi) I))) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ tptp.pure_assn (= R5 (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT Ts) I))))) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Ts) Tsi)))))))
% 7.27/7.60 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X3)) (@ tptp.some_nat Y)))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X3)) (@ tptp.some_nat Y)))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBTi)) (@ (@ tptp.time_T8353473612707095248on_nat (@ tptp.vEBT_vebt_maxti T)) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBTi)) (@ (@ tptp.time_T8353473612707095248on_nat (@ tptp.vEBT_vebt_minti T)) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A2) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A2) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_max_int A2) A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_max_nat A2) B2))) (= (@ (@ tptp.ord_max_nat _let_1) B2) _let_1))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) B2) _let_1))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_max_int A2) B2))) (= (@ (@ tptp.ord_max_int _let_1) B2) _let_1))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.vEBT_vebt_minti Ti)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ tptp.vEBT_vebt_mint T))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.vEBT_vebt_maxti Ti)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ tptp.vEBT_vebt_maxt T))))))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (A2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) A2) (= (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.ord_max_rat A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (= (@ (@ tptp.ord_max_num A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.ord_max_nat A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.ord_max_int A2) B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A2) B2) (= (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (= (@ (@ tptp.ord_max_rat A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (= (@ (@ tptp.ord_max_num A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.ord_max_nat A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.ord_max_int A2) B2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (C2 tptp.extended_enat) (A2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B2) C2)) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat B2) A2) (@ (@ tptp.ord_le2932123472753598470d_enat C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B2) C2)) A2) (and (@ (@ tptp.ord_less_eq_rat B2) A2) (@ (@ tptp.ord_less_eq_rat C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (C2 tptp.num) (A2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B2) C2)) A2) (and (@ (@ tptp.ord_less_eq_num B2) A2) (@ (@ tptp.ord_less_eq_num C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C2)) A2) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C2)) A2) (and (@ (@ tptp.ord_less_eq_int B2) A2) (@ (@ tptp.ord_less_eq_int C2) A2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y3)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X2) Y3)) Z) (and (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X2) Y3)) Z) (and (@ (@ tptp.ord_less_rat X2) Z) (@ (@ tptp.ord_less_rat Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X2) Y3)) Z) (and (@ (@ tptp.ord_less_num X2) Z) (@ (@ tptp.ord_less_num Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X2) Y3)) Z) (and (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X2) Y3)) Z) (and (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_int Y3) Z)))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A2) B2) (= (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (= (@ (@ tptp.ord_max_real A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (= (@ (@ tptp.ord_max_rat A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (= (@ (@ tptp.ord_max_num A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_max_nat A2) B2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.ord_max_int A2) B2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (A2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A2) (= (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (= (@ (@ tptp.ord_max_real A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (= (@ (@ tptp.ord_max_rat A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (= (@ (@ tptp.ord_max_num A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.ord_max_nat A2) B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.ord_max_int A2) B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A2))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.ord_max_nat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat) (C2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat B2) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A2))) (= (@ (@ tptp.ord_max_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.ord_max_int B2) C2))))))
% 7.27/7.60 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.ord_max_nat B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A5 tptp.extended_enat) (B6 tptp.extended_enat)) (@ (@ tptp.ord_ma741700101516333627d_enat B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ tptp.ord_max_int B6) A5))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B2))) (let ((_let_2 (@ tptp.ord_max_nat A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (A2 tptp.extended_enat) (C2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat B2))) (let ((_let_2 (@ tptp.ord_ma741700101516333627d_enat A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B2))) (let ((_let_2 (@ tptp.ord_max_int A2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.60 (assert (forall ((C2 tptp.extended_enat) (A2 tptp.extended_enat) (D2 tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C2) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D2) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C2) D2)) (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (D2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A2) (=> (@ (@ tptp.ord_less_eq_rat D2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C2) D2)) (@ (@ tptp.ord_max_rat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.num) (A2 tptp.num) (D2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C2) A2) (=> (@ (@ tptp.ord_less_eq_num D2) B2) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C2) D2)) (@ (@ tptp.ord_max_num A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (D2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A2) (=> (@ (@ tptp.ord_less_eq_nat D2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C2) D2)) (@ (@ tptp.ord_max_nat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (D2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A2) (=> (@ (@ tptp.ord_less_eq_int D2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C2) D2)) (@ (@ tptp.ord_max_int A2) B2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (A2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) A2) (= A2 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= A2 (@ (@ tptp.ord_max_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (= A2 (@ (@ tptp.ord_max_num A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 (@ (@ tptp.ord_max_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= A2 (@ (@ tptp.ord_max_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= A2 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2)) (@ (@ tptp.ord_le2932123472753598470d_enat B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (= A2 (@ (@ tptp.ord_max_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (= A2 (@ (@ tptp.ord_max_num A2) B2)) (@ (@ tptp.ord_less_eq_num B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.ord_max_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.ord_max_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (C2 tptp.extended_enat) (A2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B2) C2)) A2) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) A2) (not (@ (@ tptp.ord_le2932123472753598470d_enat C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (not (@ (@ tptp.ord_less_eq_rat C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (C2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_eq_num B2) A2) (not (@ (@ tptp.ord_less_eq_num C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (not (@ (@ tptp.ord_less_eq_nat C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_eq_int B2) A2) (not (@ (@ tptp.ord_less_eq_int C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (A2 tptp.extended_enat) (C2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C2) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B2) C2)) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C2) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B2) C2)) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (=> (@ (@ tptp.ord_less_eq_num C2) A2) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B2) C2)) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C2) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C2)) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C2) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C2)) A2)))))
% 7.27/7.60 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B6 tptp.extended_enat) (A5 tptp.extended_enat)) (= A5 (@ (@ tptp.ord_ma741700101516333627d_enat A5) B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.ord_max_rat A5) B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_num (lambda ((B6 tptp.num) (A5 tptp.num)) (= A5 (@ (@ tptp.ord_max_num A5) B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.ord_max_nat A5) B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((B6 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.ord_max_int A5) B6)))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A2) (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.ord_max_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (@ (@ tptp.ord_less_eq_num A2) (@ (@ tptp.ord_max_num A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.ord_max_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.ord_max_int A2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (A2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B2) (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.ord_max_rat A2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (@ (@ tptp.ord_less_eq_num B2) (@ (@ tptp.ord_max_num A2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.ord_max_nat A2) B2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.ord_max_int A2) B2))))
% 7.27/7.60 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B6 tptp.extended_enat) (A5 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A5) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_num (lambda ((B6 tptp.num) (A5 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((B6 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A5 tptp.extended_enat) (B6 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A5) B6) B6))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B6) B6))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B6 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B6) B6))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B6) B6))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B6 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B6) B6))))
% 7.27/7.60 (assert (forall ((C2 tptp.extended_enat) (A2 tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.num) (A2 tptp.num) (B2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_num A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_int A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.extended_enat) (B2 tptp.extended_enat) (A2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.num) (B2 tptp.num) (A2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_num A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_int A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.extended_enat) (B2 tptp.extended_enat) (A2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (B2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_real A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.num) (B2 tptp.num) (A2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_num A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_int A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.extended_enat) (A2 tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_real A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.num) (A2 tptp.num) (B2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_num A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B2))))))
% 7.27/7.60 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_int A2) B2))))))
% 7.27/7.60 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B6 tptp.extended_enat) (A5 tptp.extended_enat)) (and (= A5 (@ (@ tptp.ord_ma741700101516333627d_enat A5) B6)) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((B6 tptp.real) (A5 tptp.real)) (and (= A5 (@ (@ tptp.ord_max_real A5) B6)) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (and (= A5 (@ (@ tptp.ord_max_rat A5) B6)) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((B6 tptp.num) (A5 tptp.num)) (and (= A5 (@ (@ tptp.ord_max_num A5) B6)) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (and (= A5 (@ (@ tptp.ord_max_nat A5) B6)) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((B6 tptp.int) (A5 tptp.int)) (and (= A5 (@ (@ tptp.ord_max_int A5) B6)) (not (= A5 B6))))))
% 7.27/7.60 (assert (forall ((B2 tptp.extended_enat) (C2 tptp.extended_enat) (A2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B2) C2)) A2) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A2) (not (@ (@ tptp.ord_le72135733267957522d_enat C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (C2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_real B2) A2) (not (@ (@ tptp.ord_less_real C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (C2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_rat B2) A2) (not (@ (@ tptp.ord_less_rat C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (C2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_num B2) A2) (not (@ (@ tptp.ord_less_num C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat C2) A2)))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B2) C2)) A2) (not (=> (@ (@ tptp.ord_less_int B2) A2) (not (@ (@ tptp.ord_less_int C2) A2)))))))
% 7.27/7.60 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y3)) (or (@ _let_1 X2) (@ _let_1 Y3))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (forall ((A3 tptp.real) (B3 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (=> (@ (@ P B3) C3) (=> (@ (@ tptp.ord_less_eq_real A3) B3) (=> (@ (@ tptp.ord_less_eq_real B3) C3) (@ _let_1 C3))))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A3 tptp.real) (B3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X4) (@ (@ tptp.ord_less_eq_real X4) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B3) A3)) D5)) (@ (@ P A3) B3)))))))) (@ (@ P A2) B2))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_option_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.vEBT_vebt_maxti Ti)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ tptp.vEBT_vebt_maxt T)))))) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (Ti tptp.vEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_option_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.vEBT_vebt_minti Ti)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ tptp.vEBT_vebt_mint T)))))) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c2 X2) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= Xa tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N3 tptp.nat)) (= Xa (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low Xa) _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 Xa) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2)) (not (and (=> _let_7 (= Y3 tptp.one_one_nat)) (=> (not _let_7) (= Y3 (@ (@ (@ 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))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d2 X2) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A3 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa (@ tptp.suc tptp.zero_zero_nat)) _let_1)) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (exists ((Va3 tptp.nat)) (= Xa (@ tptp.suc (@ tptp.suc Va3)))) _let_1)) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low Xa) _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) Xa))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2)) (not (and (=> _let_7 (= Y3 tptp.one_one_nat)) (=> (not _let_7) (= Y3 (@ (@ (@ 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)))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_maxt _let_5))) (let ((_let_7 (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2))) (let ((_let_8 (@ (@ tptp.ord_less_nat X2) Mi))) (and (=> _let_8 (= _let_7 tptp.one_one_nat)) (=> (not _let_8) (= _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary) _let_3)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))
% 7.27/7.60 (assert (forall ((Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_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 Mi) Ma))) _let_1) TreeList) Summary)) X2))) (let ((_let_8 (@ (@ tptp.ord_less_nat Ma) X2))) (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))))))))))))))
% 7.27/7.60 (assert (forall ((B2 Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B2)) tptp.zero_zero_nat))) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= _let_1 tptp.none_nat))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (Va tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc (@ tptp.suc Va))) tptp.one_one_nat)))
% 7.27/7.60 (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)))
% 7.27/7.60 (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)))
% 7.27/7.60 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((Uu Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ tptp.vEBT_Leaf Uu) B2)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((A2 Bool) (Uw Bool)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ tptp.vEBT_Leaf A2) Uw)) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vd3 tptp.list_VEBT_VEBT) (Ve3 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd3) Ve3)) Vf2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd3 tptp.vEBT_VEBT) (Ve3 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd3)) Ve3) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_p_r_e_d2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_s_u_c_c2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 7.27/7.60 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_nat X3) Y) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs2) (=> (@ (@ tptp.ord_less_nat X3) Z4) (@ (@ tptp.ord_less_eq_nat Y) Z4))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (@ (@ 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) X2))) (@ (@ tptp.plus_plus_real _let_1) (@ _let_2 (@ _let_2 U))))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (@ (@ 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) X2))) (@ (@ tptp.plus_plus_real _let_1) (@ _let_2 (@ _let_2 U))))))))))
% 7.27/7.60 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd3 tptp.vEBT_VEBT) (Ve3 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd3)) Ve3) tptp.none_nat)))
% 7.27/7.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.none_nat)))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_V8346862874174094_d_u_p (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_V8646137997579335489_i_l_d (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.nat) (Y3 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X2) Y3))) (and (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y3)))) (=> (@ (@ tptp.ord_less_nat X2) Y3) (@ P tptp.zero_zero_int))))))
% 7.27/7.60 (assert (forall ((Xa tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Xb 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 Xa) Tree_is)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) Xb))) (@ tptp.pure_assn (and (= tptp.none_nat tptp.none_nat) (= N N))))) (@ tptp.pure_assn (= Xc (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) N) Xa) Xb))))) H2) (@ (@ tptp.rep_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) N) TreeList) Summary)) Xc)) H2))))
% 7.27/7.60 (assert (forall ((Xa tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Xb 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 Xa) Tree_is)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) Xb))) (@ 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) Xa) Xb))))) H2) (@ (@ tptp.rep_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) N) TreeList) Summary)) Xc)) H2))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (or (= Xa Mi2) (= Xa Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y3) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y3) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (= Y3 (not (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (= Y3 (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (= Y3 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))
% 7.27/7.60 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X2))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) H2) (and (@ (@ tptp.rep_assn P) H2) B2))))
% 7.27/7.60 (assert (forall ((Q3 tptp.array_VEBT_VEBTi) (Y3 tptp.list_VEBT_VEBTi) (H2 tptp.heap_e7401611519738050253t_unit)) (not (@ (@ tptp.rep_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Q3) Y3)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (Q tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q) (@ tptp.pure_assn B2))) (and (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) B2)) (@ _let_1 Q))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ tptp.pure_assn B2)) (and (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) B2)) (@ _let_1 tptp.one_one_assn))))))
% 7.27/7.60 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A2) B2)) H2) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A2) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B2) H_2))))))))
% 7.27/7.60 (assert (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (exists ((H1 tptp.produc3658429121746597890et_nat) (H22 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A) H1) (@ (@ tptp.rep_assn B) H22))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (= tptp.entails (lambda ((P3 tptp.assn) (Q7 tptp.assn)) (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P3) H) (@ (@ tptp.rep_assn Q7) H))))))
% 7.27/7.60 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 7.27/7.60 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 7.27/7.60 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.one_one_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (not (@ (@ tptp.ord_less_real X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (not (@ (@ tptp.ord_less_rat X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (not (@ (@ tptp.ord_less_num X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (not (@ (@ tptp.ord_less_nat X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (not (@ (@ tptp.ord_less_int X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (@ (@ tptp.ord_less_real T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (@ (@ tptp.ord_less_rat T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (@ (@ tptp.ord_less_num T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (@ (@ tptp.ord_less_nat T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (@ (@ tptp.ord_less_int T) X8))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (= (and (@ P X8) (@ Q X8)) (and (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (= (or (@ P X8) (@ Q X8)) (or (@ P5 X8) (@ Q2 X8))))))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (not (= X8 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X8))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X8))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X8))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X8))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X8))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (not (@ (@ tptp.ord_less_real T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (not (@ (@ tptp.ord_less_rat T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (not (@ (@ tptp.ord_less_num T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (not (@ (@ tptp.ord_less_nat T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (not (@ (@ tptp.ord_less_int T) X8)))))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X2) (or (= X2 Mi) (= X2 Ma)))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (not (@ (@ tptp.ord_less_eq_real X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (not (@ (@ tptp.ord_less_eq_rat X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (not (@ (@ tptp.ord_less_eq_num X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (not (@ (@ tptp.ord_less_eq_nat X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (not (@ (@ tptp.ord_less_eq_int X8) T)))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X8) (@ (@ tptp.ord_less_eq_real T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X8) (@ (@ tptp.ord_less_eq_rat T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X8) (@ (@ tptp.ord_less_eq_num T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X8) (@ (@ tptp.ord_less_eq_nat T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X8) (@ (@ tptp.ord_less_eq_int T) X8))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (@ (@ tptp.ord_less_eq_real X8) T))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (@ (@ tptp.ord_less_eq_rat X8) T))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (@ (@ tptp.ord_less_eq_num X8) T))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (@ (@ tptp.ord_less_eq_nat X8) T))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (@ (@ tptp.ord_less_eq_int X8) T))))))
% 7.27/7.60 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (=> (@ (@ tptp.ord_less_real X8) Z2) (not (@ (@ tptp.ord_less_eq_real T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X8) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X8 tptp.num)) (=> (@ (@ tptp.ord_less_num X8) Z2) (not (@ (@ tptp.ord_less_eq_num T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X8) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X8)))))))
% 7.27/7.60 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (=> (@ (@ tptp.ord_less_int X8) Z2) (not (@ (@ tptp.ord_less_eq_int T) X8)))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real Bool)) (D tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D))))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D))))) (forall ((X8 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X8) (@ (@ tptp.times_times_real K5) D)))) (= (and (@ P X8) (@ Q X8)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat Bool)) (D tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D))))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D))))) (forall ((X8 tptp.rat) (K5 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X8) (@ (@ tptp.times_times_rat K5) D)))) (= (and (@ P X8) (@ Q X8)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (D tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (forall ((X8 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X8) (@ (@ tptp.times_times_int K5) D)))) (= (and (@ P X8) (@ Q X8)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real Bool)) (D tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D))))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D))))) (forall ((X8 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X8) (@ (@ tptp.times_times_real K5) D)))) (= (or (@ P X8) (@ Q X8)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat Bool)) (D tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D))))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D))))) (forall ((X8 tptp.rat) (K5 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X8) (@ (@ tptp.times_times_rat K5) D)))) (= (or (@ P X8) (@ Q X8)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (D tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (forall ((X8 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X8) (@ (@ tptp.times_times_int K5) D)))) (= (or (@ P X8) (@ Q X8)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (=> (not (= X2 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va3 tptp.nat)) (not (= X2 (@ tptp.suc (@ tptp.suc Va3))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (X5 tptp.int) (P Bool) (P5 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X2 X5) (=> (=> _let_2 (= P P5)) (= (and (@ _let_1 X2) P) (and _let_2 P5))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (X5 tptp.int) (P Bool) (P5 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X2 X5) (=> (=> _let_2 (= P P5)) (= (=> (@ _let_1 X2) P) (=> _let_2 P5))))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ tptp.vEBT_VEBT_cnt (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.one_one_real)))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ tptp.vEBT_VEBT_cnt2 (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.one_one_nat)))
% 7.27/7.60 (assert (forall ((D2 tptp.int) (P5 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P5 X4) (@ P5 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D2))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (exists ((X_12 tptp.int)) (@ P5 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 7.27/7.60 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P1 X4) (@ P1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D2))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P1 X4))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 7.27/7.60 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd3 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd3)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 7.27/7.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X8 tptp.int)) (=> (@ P X8) (@ P (@ (@ tptp.plus_plus_int X8) (@ (@ tptp.times_times_int K) D2))))))))))
% 7.27/7.60 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X8 tptp.int)) (=> (@ P X8) (@ P (@ (@ tptp.minus_minus_int X8) (@ (@ tptp.times_times_int K) D2))))))))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_V8646137997579335489_i_l_d tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 7.27/7.60 (assert (= (@ tptp.vEBT_V8346862874174094_d_u_p tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ tptp.vEBT_VEBT_space2 (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ tptp.vEBT_VEBT_space (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (not (or (= Xa Mi2) (= Xa Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))))))))
% 7.27/7.60 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X2) (@ (@ tptp.vEBT_VEBT_membermima Tree) X2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A2) B2)) (@ (@ tptp.set_or370866239135849197et_int C2) D2)) (or (not (@ (@ tptp.ord_less_eq_set_int A2) B2)) (and (@ (@ tptp.ord_less_eq_set_int C2) A2) (@ (@ tptp.ord_less_eq_set_int B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B2)) (@ (@ tptp.set_or633870826150836451st_rat C2) D2)) (or (not (@ (@ tptp.ord_less_eq_rat A2) B2)) (and (@ (@ tptp.ord_less_eq_rat C2) A2) (@ (@ tptp.ord_less_eq_rat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B2)) (@ (@ tptp.set_or7049704709247886629st_num C2) D2)) (or (not (@ (@ tptp.ord_less_eq_num A2) B2)) (and (@ (@ tptp.ord_less_eq_num C2) A2) (@ (@ tptp.ord_less_eq_num B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C2) D2)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (and (@ (@ tptp.ord_less_eq_nat C2) A2) (@ (@ tptp.ord_less_eq_nat B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B2)) (@ (@ tptp.set_or1266510415728281911st_int C2) D2)) (or (not (@ (@ tptp.ord_less_eq_int A2) B2)) (and (@ (@ tptp.ord_less_eq_int C2) A2) (@ (@ tptp.ord_less_eq_int B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger A2) B2)) (@ (@ tptp.set_or189985376899183464nteger C2) D2)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (and (@ (@ tptp.ord_le3102999989581377725nteger C2) A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ tptp.set_or1222579329274155063t_real C2) D2)) (or (not (@ (@ tptp.ord_less_eq_real A2) B2)) (and (@ (@ tptp.ord_less_eq_real C2) A2) (@ (@ tptp.ord_less_eq_real B2) D2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (= (@ (@ tptp.set_or633870826150836451st_rat A2) B2) tptp.bot_bot_set_rat))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (= (@ (@ tptp.set_or7049704709247886629st_num A2) B2) tptp.bot_bot_set_num))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.set_or1269000886237332187st_nat A2) B2) tptp.bot_bot_set_nat))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.set_or1266510415728281911st_int A2) B2) tptp.bot_bot_set_int))))
% 7.27/7.60 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (= (@ (@ tptp.set_or189985376899183464nteger A2) B2) tptp.bot_bo3990330152332043303nteger))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (= (@ (@ tptp.set_or1222579329274155063t_real A2) B2) tptp.bot_bot_set_real))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A2) B2)) (not (@ (@ tptp.ord_less_eq_set_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B2)) (not (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B2)) (not (@ (@ tptp.ord_less_eq_num A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (not (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B2)) (not (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or189985376899183464nteger A2) B2)) (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (not (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A2) B2) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A2) B2) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A2) B2) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A2) B2) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A2) B2) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.set_or189985376899183464nteger A2) B2) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A2) B2) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A2) B2)))))
% 7.27/7.60 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X3 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X3) (@ (@ tptp.vEBT_VEBT_membermima T2) X3)))))
% 7.27/7.60 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 7.27/7.60 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 7.27/7.60 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X2))))
% 7.27/7.60 (assert (forall ((L tptp.set_int) (H2 tptp.set_int) (L4 tptp.set_int) (H4 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H2) (@ (@ tptp.set_or370866239135849197et_int L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (not (@ (@ tptp.ord_less_eq_set_int L4) H4)))))))
% 7.27/7.60 (assert (forall ((L tptp.rat) (H2 tptp.rat) (L4 tptp.rat) (H4 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H2) (@ (@ tptp.set_or633870826150836451st_rat L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_less_eq_rat L) H2)) (not (@ (@ tptp.ord_less_eq_rat L4) H4)))))))
% 7.27/7.60 (assert (forall ((L tptp.num) (H2 tptp.num) (L4 tptp.num) (H4 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H2) (@ (@ tptp.set_or7049704709247886629st_num L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_less_eq_num L) H2)) (not (@ (@ tptp.ord_less_eq_num L4) H4)))))))
% 7.27/7.60 (assert (forall ((L tptp.nat) (H2 tptp.nat) (L4 tptp.nat) (H4 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L4) H4)))))))
% 7.27/7.60 (assert (forall ((L tptp.int) (H2 tptp.int) (L4 tptp.int) (H4 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L4) H4)))))))
% 7.27/7.60 (assert (forall ((L tptp.code_integer) (H2 tptp.code_integer) (L4 tptp.code_integer) (H4 tptp.code_integer)) (= (= (@ (@ tptp.set_or189985376899183464nteger L) H2) (@ (@ tptp.set_or189985376899183464nteger L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_le3102999989581377725nteger L) H2)) (not (@ (@ tptp.ord_le3102999989581377725nteger L4) H4)))))))
% 7.27/7.60 (assert (forall ((L tptp.real) (H2 tptp.real) (L4 tptp.real) (H4 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L4) H4)) (or (and (= L L4) (= H2 H4)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L4) H4)))))))
% 7.27/7.60 (assert (forall ((I tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ (@ tptp.set_or370866239135849197et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I) (@ (@ tptp.ord_less_eq_set_int I) U)))))
% 7.27/7.60 (assert (forall ((I tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 7.27/7.60 (assert (forall ((I tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 7.27/7.60 (assert (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 7.27/7.60 (assert (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 7.27/7.60 (assert (forall ((I tptp.code_integer) (L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.member_Code_integer I) (@ (@ tptp.set_or189985376899183464nteger L) U)) (and (@ (@ tptp.ord_le3102999989581377725nteger L) I) (@ (@ tptp.ord_le3102999989581377725nteger I) U)))))
% 7.27/7.60 (assert (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 7.27/7.60 (assert (forall ((D tptp.int) (A tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.plus_plus_int X4) D))))) (forall ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X8) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X8) (@ Q X8)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (A tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.plus_plus_int X4) D))))) (forall ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X8) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X8) (@ Q X8)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) D))))) (forall ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X8) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X8) (@ Q X8)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) D))))) (forall ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X8) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X8) (@ Q X8)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M8 tptp.nat)) (=> (@ P X2) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M8))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X8 tptp.nat)) (=> (@ P X8) (@ (@ tptp.ord_less_eq_nat X8) M5)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (not (= X2 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B3) Acc)))))))))
% 7.27/7.60 (assert (forall ((A2 Bool) (B2 Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A2) B2)) X2) (and (=> _let_2 A2) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X8) (@ _let_1 (@ (@ tptp.plus_plus_int X8) D)))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) A) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X8) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X8) D)) T))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) A) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X8 T)) (not (= (@ (@ tptp.plus_plus_int X8) D) T)))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X8 T) (= (@ (@ tptp.plus_plus_int X8) D) T))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) B) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X8) (@ _let_1 (@ (@ tptp.minus_minus_int X8) D))))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X8) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X8) D)) T)))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) B) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X8 T)) (not (= (@ (@ tptp.minus_minus_int X8) D) T)))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X8 T) (= (@ (@ tptp.minus_minus_int X8) D) T))))))))
% 7.27/7.60 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D2))))) (= (exists ((X7 tptp.int)) (@ P X7)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X3))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X8) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X8) D)) T)))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X8) (@ _let_1 (@ (@ tptp.minus_minus_int X8) D))))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A) (forall ((X8 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X8) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X8) D)) T))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X8) (@ _let_1 (@ (@ tptp.plus_plus_int X8) D)))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P5 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P5 X4) (@ P5 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P5 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B) (@ P (@ (@ tptp.plus_plus_int Y) X3))))))))))))))
% 7.27/7.60 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P5 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P5 X4) (@ P5 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P5 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) A) (@ P (@ (@ tptp.minus_minus_int Y) X3))))))))))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y3) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A2) B2)) (@ (@ tptp.set_or370866239135849197et_int C2) D2)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_set_int B2) D2) (or (@ (@ tptp.ord_less_set_int C2) A2) (@ (@ tptp.ord_less_set_int B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B2)) (@ (@ tptp.set_or633870826150836451st_rat C2) D2)) (and (or (not (@ (@ tptp.ord_less_eq_rat A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) D2) (or (@ (@ tptp.ord_less_rat C2) A2) (@ (@ tptp.ord_less_rat B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B2)) (@ (@ tptp.set_or7049704709247886629st_num C2) D2)) (and (or (not (@ (@ tptp.ord_less_eq_num A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_num B2) D2) (or (@ (@ tptp.ord_less_num C2) A2) (@ (@ tptp.ord_less_num B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C2) D2)) (and (or (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B2) D2) (or (@ (@ tptp.ord_less_nat C2) A2) (@ (@ tptp.ord_less_nat B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B2)) (@ (@ tptp.set_or1266510415728281911st_int C2) D2)) (and (or (not (@ (@ tptp.ord_less_eq_int A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) D2) (or (@ (@ tptp.ord_less_int C2) A2) (@ (@ tptp.ord_less_int B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C2))) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ (@ tptp.set_or189985376899183464nteger A2) B2)) (@ (@ tptp.set_or189985376899183464nteger C2) D2)) (and (or (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) D2) (or (@ (@ tptp.ord_le6747313008572928689nteger C2) A2) (@ (@ tptp.ord_le6747313008572928689nteger B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C2))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ tptp.set_or1222579329274155063t_real C2) D2)) (and (or (not (@ (@ tptp.ord_less_eq_real A2) B2)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B2) D2) (or (@ (@ tptp.ord_less_real C2) A2) (@ (@ tptp.ord_less_real B2) D2)))) (@ _let_1 D2))))))
% 7.27/7.60 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y3 (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y3) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (= Y3 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 7.27/7.60 (assert (= tptp.time_htt_VEBT_VEBTi (lambda ((P3 tptp.assn) (C4 tptp.heap_T8145700208782473153_VEBTi) (Q7 (-> tptp.vEBT_VEBTi tptp.assn)) (T2 tptp.nat)) (and (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P3) C4) Q7) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ tptp.rep_assn P3) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi C4) H)) T2)))))))
% 7.27/7.60 (assert (= tptp.time_htt_o (lambda ((P3 tptp.assn) (C4 tptp.heap_Time_Heap_o) (Q7 (-> Bool tptp.assn)) (T2 tptp.nat)) (and (@ (@ (@ tptp.hoare_hoare_triple_o P3) C4) Q7) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ tptp.rep_assn P3) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_o C4) H)) T2)))))))
% 7.27/7.60 (assert (= tptp.time_htt_option_nat (lambda ((P3 tptp.assn) (C4 tptp.heap_T2636463487746394924on_nat) (Q7 (-> tptp.option_nat tptp.assn)) (T2 tptp.nat)) (and (@ (@ (@ tptp.hoare_7629718768684598413on_nat P3) C4) Q7) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ tptp.rep_assn P3) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_option_nat C4) H)) T2)))))))
% 7.27/7.60 (assert (= tptp.time_htt_nat (lambda ((P3 tptp.assn) (C4 tptp.heap_Time_Heap_nat) (Q7 (-> tptp.nat tptp.assn)) (T2 tptp.nat)) (and (@ (@ (@ tptp.hoare_3067605981109127869le_nat P3) C4) Q7) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ tptp.rep_assn P3) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_nat C4) H)) T2)))))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H3) As2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi C2) H3)) T))) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi P) C2) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H3) As2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_o C2) H3)) T))) (@ (@ (@ (@ tptp.time_htt_o P) C2) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H3) As2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_option_nat C2) H3)) T))) (@ (@ (@ (@ tptp.time_htt_option_nat P) C2) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H3) As2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_nat C2) H3)) T))) (@ (@ (@ (@ tptp.time_htt_nat P) C2) Q) T)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A2))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A2) B2)))) (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))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X2) tptp.bot_bot_set_nat) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.assn)) (= (@ (@ tptp.ord_max_assn X2) tptp.bot_bot_assn) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X2) tptp.bot_bot_set_int) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat X2) tptp.bot_bot_nat) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) tptp.bot_bo4199563552545308370d_enat) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.assn)) (= (@ (@ tptp.ord_max_assn tptp.bot_bot_assn) X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ _let_1 tptp.one_one_int)) (@ _let_1 X2)))))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 7.27/7.60 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.num)) (@ (@ tptp.ord_less_eq_num A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) A2)))
% 7.27/7.60 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))))
% 7.27/7.60 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 7.27/7.60 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)))
% 7.27/7.60 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 7.27/7.60 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.entails P) tptp.bot_bot_assn) (forall ((H tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H))))))
% 7.27/7.60 (assert (forall ((P6 tptp.array_VEBT_VEBTi) (X2 tptp.list_VEBT_VEBTi) (Y3 tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ tptp.snga_assn_VEBT_VEBTi P6))) (= (@ (@ tptp.times_times_assn (@ _let_1 X2)) (@ _let_1 Y3)) tptp.bot_bot_assn))))
% 7.27/7.60 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 7.27/7.60 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 7.27/7.60 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 7.27/7.60 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real V)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.27/7.60 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X2))))
% 7.27/7.60 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 7.27/7.60 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 7.27/7.60 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 7.27/7.60 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 7.27/7.60 (assert (= tptp.bot_bot_option_nat tptp.none_nat))
% 7.27/7.60 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P)))
% 7.27/7.60 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y3) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y3)) (@ tptp.archim7802044766580827645g_real X2)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y3)) (@ tptp.archim2889992004027027881ng_rat X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y3)) (@ (@ tptp.ord_less_rat X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) Y3))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) Y3))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y3)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.num)) (@ (@ tptp.ord_less_eq_num A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A2) B2)) (and (@ (@ tptp.ord_less_eq_rat B2) A2) (not (= B2 A2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A2) B2)) (and (@ (@ tptp.ord_less_eq_num B2) A2) (not (= B2 A2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= B2 A2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A2) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A2) (not (= B2 A2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_num Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((X3 tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y) (@ (@ tptp.ord_less_eq_set_int Y) X3)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((X3 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y) (@ (@ tptp.ord_less_eq_rat Y) X3)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((X3 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y) (@ (@ tptp.ord_less_eq_num Y) X3)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((X3 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y) (@ (@ tptp.ord_less_eq_nat Y) X3)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((X3 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y) (@ (@ tptp.ord_less_eq_int Y) X3)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ (@ tptp.ord_less_eq_set_int A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (@ (@ tptp.ord_less_eq_rat A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (@ (@ tptp.ord_less_eq_num A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (@ (@ tptp.ord_less_eq_nat A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (@ (@ tptp.ord_less_eq_int A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_set_int Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A2 tptp.rat) (B2 tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2)))))
% 7.27/7.60 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A2 tptp.num) (B2 tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2)))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2)))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B2 tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B6) A5) (@ (@ tptp.ord_less_eq_set_int A5) B6)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A5 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B6) A5) (@ (@ tptp.ord_less_eq_rat A5) B6)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A5 tptp.num) (B6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B6) A5) (@ (@ tptp.ord_less_eq_num A5) B6)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A5 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B6) A5) (@ (@ tptp.ord_less_eq_nat A5) B6)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A5 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B6) A5) (@ (@ tptp.ord_less_eq_int A5) B6)))))
% 7.27/7.60 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= A2 B2)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B6) (@ (@ tptp.ord_less_eq_set_int B6) A5)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A5 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B6) (@ (@ tptp.ord_less_eq_rat B6) A5)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A5 tptp.num) (B6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B6) (@ (@ tptp.ord_less_eq_num B6) A5)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A5 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B6) (@ (@ tptp.ord_less_eq_nat B6) A5)))))
% 7.27/7.60 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A5 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B6) (@ (@ tptp.ord_less_eq_int B6) A5)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.num tptp.num)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.nat tptp.num)) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.int tptp.num)) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.num tptp.nat)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F B2)) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_set_int X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (or (= A2 B2) (not (@ (@ tptp.ord_less_eq_rat A2) B2)) (not (@ (@ tptp.ord_less_eq_rat B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (or (= A2 B2) (not (@ (@ tptp.ord_less_eq_num A2) B2)) (not (@ (@ tptp.ord_less_eq_num B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (or (= A2 B2) (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (not (@ (@ tptp.ord_less_eq_nat B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (or (= A2 B2) (not (@ (@ tptp.ord_less_eq_int A2) B2)) (not (@ (@ tptp.ord_less_eq_int B2) A2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y3) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C2 tptp.num)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.num tptp.num)) (B2 tptp.num) (C2 tptp.num)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.num tptp.nat)) (B2 tptp.num) (C2 tptp.num)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (F (-> tptp.num tptp.int)) (B2 tptp.num) (C2 tptp.num)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C2 tptp.nat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.nat tptp.num)) (B2 tptp.nat) (C2 tptp.nat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X2) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X2) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (= (@ (@ tptp.ord_less_eq_set_int X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= (@ (@ tptp.ord_less_eq_rat X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (= (@ (@ tptp.ord_less_eq_num X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (= Y3 X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (= Y3 X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (= Y3 X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (= Y3 X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (= Y3 X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (@ (@ tptp.ord_less_real Y3) X2) P))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (=> (@ (@ tptp.ord_less_rat Y3) X2) P))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X2) Y3) (=> (@ (@ tptp.ord_less_num Y3) X2) P))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X2) P))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y3) (=> (@ (@ tptp.ord_less_int Y3) X2) P))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.num tptp.real)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.real tptp.rat)) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (not (@ (@ tptp.ord_less_rat X2) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num)) (not (@ (@ tptp.ord_less_num X2) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (= (@ F B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C2 tptp.real)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.real tptp.rat)) (B2 tptp.real) (C2 tptp.real)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.real tptp.num)) (B2 tptp.real) (C2 tptp.real)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C2 tptp.real)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C2 tptp.real)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_real Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_rat Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_num Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (not (@ (@ tptp.ord_less_real B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (not (@ (@ tptp.ord_less_rat B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (@ (@ tptp.ord_less_num B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (@ (@ tptp.ord_less_int B2) A2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_rat X2) Y3) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_num X2) Y3) (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_nat X2) Y3) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_int X2) Y3) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (= A2 B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_real B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (or (@ (@ tptp.ord_less_real Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (or (@ (@ tptp.ord_less_rat Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (or (@ (@ tptp.ord_less_num Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (or (@ (@ tptp.ord_less_int Y3) X2) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_real B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_rat B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_num B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_int B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A2 tptp.real) (B2 tptp.real)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.real)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A2 tptp.rat) (B2 tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.rat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A2 tptp.num) (B2 tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.num)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B2 tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.int)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A2) B2))))))
% 7.27/7.60 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P3 N4) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N4) (not (@ P3 M6)))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (not (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (not (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (not (@ (@ tptp.ord_less_num A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (not (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y3) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y3) X2)) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y3) X2)) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y3) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X4) (@ P Y5))) (@ P X4))) (@ P A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (= B2 C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_real B2) C2) (@ (@ tptp.ord_less_real A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_rat B2) C2) (@ (@ tptp.ord_less_rat A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_num B2) C2) (@ (@ tptp.ord_less_num A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_nat B2) C2) (@ (@ tptp.ord_less_nat A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_int B2) C2) (@ (@ tptp.ord_less_int A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (not (@ (@ tptp.ord_less_real B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (not (@ (@ tptp.ord_less_rat B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (@ (@ tptp.ord_less_num B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (@ (@ tptp.ord_less_int B2) A2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z2) (@ (@ tptp.ord_less_real Z2) Y3))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X2) Z2) (@ (@ tptp.ord_less_rat Z2) Y3))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X2) X_1))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_1))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))))
% 7.27/7.60 (assert (forall ((X2 tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X2) X_1))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int)) (exists ((Y4 tptp.int)) (@ (@ tptp.ord_less_int Y4) X2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 7.27/7.60 (assert (forall ((Vd3 Bool) (Ve3 Bool) (V tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb tptp.array_VEBT_VEBTi) (Vc tptp.vEBT_VEBTi)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_Leaf Vd3) Ve3)) (@ (@ (@ (@ tptp.vEBT_Nodei V) Va) Vb) Vc)) tptp.bot_bot_assn)))
% 7.27/7.60 (assert (forall ((V tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (Vd3 Bool) (Ve3 Bool)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node V) Va) Vb) Vc)) (@ (@ tptp.vEBT_Leafi Vd3) Ve3)) tptp.bot_bot_assn)))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A2) X2) (= A2 X2) (@ (@ tptp.ord_less_eq_int X2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A2) B2))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A2)) (@ tptp.archim7802044766580827645g_real B2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A2) B2))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A2)) (@ tptp.archim2889992004027027881ng_rat B2))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (or (@ (@ tptp.ord_less_set_int X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (or (@ (@ tptp.ord_less_rat X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (or (@ (@ tptp.ord_less_num X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y3) (@ (@ tptp.ord_less_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.num tptp.real)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (F (-> tptp.num tptp.num)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (F (-> tptp.num tptp.nat)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (F (-> tptp.num tptp.int)) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C2))))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.real)) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.num tptp.real)) (B2 tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.real tptp.rat)) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C2) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C2) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C2) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C2) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C2)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_set_int Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ _let_1 Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (=> (@ (@ tptp.ord_less_real Y3) Z) (@ (@ tptp.ord_less_real X2) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (=> (@ (@ tptp.ord_less_set_int Y3) Z) (@ (@ tptp.ord_less_set_int X2) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (=> (@ (@ tptp.ord_less_rat Y3) Z) (@ (@ tptp.ord_less_rat X2) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (=> (@ (@ tptp.ord_less_num Y3) Z) (@ (@ tptp.ord_less_num X2) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z) (@ (@ tptp.ord_less_nat X2) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ (@ tptp.ord_less_int X2) Z)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (@ (@ tptp.ord_less_set_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (@ (@ tptp.ord_less_num A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_int A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_num A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X2) Y3) (@ (@ tptp.ord_less_eq_set_int X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_eq_real Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X2) Y3)) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X2) Y3)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X2) Y3)) (@ (@ tptp.ord_less_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y3)) (@ (@ tptp.ord_less_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y3)) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y) (not (= X3 Y))))))
% 7.27/7.60 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y) (not (= X3 Y))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y) (not (= X3 Y))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y) (not (= X3 Y))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y) (not (= X3 Y))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y) (not (= X3 Y))))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y) (= X3 Y)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_set_int (lambda ((X3 tptp.set_int) (Y tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X3) Y) (= X3 Y)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y) (= X3 Y)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_num (lambda ((X3 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y) (= X3 Y)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y) (= X3 Y)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y) (= X3 Y)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (@ (@ tptp.ord_less_eq_real B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A2) (@ (@ tptp.ord_less_eq_set_int B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (@ (@ tptp.ord_less_eq_rat B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (@ (@ tptp.ord_less_eq_num B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (@ (@ tptp.ord_less_eq_nat B2) A2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.ord_less_eq_real A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B2) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_eq_rat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (@ (@ tptp.ord_less_eq_num A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((B6 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B6) A5) (not (@ (@ tptp.ord_less_eq_real A5) B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_set_int (lambda ((B6 tptp.set_int) (A5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B6) A5) (not (@ (@ tptp.ord_less_eq_set_int A5) B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B6) A5) (not (@ (@ tptp.ord_less_eq_rat A5) B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((B6 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B6) A5) (not (@ (@ tptp.ord_less_eq_num A5) B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B6) A5) (not (@ (@ tptp.ord_less_eq_nat A5) B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((B6 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B6) A5) (not (@ (@ tptp.ord_less_eq_int A5) B6))))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (=> (@ (@ tptp.ord_less_eq_real C2) B2) (@ (@ tptp.ord_less_real C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A2) (=> (@ (@ tptp.ord_less_eq_set_int C2) B2) (@ (@ tptp.ord_less_set_int C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C2) B2) (@ (@ tptp.ord_less_rat C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (=> (@ (@ tptp.ord_less_eq_num C2) B2) (@ (@ tptp.ord_less_num C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C2) B2) (@ (@ tptp.ord_less_nat C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C2) B2) (@ (@ tptp.ord_less_int C2) A2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.real) (A2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C2))) (=> (@ (@ tptp.ord_less_eq_real B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C2))) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((B6 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B6) A5) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_set_int (lambda ((B6 tptp.set_int) (A5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B6) A5) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B6) A5) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((B6 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B6) A5) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B6) A5) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((B6 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B6) A5) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_real (lambda ((B6 tptp.real) (A5 tptp.real)) (or (@ (@ tptp.ord_less_real B6) A5) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_set_int (lambda ((B6 tptp.set_int) (A5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B6) A5) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (or (@ (@ tptp.ord_less_rat B6) A5) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_num (lambda ((B6 tptp.num) (A5 tptp.num)) (or (@ (@ tptp.ord_less_num B6) A5) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (or (@ (@ tptp.ord_less_nat B6) A5) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((B6 tptp.int) (A5 tptp.int)) (or (@ (@ tptp.ord_less_int B6) A5) (= A5 B6)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (forall ((W3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W3) (=> (@ (@ tptp.ord_less_real W3) Y3) (@ (@ tptp.ord_less_eq_real W3) Z)))) (@ (@ tptp.ord_less_eq_real Y3) Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (=> (forall ((W3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) W3) (=> (@ (@ tptp.ord_less_rat W3) Y3) (@ (@ tptp.ord_less_eq_rat W3) Z)))) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (=> (forall ((W3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W3) (=> (@ (@ tptp.ord_less_real W3) X2) (@ (@ tptp.ord_less_eq_real Y3) W3)))) (@ (@ tptp.ord_less_eq_real Y3) Z)))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X2) (=> (forall ((W3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W3) (=> (@ (@ tptp.ord_less_rat W3) X2) (@ (@ tptp.ord_less_eq_rat Y3) W3)))) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B6) (not (@ (@ tptp.ord_less_eq_real B6) A5))))))
% 7.27/7.60 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A5))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B6) (not (@ (@ tptp.ord_less_eq_rat B6) A5))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B6) (not (@ (@ tptp.ord_less_eq_num B6) A5))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B6) (not (@ (@ tptp.ord_less_eq_nat B6) A5))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B6) (not (@ (@ tptp.ord_less_eq_int B6) A5))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_real B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C2) (@ _let_1 C2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_real B2) C2) (@ (@ tptp.ord_less_real A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_set_int B2) C2) (@ (@ tptp.ord_less_set_int A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat B2) C2) (@ (@ tptp.ord_less_rat A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_num B2) C2) (@ (@ tptp.ord_less_num A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat B2) C2) (@ (@ tptp.ord_less_nat A2) C2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int B2) C2) (@ (@ tptp.ord_less_int A2) C2)))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B6) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B6) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B6) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B6) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B6) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B6) (not (= A5 B6))))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B6 tptp.real)) (or (@ (@ tptp.ord_less_real A5) B6) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B6) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (or (@ (@ tptp.ord_less_rat A5) B6) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B6 tptp.num)) (or (@ (@ tptp.ord_less_num A5) B6) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (or (@ (@ tptp.ord_less_nat A5) B6) (= A5 B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B6 tptp.int)) (or (@ (@ tptp.ord_less_int A5) B6) (= A5 B6)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y3) X2)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y3) X2)) (@ (@ tptp.ord_less_rat X2) Y3))))
% 7.27/7.60 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y3) X2)) (@ (@ tptp.ord_less_num X2) Y3))))
% 7.27/7.60 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y3) X2)) (@ (@ tptp.ord_less_nat X2) Y3))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y3) X2)) (@ (@ tptp.ord_less_int X2) Y3))))
% 7.27/7.60 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y) (not (@ (@ tptp.ord_less_eq_real Y) X3))))))
% 7.27/7.60 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y) (not (@ (@ tptp.ord_less_eq_set_int Y) X3))))))
% 7.27/7.60 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y) (not (@ (@ tptp.ord_less_eq_rat Y) X3))))))
% 7.27/7.60 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y) (not (@ (@ tptp.ord_less_eq_num Y) X3))))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y) (not (@ (@ tptp.ord_less_eq_nat Y) X3))))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y) (not (@ (@ tptp.ord_less_eq_int Y) X3))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y3) Z))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (Z tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat X4) Z))) (@ (@ tptp.ord_less_eq_rat Y3) Z))))
% 7.27/7.60 (assert (forall ((Z tptp.real) (Y3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (@ (@ tptp.ord_less_eq_real Y3) X4))) (@ (@ tptp.ord_less_eq_real Y3) Z))))
% 7.27/7.60 (assert (forall ((Z tptp.rat) (Y3 tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (@ (@ tptp.ord_less_eq_rat Y3) X4))) (@ (@ tptp.ord_less_eq_rat Y3) Z))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (= (not (@ (@ tptp.ord_less_set_int X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (= (@ (@ tptp.ord_less_eq_real X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X2) Y3)) (= (@ (@ tptp.ord_less_eq_set_int X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (= (@ (@ tptp.ord_less_eq_rat X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (= (@ (@ tptp.ord_less_eq_num X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (= (@ (@ tptp.ord_less_eq_nat X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (= (@ (@ tptp.ord_less_eq_int X2) Y3) (= X2 Y3)))))
% 7.27/7.60 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (not (@ (@ tptp.ord_less_real A2) B2)) (or (not (@ (@ tptp.ord_less_eq_real A2) B2)) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A2) B2)) (or (not (@ (@ tptp.ord_less_eq_set_int A2) B2)) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A2) B2)) (or (not (@ (@ tptp.ord_less_eq_rat A2) B2)) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (not (@ (@ tptp.ord_less_num A2) B2)) (or (not (@ (@ tptp.ord_less_eq_num A2) B2)) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A2) B2)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_int A2) B2)) (or (not (@ (@ tptp.ord_less_eq_int A2) B2)) (= A2 B2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_eq_real Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y3) X2) (not (@ (@ tptp.ord_less_real X2) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (not (@ (@ tptp.ord_less_set_int X2) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (not (@ (@ tptp.ord_less_rat X2) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (not (@ (@ tptp.ord_less_num X2) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (not (@ (@ tptp.ord_less_nat X2) Y3)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (not (@ (@ tptp.ord_less_int X2) Y3)))))
% 7.27/7.60 (assert (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))))
% 7.27/7.60 (assert (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))))
% 7.27/7.60 (assert (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))))
% 7.27/7.60 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 7.27/7.60 (assert (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))))
% 7.27/7.60 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A2) tptp.zero_zero_complex) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) tptp.zero_zero_real) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 7.27/7.60 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn tptp.bot_bot_assn) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)))
% 7.27/7.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn A2) tptp.bot_bot_assn) (= A2 tptp.bot_bot_assn))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A2) tptp.bot_bo4199563552545308370d_enat) (= A2 tptp.bot_bo4199563552545308370d_enat))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) tptp.bot_bot_assn) (= A2 tptp.bot_bot_assn))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A2) tptp.bot_bo4199563552545308370d_enat) (= A2 tptp.bot_bo4199563552545308370d_enat))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_nat)) (= (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (= (not (= A2 tptp.bot_bot_assn)) (@ (@ tptp.ord_less_assn tptp.bot_bot_assn) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat)) (= (not (= A2 tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (= (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 7.27/7.60 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) tptp.bot_bot_assn))))
% 7.27/7.60 (assert (forall ((A2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A2) tptp.bot_bo4199563552545308370d_enat))))
% 7.27/7.60 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.bot_bot_nat))))
% 7.27/7.60 (assert (forall ((X22 tptp.num) (X33 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X33)))))
% 7.27/7.60 (assert (forall ((X33 tptp.num)) (not (= tptp.one (@ tptp.bit1 X33)))))
% 7.27/7.60 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A5 tptp.extended_enat) (B6 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_set_int (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B6 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B6)) B6) A5))))
% 7.27/7.60 (assert (forall ((Y3 tptp.extended_enat) (X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y3) X2) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (= (@ (@ tptp.ord_max_set_int X2) Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= (@ (@ tptp.ord_max_rat X2) Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (= (@ (@ tptp.ord_max_num X2) Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= (@ (@ tptp.ord_max_nat X2) Y3) X2))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= (@ (@ tptp.ord_max_int X2) Y3) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X2) Y3) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y3) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (= (@ (@ tptp.ord_max_set_int X2) Y3) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (= (@ (@ tptp.ord_max_rat X2) Y3) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (= (@ (@ tptp.ord_max_num X2) Y3) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (= (@ (@ tptp.ord_max_nat X2) Y3) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (= (@ (@ tptp.ord_max_int X2) Y3) Y3))))
% 7.27/7.60 (assert (forall ((C2 tptp.heap_T8145700208782473153_VEBTi) (T tptp.nat) (T3 tptp.nat)) (let ((_let_1 (@ tptp.time_T5737551269749752165_VEBTi C2))) (=> (@ _let_1 T) (=> (@ (@ tptp.ord_less_eq_nat T) T3) (@ _let_1 T3))))))
% 7.27/7.60 (assert (forall ((C2 tptp.heap_Time_Heap_o) (T tptp.nat) (T3 tptp.nat)) (let ((_let_1 (@ tptp.time_TBOUND_o C2))) (=> (@ _let_1 T) (=> (@ (@ tptp.ord_less_eq_nat T) T3) (@ _let_1 T3))))))
% 7.27/7.60 (assert (forall ((C2 tptp.heap_T2636463487746394924on_nat) (T tptp.nat) (T3 tptp.nat)) (let ((_let_1 (@ tptp.time_T8353473612707095248on_nat C2))) (=> (@ _let_1 T) (=> (@ (@ tptp.ord_less_eq_nat T) T3) (@ _let_1 T3))))))
% 7.27/7.60 (assert (forall ((C2 tptp.heap_Time_Heap_nat) (T tptp.nat) (T3 tptp.nat)) (let ((_let_1 (@ tptp.time_TBOUND_nat C2))) (=> (@ _let_1 T) (=> (@ (@ tptp.ord_less_eq_nat T) T3) (@ _let_1 T3))))))
% 7.27/7.60 (assert (forall ((P Bool) (M tptp.heap_T8145700208782473153_VEBTi) (Bm tptp.nat) (N tptp.heap_T8145700208782473153_VEBTi) (Bn tptp.nat)) (=> (=> P (@ (@ tptp.time_T5737551269749752165_VEBTi M) Bm)) (=> (=> (not P) (@ (@ tptp.time_T5737551269749752165_VEBTi N) Bn)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ (@ tptp.if_Hea8453224502484754311_VEBTi P) M) N)) (@ (@ tptp.ord_max_nat Bm) Bn))))))
% 7.27/7.60 (assert (forall ((P Bool) (M tptp.heap_Time_Heap_o) (Bm tptp.nat) (N tptp.heap_Time_Heap_o) (Bn tptp.nat)) (=> (=> P (@ (@ tptp.time_TBOUND_o M) Bm)) (=> (=> (not P) (@ (@ tptp.time_TBOUND_o N) Bn)) (@ (@ tptp.time_TBOUND_o (@ (@ (@ tptp.if_Heap_Time_Heap_o P) M) N)) (@ (@ tptp.ord_max_nat Bm) Bn))))))
% 7.27/7.60 (assert (forall ((P Bool) (M tptp.heap_T2636463487746394924on_nat) (Bm tptp.nat) (N tptp.heap_T2636463487746394924on_nat) (Bn tptp.nat)) (=> (=> P (@ (@ tptp.time_T8353473612707095248on_nat M) Bm)) (=> (=> (not P) (@ (@ tptp.time_T8353473612707095248on_nat N) Bn)) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ (@ tptp.if_Hea5867803462524415986on_nat P) M) N)) (@ (@ tptp.ord_max_nat Bm) Bn))))))
% 7.27/7.60 (assert (forall ((P Bool) (M tptp.heap_Time_Heap_nat) (Bm tptp.nat) (N tptp.heap_Time_Heap_nat) (Bn tptp.nat)) (=> (=> P (@ (@ tptp.time_TBOUND_nat M) Bm)) (=> (=> (not P) (@ (@ tptp.time_TBOUND_nat N) Bn)) (@ (@ tptp.time_TBOUND_nat (@ (@ (@ tptp.if_Hea2662716070787841314ap_nat P) M) N)) (@ (@ tptp.ord_max_nat Bm) Bn))))))
% 7.27/7.60 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A5 tptp.extended_enat) (B6 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_set_int (lambda ((A5 tptp.set_int) (B6 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B6 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B6 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B6)) B6) A5))))
% 7.27/7.60 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B6)) B6) A5))))
% 7.27/7.60 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6)))))
% 7.27/7.60 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A2) B2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 7.27/7.60 (assert (forall ((M tptp.heap_T8145700208782473153_VEBTi) (T tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.time_T5737551269749752165_VEBTi M) T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi M) H2)) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_Time_Heap_o) (T tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.time_TBOUND_o M) T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_o M) H2)) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_T2636463487746394924on_nat) (T tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.time_T8353473612707095248on_nat M) T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_option_nat M) H2)) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_Time_Heap_nat) (T tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.time_TBOUND_nat M) T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_nat M) H2)) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_T8145700208782473153_VEBTi) (T tptp.nat)) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi M) H3)) T)) (@ (@ tptp.time_T5737551269749752165_VEBTi M) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_Time_Heap_o) (T tptp.nat)) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_o M) H3)) T)) (@ (@ tptp.time_TBOUND_o M) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_T2636463487746394924on_nat) (T tptp.nat)) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_option_nat M) H3)) T)) (@ (@ tptp.time_T8353473612707095248on_nat M) T))))
% 7.27/7.60 (assert (forall ((M tptp.heap_Time_Heap_nat) (T tptp.nat)) (=> (forall ((H3 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_nat M) H3)) T)) (@ (@ tptp.time_TBOUND_nat M) T))))
% 7.27/7.60 (assert (= tptp.time_T5737551269749752165_VEBTi (lambda ((M6 tptp.heap_T8145700208782473153_VEBTi) (T2 tptp.nat)) (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi M6) H)) T2)))))
% 7.27/7.60 (assert (= tptp.time_TBOUND_o (lambda ((M6 tptp.heap_Time_Heap_o) (T2 tptp.nat)) (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_o M6) H)) T2)))))
% 7.27/7.60 (assert (= tptp.time_T8353473612707095248on_nat (lambda ((M6 tptp.heap_T2636463487746394924on_nat) (T2 tptp.nat)) (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_option_nat M6) H)) T2)))))
% 7.27/7.60 (assert (= tptp.time_TBOUND_nat (lambda ((M6 tptp.heap_Time_Heap_nat) (T2 tptp.nat)) (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_nat M6) H)) T2)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.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))))))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ (@ tptp.times_times_assn (@ tptp.pure_assn B2)) P)) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_o (@ (@ tptp.times_times_assn (@ tptp.pure_assn B2)) P)) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_o P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_option_nat (@ (@ tptp.times_times_assn (@ tptp.pure_assn B2)) P)) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_option_nat P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((B2 Bool) (P tptp.assn) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_nat (@ (@ tptp.times_times_assn (@ tptp.pure_assn B2)) P)) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_nat P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_o (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_o P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_option_nat (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_option_nat P) F) Q) T)))))
% 7.27/7.60 (assert (forall ((P tptp.assn) (B2 Bool) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (T tptp.nat)) (= (@ (@ (@ (@ tptp.time_htt_nat (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) F) Q) T) (=> B2 (@ (@ (@ (@ tptp.time_htt_nat P) F) Q) T)))))
% 7.27/7.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6)))))
% 7.27/7.60 (assert (forall ((B2 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ 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))))))))))
% 7.27/7.60 (assert (forall ((P5 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (T3 tptp.nat) (P tptp.assn) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi P5) C2) Q2) T3) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 X4)) (@ Q X4))) (=> (@ (@ tptp.ord_less_eq_nat T3) T) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi P) C2) Q) T)))))))
% 7.27/7.60 (assert (forall ((P5 tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q2 (-> Bool tptp.assn)) (T3 tptp.nat) (P tptp.assn) (Q (-> Bool tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.time_htt_o P5) C2) Q2) T3) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 Bool)) (@ (@ tptp.entails (@ Q2 X4)) (@ Q X4))) (=> (@ (@ tptp.ord_less_eq_nat T3) T) (@ (@ (@ (@ tptp.time_htt_o P) C2) Q) T)))))))
% 7.27/7.60 (assert (forall ((P5 tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q2 (-> tptp.option_nat tptp.assn)) (T3 tptp.nat) (P tptp.assn) (Q (-> tptp.option_nat tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.time_htt_option_nat P5) C2) Q2) T3) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 tptp.option_nat)) (@ (@ tptp.entails (@ Q2 X4)) (@ Q X4))) (=> (@ (@ tptp.ord_less_eq_nat T3) T) (@ (@ (@ (@ tptp.time_htt_option_nat P) C2) Q) T)))))))
% 7.27/7.60 (assert (forall ((P5 tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q2 (-> tptp.nat tptp.assn)) (T3 tptp.nat) (P tptp.assn) (Q (-> tptp.nat tptp.assn)) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.time_htt_nat P5) C2) Q2) T3) (=> (@ (@ tptp.entails P) P5) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.entails (@ Q2 X4)) (@ Q X4))) (=> (@ (@ tptp.ord_less_eq_nat T3) T) (@ (@ (@ (@ tptp.time_htt_nat P) C2) Q) T)))))))
% 7.27/7.60 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A2)) tptp.one_one_int))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_1)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ (@ (@ tptp.time_htt_o (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ tptp.vEBT_vebt_memberi Ti) X2)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_member T) X2)))))) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one)))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ tptp.vEBT_vebt_inserti Ti) X2)) (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_vebt_insert T) X2))) (@ (@ tptp.plus_plus_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ (@ (@ tptp.time_htt_option_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ tptp.vEBT_vebt_predi Ti) X2)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_pred T) X2)))))) (@ (@ tptp.plus_plus_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))))))
% 7.27/7.60 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Ti tptp.vEBT_VEBTi) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ (@ (@ tptp.time_htt_option_nat (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ (@ tptp.vEBT_vebt_succi Ti) X2)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw T) Ti)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_vebt_succ T) X2)))))) (@ (@ tptp.plus_plus_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.archim7802044766580827645g_real (@ _let_1 X2)) (@ tptp.archim7802044766580827645g_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_2) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _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))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 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 Mi2) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 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 Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (= Xa Mi2))) (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))))) Xa))) (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 (= Xa Ma2)))) (let ((_let_13 (= Y3 tptp.one_one_nat))) (let ((_let_14 (or (@ (@ tptp.ord_less_nat Xa) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa)))) (=> (= X2 _let_2) (=> (and (=> _let_14 _let_13) (=> (not _let_14) (and (=> _let_12 _let_13) (=> (not _let_12) (= Y3 (@ (@ (@ 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) Xa)))))))))))))))))))))))))))))))
% 7.27/7.60 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 7.27/7.60 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 7.27/7.60 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 7.27/7.60 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 7.27/7.60 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 7.27/7.60 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 7.27/7.60 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 7.27/7.60 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 7.27/7.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X2) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (= X2 (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X2) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (= X2 (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X2) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (= X2 (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X2) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W)) (= X2 (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger X2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B2)) W)) (= X2 (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W) (@ tptp.ring_1_of_int_rat X2)) (= (@ (@ tptp.power_power_int B2) W) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W) (@ tptp.ring_1_of_int_real X2)) (= (@ (@ tptp.power_power_int B2) W) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W) (@ tptp.ring_1_of_int_int X2)) (= (@ (@ tptp.power_power_int B2) W) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W) (@ tptp.ring_17405671764205052669omplex X2)) (= (@ (@ tptp.power_power_int B2) W) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B2)) W) (@ tptp.ring_18347121197199848620nteger X2)) (= (@ (@ tptp.power_power_int B2) W) X2))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 7.27/7.60 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y3) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y3) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y3) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= (@ tptp.ring_1_of_int_int Y3) _let_1) (= Y3 _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N) (@ tptp.ring_18347121197199848620nteger Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.ring_17405671764205052669omplex Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.ring_1_of_int_real Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.ring_1_of_int_rat Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y3))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y3)) (= _let_1 Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B2)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B2)) W)) (@ tptp.ring_18347121197199848620nteger X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B2)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B2) W)))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B2)) W)) (@ tptp.ring_18347121197199848620nteger X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (assert (forall ((B2 tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X2))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 7.27/7.60 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_rat Z)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) (@ tptp.nat2 Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y3))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))) A2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real A2)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A2)) (@ _let_1 A2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A2)) _let_1) (@ (@ tptp.ord_less_eq_int A2) _let_1)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A2)) _let_1) (@ (@ tptp.ord_less_int A2) _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A2)) (@ _let_1 A2)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.27/7.60 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X2))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y3) (@ (@ tptp.times_times_real Y3) _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y3) (@ (@ tptp.times_times_rat Y3) _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y3) (@ (@ tptp.times_times_int Y3) _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.ord_max_int X2) Y3)) (@ (@ tptp.ord_max_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.ring_1_of_int_real Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.ord_max_int X2) Y3)) (@ (@ tptp.ord_max_rat (@ tptp.ring_1_of_int_rat X2)) (@ tptp.ring_1_of_int_rat Y3)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.ord_max_int X2) Y3)) (@ (@ tptp.ord_max_int (@ tptp.ring_1_of_int_int X2)) (@ tptp.ring_1_of_int_int Y3)))))
% 7.27/7.60 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y3)))))
% 7.27/7.60 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 7.27/7.60 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P3 (@ tptp.nat2 X3)))))))
% 7.27/7.60 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P3 (@ tptp.nat2 X3)))))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z6)) (= Z Z6)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) N) (@ (@ tptp.ord_less_eq_int X2) (@ tptp.semiri1314217659103216013at_int N)))))
% 7.27/7.60 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R2))))))
% 7.27/7.60 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R2) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R2))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B2))) (@ (@ tptp.plus_plus_nat A2) B2))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) A2))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) A2))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))))))
% 7.27/7.60 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6))))))
% 7.27/7.60 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6))))))
% 7.27/7.60 (assert (= tptp.minus_minus_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6))))))
% 7.27/7.60 (assert (= tptp.divide_divide_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X4)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X4)))))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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))))
% 7.27/7.60 (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)))
% 7.27/7.60 (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)))
% 7.27/7.60 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 7.27/7.60 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 7.27/7.60 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X2)) (@ _let_1 X2)))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (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)))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (= tptp.suc (lambda ((A5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) tptp.one_one_int)))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X2) Y3)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y3))))))))
% 7.27/7.60 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y3)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y3))))))
% 7.27/7.60 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y3)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y3))))))
% 7.27/7.60 (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)))))
% 7.27/7.60 (assert (= tptp.ord_less_eq_int (lambda ((N4 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 7.27/7.60 (assert (= tptp.ord_less_int (lambda ((N4 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N4)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 7.27/7.60 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I4)))))))
% 7.27/7.60 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I4)))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (A2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A2))) (= (= (@ tptp.archim7802044766580827645g_real X2) A2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1))))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (A2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A2))) (= (= (@ tptp.archim2889992004027027881ng_rat X2) A2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1))))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.archim7802044766580827645g_real X2) Z))))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X2) Z))))))
% 7.27/7.60 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1)))))
% 7.27/7.60 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 7.27/7.60 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 7.27/7.60 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (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))))))
% 7.27/7.60 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))))))
% 7.27/7.60 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2)))) tptp.one_one_real)))
% 7.27/7.60 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z6))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) 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)))))))))))
% 7.27/7.60 (assert (forall ((Q3 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P6) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P6) Q3)))) Q3)))))
% 7.27/7.60 (assert (forall ((Q3 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat P6) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P6) Q3)))) Q3)))))
% 7.27/7.60 (assert (forall ((Q3 tptp.real) (P6 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 P6) Q3)))) tptp.one_one_real)) Q3)) P6))))
% 7.27/7.60 (assert (forall ((Q3 tptp.rat) (P6 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 P6) Q3)))) tptp.one_one_rat)) Q3)) P6))))
% 7.27/7.60 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 7.27/7.60 (assert (forall ((N tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat A2)) (@ tptp.semiri681578069525770553at_rat B2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real A2)) (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat A2)) (@ tptp.semiri1316708129612266289at_nat B2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat A2) B2)))))
% 7.27/7.60 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri8010041392384452111omplex K) tptp.zero_zero_complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 7.27/7.60 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri681578069525770553at_rat K) tptp.zero_zero_rat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 7.27/7.60 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri5074537144036343181t_real K) tptp.zero_zero_real)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 7.27/7.60 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri1314217659103216013at_int K) tptp.zero_zero_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 7.27/7.60 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri1316708129612266289at_nat K) tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 7.27/7.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 (@ (@ tptp.vEBT_Leaf false) B3)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A3))) (let ((_let_3 (@ _let_2 B3))) (=> (= X2 _let_3) (=> (= Xa _let_1) (=> (= Y3 (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa _let_1) (=> (= Y3 _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))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 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 Mi2) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 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 Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.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 (= Xa Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa))) (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 (= Xa 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) Mi2))) (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 Xa) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa)))) (=> (= X2 _let_2) (=> (and (=> _let_24 (= Y3 _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y3 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (not _let_23) (= Y3 (@ (@ (@ 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) Xa)))))))))))))))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c2 X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_low Xa) _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 Xa) Mi2))) (=> (= X2 _let_2) (=> (and (=> _let_8 (= Y3 tptp.one_one_nat)) (=> (not _let_8) (= Y3 (@ (@ (@ 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) Xa))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa tptp.one_one_nat))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= X2 _let_2) (=> (and (=> _let_4 (= Y3 (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y3 (@ _let_1 true))) (=> (not _let_3) (= Y3 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa) Xa))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa Mi2) (= Xa Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d2 X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 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 ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X2 _let_2) (=> (= Xa _let_1) (=> (= Y3 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 ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_low Xa) _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) Xa))) (=> (= X2 _let_2) (=> (and (=> _let_8 (= Y3 tptp.one_one_nat)) (=> (not _let_8) (= Y3 (@ (@ (@ 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) Xa)))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) Mi2) Xa))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa Mi2) (= Xa 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) Xa)))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= Xa 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) Xa))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high Xa) _let_5))) (let ((_let_7 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ tptp.plus_plus_nat _let_4) (@ (@ (@ tptp.if_nat (= Xa Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (= Xa Ma2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa)) 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 Xa) _let_5)))) tptp.one_one_nat))))))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ tptp.ord_less_nat Xa))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_5 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa) (@ _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 Xa) _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) Xa))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y3 (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (= X2 _let_2) (=> (= Y3 (=> (not (= Xa Mi2)) (=> (not (= Xa Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa)) (=> (not (= Xa Mi2)) (=> (not (= Xa Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y3 (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y3 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa)) (not (=> (not (= Xa Mi2)) (=> (not (= Xa Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (= Y3 (or (= Xa Mi2) (= Xa Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y3 (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y3 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi2) (= Xa Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A2) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A2) _let_1)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A2) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A2) _let_1)))))))
% 7.27/7.61 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 7.27/7.61 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y3) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)) (@ tptp.some_nat Z)))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X2) Y3) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)) (@ tptp.some_nat Z)))))
% 7.27/7.61 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 7.27/7.61 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 7.27/7.61 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 7.27/7.61 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 7.27/7.61 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 7.27/7.61 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 7.27/7.61 (assert (forall ((Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X2))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat X2) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y3 tptp.none_nat))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (exists ((Va3 tptp.nat)) (= Xa (@ tptp.suc (@ tptp.suc Va3)))) (not (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y3 tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _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) Xa))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y3 (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y3 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa) Y3) (=> (forall ((Uu2 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B3)) (=> (= Xa tptp.zero_zero_nat) (not (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y3 tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N3 tptp.nat)) (= Xa (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _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 Xa) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y3 (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y3 (@ (@ (@ 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))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y3 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _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 Xa) Mi2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y3 (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y3 (@ (@ (@ 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) Xa))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X2 _let_2) (=> (= Xa _let_1) (=> (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y3 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (=> (= Xa _let_1) (=> (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y3 tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _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) Xa))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y3 (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y3 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa)))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (let ((_let_3 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.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) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_3)) (@ _let_2 (@ _let_2 U))))))))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.log _let_2))) (let ((_let_4 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_1))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_2) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_4))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_4)) (@ _let_3 (@ _let_3 U)))))))))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (let ((_let_3 (@ tptp.bit1 (@ tptp.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) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_3)) (@ _let_2 (@ _let_2 U))))))))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X2) A)) B) (and (@ (@ tptp.member_nat X2) B) (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ (@ tptp.insert_VEBT_VEBT X2) A)) B) (and (@ (@ tptp.member_VEBT_VEBT X2) B) (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X2) A)) B) (and (@ (@ tptp.member_real X2) B) (@ (@ tptp.ord_less_eq_set_real A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X2) A)) B) (and (@ (@ tptp.member_int X2) B) (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.minus_5127226145743854075T_VEBT A))) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A))) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ _let_1 (@ (@ tptp.insert_real X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A))) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ _let_1 (@ (@ tptp.insert_int X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (=> (not (@ (@ tptp.member_nat X2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) B) (= (@ (@ tptp.minus_5127226145743854075T_VEBT (@ (@ tptp.insert_VEBT_VEBT X2) A)) B) (@ (@ tptp.minus_5127226145743854075T_VEBT A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (B tptp.set_real) (A tptp.set_real)) (=> (@ (@ tptp.member_real X2) B) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X2) A)) B) (@ (@ tptp.minus_minus_set_real A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.member_int X2) B) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X2) A)) B) (@ (@ tptp.minus_minus_set_int A) B)))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) B) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X2) A)) B) (@ (@ tptp.minus_minus_set_nat A) B)))))
% 7.27/7.61 (assert (forall ((A2 tptp.vEBT_VEBT)) (= (@ tptp.collect_VEBT_VEBT (@ (lambda ((Y6 tptp.vEBT_VEBT) (Z3 tptp.vEBT_VEBT)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex)) (= (@ tptp.collect_complex (@ (lambda ((Y6 tptp.complex) (Z3 tptp.complex)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))
% 7.27/7.61 (assert (forall ((A2 tptp.product_prod_int_int)) (= (@ tptp.collec213857154873943460nt_int (@ (lambda ((Y6 tptp.product_prod_int_int) (Z3 tptp.product_prod_int_int)) (= Y6 Z3)) A2)) (@ (@ tptp.insert5033312907999012233nt_int A2) tptp.bot_bo1796632182523588997nt_int))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (= (@ tptp.collect_nat (@ (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (= (@ tptp.collect_int (@ (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))
% 7.27/7.61 (assert (forall ((A2 tptp.vEBT_VEBT)) (= (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (= X3 A2))) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex)) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= X3 A2))) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))
% 7.27/7.61 (assert (forall ((A2 tptp.product_prod_int_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (= X3 A2))) (@ (@ tptp.insert5033312907999012233nt_int A2) tptp.bot_bo1796632182523588997nt_int))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (= X3 A2))) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (= X3 A2))) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))
% 7.27/7.61 (assert (forall ((B2 tptp.vEBT_VEBT) (A2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.insert_VEBT_VEBT B2) tptp.bot_bo8194388402131092736T_VEBT))) (= (= _let_1 (@ (@ tptp.insert_VEBT_VEBT A2) A)) (and (= A2 B2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A) _let_1))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.insert_VEBT_VEBT B2) tptp.bot_bo8194388402131092736T_VEBT))) (= (= (@ (@ tptp.insert_VEBT_VEBT A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A2))) (= (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) (@ _let_1 A)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A)))))
% 7.27/7.61 (assert (= tptp.insert_VEBT_VEBT (lambda ((A5 tptp.vEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (or (= X3 A5) (@ (@ tptp.member_VEBT_VEBT X3) B5)))))))
% 7.27/7.61 (assert (= tptp.insert_real (lambda ((A5 tptp.real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (or (= X3 A5) (@ (@ tptp.member_real X3) B5)))))))
% 7.27/7.61 (assert (= tptp.insert_nat (lambda ((A5 tptp.nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (or (= X3 A5) (@ (@ tptp.member_nat X3) B5)))))))
% 7.27/7.61 (assert (= tptp.insert_int (lambda ((A5 tptp.int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (or (= X3 A5) (@ (@ tptp.member_int X3) B5)))))))
% 7.27/7.61 (assert (= tptp.insert_complex (lambda ((A5 tptp.complex) (B5 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (or (= X3 A5) (@ (@ tptp.member_complex X3) B5)))))))
% 7.27/7.61 (assert (= tptp.insert5033312907999012233nt_int (lambda ((A5 tptp.product_prod_int_int) (B5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (or (= X3 A5) (@ (@ tptp.member5262025264175285858nt_int X3) B5)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (@ (@ tptp.insert_VEBT_VEBT A2) (@ tptp.collect_VEBT_VEBT P)) (@ tptp.collect_VEBT_VEBT (lambda ((U2 tptp.vEBT_VEBT)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A2) (@ tptp.collect_nat P)) (@ tptp.collect_nat (lambda ((U2 tptp.nat)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A2) (@ tptp.collect_int P)) (@ tptp.collect_int (lambda ((U2 tptp.int)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.insert_complex A2) (@ tptp.collect_complex P)) (@ tptp.collect_complex (lambda ((U2 tptp.complex)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.insert5033312907999012233nt_int A2) (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int (lambda ((U2 tptp.product_prod_int_int)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.27/7.61 (assert (forall ((C tptp.set_nat) (D tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.ord_less_eq_set_nat C) D) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C)) (@ _let_1 D))))))
% 7.27/7.61 (assert (forall ((C tptp.set_VEBT_VEBT) (D tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A2))) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT C) D) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ _let_1 C)) (@ _let_1 D))))))
% 7.27/7.61 (assert (forall ((C tptp.set_int) (D tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.ord_less_eq_set_int C) D) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C)) (@ _let_1 D))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (not (@ (@ tptp.member_nat X2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_le4337996190870823476T_VEBT A))) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ _let_1 (@ (@ tptp.insert_real X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ _let_1 (@ (@ tptp.insert_int X2) B)) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((B tptp.set_nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.insert_nat A2) B))))
% 7.27/7.61 (assert (forall ((B tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT B) (@ (@ tptp.insert_VEBT_VEBT A2) B))))
% 7.27/7.61 (assert (forall ((B tptp.set_int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.insert_int A2) B))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat B2) B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (B2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.ord_le4337996190870823476T_VEBT A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT B2) B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int B2) B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) B))) (let ((_let_2 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_3 (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (B tptp.set_real) (A tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A) B))) (let ((_let_2 (@ tptp.insert_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_real X2) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) B))) (let ((_let_2 (@ tptp.insert_int X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_int X2) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (let ((_let_2 (@ tptp.insert_nat X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_nat X2) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (A2 tptp.vEBT_VEBT)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (= A2 X3) (@ P X3)))) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))) (=> (not _let_1) (= (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (= A2 X3) (@ P X3)))) tptp.bot_bo8194388402131092736T_VEBT))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.complex Bool)) (A2 tptp.complex)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (= A2 X3) (@ P X3)))) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))) (=> (not _let_1) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (= A2 X3) (@ P X3)))) tptp.bot_bot_set_complex))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (A2 tptp.product_prod_int_int)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (= A2 X3) (@ P X3)))) (@ (@ tptp.insert5033312907999012233nt_int A2) tptp.bot_bo1796632182523588997nt_int))) (=> (not _let_1) (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (= A2 X3) (@ P X3)))) tptp.bot_bo1796632182523588997nt_int))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= A2 X3) (@ P X3)))) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= A2 X3) (@ P X3)))) tptp.bot_bot_set_nat))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.int Bool)) (A2 tptp.int)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= A2 X3) (@ P X3)))) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= A2 X3) (@ P X3)))) tptp.bot_bot_set_int))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (A2 tptp.vEBT_VEBT)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (= X3 A2) (@ P X3)))) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))) (=> (not _let_1) (= (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (= X3 A2) (@ P X3)))) tptp.bot_bo8194388402131092736T_VEBT))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.complex Bool)) (A2 tptp.complex)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (= X3 A2) (@ P X3)))) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))) (=> (not _let_1) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (= X3 A2) (@ P X3)))) tptp.bot_bot_set_complex))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (A2 tptp.product_prod_int_int)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (= X3 A2) (@ P X3)))) (@ (@ tptp.insert5033312907999012233nt_int A2) tptp.bot_bo1796632182523588997nt_int))) (=> (not _let_1) (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (= X3 A2) (@ P X3)))) tptp.bot_bo1796632182523588997nt_int))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= X3 A2) (@ P X3)))) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= X3 A2) (@ P X3)))) tptp.bot_bot_set_nat))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.int Bool)) (A2 tptp.int)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= X3 A2) (@ P X3)))) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= X3 A2) (@ P X3)))) tptp.bot_bot_set_int))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) _let_1) (or (= A tptp.bot_bo8194388402131092736T_VEBT) (= A _let_1))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A) _let_1) (or (= A tptp.bot_bot_set_nat) (= A _let_1))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A) _let_1) (or (= A tptp.bot_bot_set_int) (= A _let_1))))))
% 7.27/7.61 (assert (forall ((X tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT X) _let_1) (or (= X tptp.bot_bo8194388402131092736T_VEBT) (= X _let_1))))))
% 7.27/7.61 (assert (forall ((X tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X) _let_1) (or (= X tptp.bot_bot_set_nat) (= X _let_1))))))
% 7.27/7.61 (assert (forall ((X tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X) _let_1) (or (= X tptp.bot_bot_set_int) (= X _let_1))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A2))) (let ((_let_2 (@ tptp.minus_5127226145743854075T_VEBT A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 B)) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A2))) (=> (@ (@ tptp.member_VEBT_VEBT A2) A) (= (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) A)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (A tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (=> (@ (@ tptp.member_real A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ _let_1 tptp.bot_bot_set_real))) A)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) A)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) A)))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A2))) (let ((_let_2 (@ tptp.minus_5127226145743854075T_VEBT A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_1 A)) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT)) A)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_real)) A)))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_int)) A)))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (not (@ (@ tptp.member_nat X2) A)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_nat)) A)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (X tptp.set_VEBT_VEBT)) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) X)) (= (@ (@ tptp.minus_5127226145743854075T_VEBT X) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT)) X))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (X tptp.set_real)) (=> (not (@ (@ tptp.member_real X2) X)) (= (@ (@ tptp.minus_minus_set_real X) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)) X))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (X tptp.set_int)) (=> (not (@ (@ tptp.member_int X2) X)) (= (@ (@ tptp.minus_minus_set_int X) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)) X))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (X tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X2) X)) (= (@ (@ tptp.minus_minus_set_nat X) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) X))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.insert_VEBT_VEBT Y3) tptp.bot_bo8194388402131092736T_VEBT))) (let ((_let_2 (@ tptp.insert_VEBT_VEBT X2))) (=> (not (= X2 Y3)) (= (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) _let_1))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int Y3) tptp.bot_bot_set_int))) (let ((_let_2 (@ tptp.insert_int X2))) (=> (not (= X2 Y3)) (= (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) _let_1))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat Y3) tptp.bot_bot_set_nat))) (let ((_let_2 (@ tptp.insert_nat X2))) (=> (not (= X2 Y3)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) _let_1))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (C tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.minus_5127226145743854075T_VEBT B))) (let ((_let_2 (@ tptp.ord_le4337996190870823476T_VEBT A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) C))) (and (@ _let_2 (@ _let_1 C)) (not (@ (@ tptp.member_VEBT_VEBT X2) A))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_real) (B tptp.set_real) (X2 tptp.real) (C tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X2) C))) (and (@ _let_2 (@ _let_1 C)) (not (@ (@ tptp.member_real X2) A))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X2 tptp.nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X2) C))) (and (@ _let_2 (@ _let_1 C)) (not (@ (@ tptp.member_nat X2) A))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (B tptp.set_int) (X2 tptp.int) (C tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X2) C))) (and (@ _let_2 (@ _let_1 C)) (not (@ (@ tptp.member_int X2) A))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) B) (@ (@ tptp.ord_le4337996190870823476T_VEBT A) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) B) (@ (@ tptp.ord_less_eq_set_nat A) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (X2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) B) (@ (@ tptp.ord_less_eq_set_int A) (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_le4337996190870823476T_VEBT A))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT X2) A))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X2))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_real) (X2 tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (let ((_let_2 (@ (@ tptp.member_real X2) A))) (let ((_let_3 (@ tptp.insert_real X2))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A) (@ _let_3 tptp.bot_bot_set_real))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (let ((_let_2 (@ (@ tptp.member_nat X2) A))) (let ((_let_3 (@ tptp.insert_nat X2))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (X2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (let ((_let_2 (@ (@ tptp.member_int X2) A))) (let ((_let_3 (@ tptp.insert_int X2))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (S tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) S) (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))) S))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (S tptp.set_real)) (=> (@ (@ tptp.member_real X2) S) (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) S))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X2) S) (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) S))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) S) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) S))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (I tptp.nat) (X2 tptp.vEBT_VEBTi)) (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2))) (@ (@ tptp.insert_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2))) (@ (@ tptp.insert_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X2))) (@ (@ tptp.insert_nat X2) (@ tptp.set_nat2 Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X2 Bool)) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X2))) (@ (@ tptp.insert_o X2) (@ tptp.set_o2 Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (I tptp.nat) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X2))) (@ (@ tptp.insert_real X2) (@ tptp.set_real2 Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X2))) (@ (@ tptp.insert_int X2) (@ tptp.set_int2 Xs)))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_le3480810397992357184T_VEBT A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B)) (=> (not _let_2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B)))))))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_real) (X2 tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_real X2))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_real A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A) (@ _let_3 tptp.bot_bot_set_real))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A) B)))))))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_nat X2))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_nat A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A) B)))))))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (X2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_int X2))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_int A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A) B)))))))))))))
% 7.27/7.61 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S2)) X2) tptp.one_one_nat)))
% 7.27/7.61 (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)))
% 7.27/7.61 (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)))
% 7.27/7.61 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_int) (X2 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) X2))) (@ (@ tptp.insert_int X2) (@ tptp.set_int2 L))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (X2 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) X2))) (@ (@ tptp.insert_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 L))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_real) (X2 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) X2))) (@ (@ tptp.insert_real X2) (@ tptp.set_real2 L))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_o) (X2 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) X2))) (@ (@ tptp.insert_o X2) (@ tptp.set_o2 L))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X2 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) X2))) (@ (@ tptp.insert_nat X2) (@ tptp.set_nat2 L))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (X2 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) X2))) (@ (@ tptp.insert_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 L))))))
% 7.27/7.61 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2)) X2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((A2 Bool) (B2 Bool) (Va tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ tptp.vEBT_Leaf A2) B2)) (@ tptp.suc (@ tptp.suc Va))) (@ _let_1 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 7.27/7.61 (assert (forall ((A2 Bool) (B2 Bool) (X2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ tptp.vEBT_Leaf A2) B2)) X2) (@ _let_1 (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 7.27/7.61 (assert (forall ((V tptp.product_prod_nat_nat) (Vd3 tptp.list_VEBT_VEBT) (Ve3 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd3) Ve3)) Vf2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Uu Bool) (B2 Bool)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ tptp.vEBT_Leaf Uu) B2)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))
% 7.27/7.61 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd3 tptp.vEBT_VEBT) (Ve3 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd3)) Ve3) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((A2 Bool) (Uw Bool)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ tptp.vEBT_Leaf A2) Uw)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))
% 7.27/7.61 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y3 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) Y3)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_p_r_e_d T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))
% 7.27/7.61 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_s_u_c_c T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Uu tptp.vEBT_VEBT) (Uua tptp.nat) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ (@ tptp.vEBT_vebt_insert Uu) Uua))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw _let_1) Xi)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi I6) tptp.vEBT_vebt_assn_raw) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) _let_1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Uu tptp.vEBT_VEBT) (Uua tptp.nat) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (let ((_let_1 (@ (@ tptp.vEBT_vebt_insert Uu) Uua))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw _let_1) Xi)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi I6) tptp.vEBT_vebt_assn_raw) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) _let_1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Uu tptp.vEBT_VEBT) (Uua tptp.nat) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (let ((_let_1 (@ (@ tptp.vEBT_vebt_insert Uu) Uua))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw _let_1) Xi)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi I6) tptp.vEBT_vebt_assn_raw) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) _let_1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Uu tptp.vEBT_VEBT) (Uua tptp.nat) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.vEBT_vebt_insert Uu) Uua))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw _let_1) Xi)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi I6) tptp.vEBT_vebt_assn_raw) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) _let_1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X2) Xa) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))))) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (not (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) Mi2) Xa))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (= Y3 (@ (@ 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 (= Xa Mi2) (= Xa 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))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) Mi) X2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y3 (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa 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) Xa)))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) Mi2) Xa))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_4))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ 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 (= Xa Mi2) (= Xa 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) Xa))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c X2) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= Xa tptp.zero_zero_nat) (not (= Y3 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N3 tptp.nat)) (= Xa (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _let_3))) (let ((_let_10 (@ _let_6 _let_4))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (= Y3 (@ _let_8 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_T_m_a_x_t _let_10))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_10) _let_9))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c Summary2) _let_4))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5)))))))))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d X2) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A3 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa (@ tptp.suc tptp.zero_zero_nat)) (not (= Y3 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (exists ((Va3 tptp.nat)) (= Xa (@ tptp.suc (@ tptp.suc Va3)))) (not (= Y3 (@ _let_1 (@ (@ (@ tptp.if_nat B3) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _let_4))) (let ((_let_11 (@ _let_7 _let_5))) (let ((_let_12 (@ tptp.vEBT_vebt_mint _let_11))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_3) TreeList2) Summary2)) (not (= Y3 (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa)) 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)))))))))))))))))))))))))))))))
% 7.27/7.61 (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)))
% 7.27/7.61 (assert (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf false) false)) tptp.one_one_nat))
% 7.27/7.61 (assert (forall ((Uv Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf true) Uv)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Uu Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf Uu) true)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((A2 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ tptp.vEBT_Leaf A2) B2)) (@ _let_1 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 7.27/7.61 (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)))
% 7.27/7.61 (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)))
% 7.27/7.61 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)) tptp.one_one_nat)))
% 7.27/7.61 (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)))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ tptp.vEBT_Leaf A2) B2)) (@ _let_1 (@ (@ (@ tptp.if_nat A2) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X2) Y3) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) _let_1) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) _let_1))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_a_x_t X2) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (not (= Y3 (@ _let_1 (@ (@ (@ tptp.if_nat B3) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_t X2) Y3) (=> (forall ((A3 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 (@ _let_1 (@ (@ (@ tptp.if_nat A3) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.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 (= X2 Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X2))) (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 (= X2 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 Mi) Ma))) _let_3) TreeList) Summary)) X2) (@ _let_27 (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat X2) Mi) (@ (@ tptp.ord_less_nat Ma) X2))) 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))))))))))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e X2) Xa) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa (@ tptp.suc tptp.zero_zero_nat)) _let_1)) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (exists ((N3 tptp.nat)) (= Xa (@ tptp.suc (@ tptp.suc N3)))) _let_1)) (=> (=> (exists ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va3)))) (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 (= Xa Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa))) (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 (= Xa 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))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_3) TreeList2) Summary2)) (not (= Y3 (@ _let_27 (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat Xa) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa))) 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))))))))))))))))))))))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high X2) _let_4))) (let ((_let_6 (@ (@ tptp.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 X2) _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 Mi) Ma))) _let_3) TreeList) Summary)) X2) (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) 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)))))))))))))))))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_8 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_10 (@ _let_6 _let_4))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2) (@ _let_8 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_T_m_a_x_t _let_10))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_10) _let_9))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c Summary) _let_4))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5)))))))))) tptp.one_one_nat))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_2) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _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))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 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 Mi2) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 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 Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ tptp.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 (= Xa Mi2))) (let ((_let_11 (@ tptp.if_nat _let_10))) (let ((_let_12 (@ (@ _let_11 _let_9) Xa))) (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 (= Xa 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))) (=> (= X2 _let_2) (=> (= Y3 (@ _let_28 (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat Xa) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa))) 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) Xa)))))))))))))))))))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _let_4))) (let ((_let_11 (@ _let_7 _let_5))) (let ((_let_12 (@ tptp.vEBT_vebt_maxt _let_11))) (=> (= X2 _let_2) (=> (= Y3 (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa) Mi2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ _let_9 (@ tptp.vEBT_T_m_a_x_t _let_11))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_12 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_10)) _let_12))) (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c _let_11) _let_10))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_9 (@ (@ tptp.vEBT_T_s_u_c_c Summary2) _let_5))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_6 tptp.none_nat)) tptp.one_one_nat) (@ _let_8 (@ tptp.vEBT_T_m_i_n_t (@ _let_7 (@ tptp.the_nat _let_6)))))))))) tptp.one_one_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d X2) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (= Y3 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 ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X2 _let_2) (=> (= Xa _let_1) (=> (= Y3 (@ (@ 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 ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= Xa _let_1) (=> (= Y3 (@ _let_2 (@ (@ (@ tptp.if_nat B3) 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 A3) B3)) _let_1)))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Xa) _let_5))) (let ((_let_12 (@ _let_8 _let_6))) (let ((_let_13 (@ tptp.vEBT_vebt_mint _let_12))) (=> (= X2 _let_2) (=> (= Y3 (@ _let_10 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa)) 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) Xa))))))))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((H2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Xaa tptp.vEBT_VEBT) (L tptp.nat) (X2 tptp.vEBT_VEBTi) (Xb 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) X2))) (let ((_let_2 (@ tptp.pure_assn (= Xb (@ 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) X2)) _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)))))))))))
% 7.27/7.61 (assert (forall ((H2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (X2 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) X2))) (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) X2)) _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)))))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (X2 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) X2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y3))) (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_s6755466524823107622T_VEBT TreeList4)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Y3) X2)) _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))))))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_real) (Y3 tptp.vEBT_VEBT) (X2 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) X2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y3))) (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 Y3) X2)) _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))))))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_o) (Y3 tptp.vEBT_VEBT) (X2 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) X2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y3))) (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 Y3) X2)) _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))))))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_nat) (Y3 tptp.vEBT_VEBT) (X2 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) X2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y3))) (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 Y3) X2)) _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))))))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_VEBT_VEBTi) (Y3 tptp.vEBT_VEBT) (X2 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) X2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y3))) (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_s7982070591426661849_VEBTi TreeList4)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Y3) X2)) _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))))))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((I tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ (@ tptp.set_or8585797421378605585et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I) (@ (@ tptp.ord_less_set_int I) U)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (= (@ (@ tptp.set_or8585797421378605585et_int A2) B2) tptp.bot_bot_set_set_int))))
% 7.27/7.61 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.set_or4029947393144176647an_rat A2) B2) tptp.bot_bot_set_rat))))
% 7.27/7.61 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (= (@ (@ tptp.set_or1222409239386451017an_num A2) B2) tptp.bot_bot_set_num))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.set_or4665077453230672383an_nat A2) B2) tptp.bot_bot_set_nat))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.set_or4662586982721622107an_int A2) B2) tptp.bot_bot_set_int))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (= (@ (@ tptp.set_or8404916559141939852nteger A2) B2) tptp.bot_bo3990330152332043303nteger))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or66887138388493659n_real A2) B2)) (not (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A2) B2)) (not (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or1222409239386451017an_num A2) B2)) (not (@ (@ tptp.ord_less_num A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or4665077453230672383an_nat A2) B2)) (not (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or4662586982721622107an_int A2) B2)) (not (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or8404916559141939852nteger A2) B2)) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.set_or66887138388493659n_real A2) B2) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_real A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A2) B2) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_rat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (= (@ (@ tptp.set_or1222409239386451017an_num A2) B2) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_num A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A2) B2) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.set_or4662586982721622107an_int A2) B2) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_int A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.set_or8404916559141939852nteger A2) B2) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((I tptp.rat) (J tptp.rat) (M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat J))) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat I) J)) (@ (@ tptp.set_or4029947393144176647an_rat M) N)) (or (@ _let_1 I) (and (@ (@ tptp.ord_less_eq_rat M) I) (@ _let_1 N)))))))
% 7.27/7.61 (assert (forall ((I tptp.num) (J tptp.num) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num J))) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or1222409239386451017an_num I) J)) (@ (@ tptp.set_or1222409239386451017an_num M) N)) (or (@ _let_1 I) (and (@ (@ tptp.ord_less_eq_num M) I) (@ _let_1 N)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat J))) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (or (@ _let_1 I) (and (@ (@ tptp.ord_less_eq_nat M) I) (@ _let_1 N)))))))
% 7.27/7.61 (assert (forall ((I tptp.int) (J tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int J))) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or4662586982721622107an_int I) J)) (@ (@ tptp.set_or4662586982721622107an_int M) N)) (or (@ _let_1 I) (and (@ (@ tptp.ord_less_eq_int M) I) (@ _let_1 N)))))))
% 7.27/7.61 (assert (forall ((I tptp.code_integer) (J tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger J))) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or8404916559141939852nteger I) J)) (@ (@ tptp.set_or8404916559141939852nteger M) N)) (or (@ _let_1 I) (and (@ (@ tptp.ord_le3102999989581377725nteger M) I) (@ _let_1 N)))))))
% 7.27/7.61 (assert (forall ((I tptp.rat) (N tptp.rat) (M tptp.rat)) (let ((_let_1 (@ tptp.set_or4029947393144176647an_rat I))) (=> (@ (@ tptp.ord_less_eq_rat I) N) (= (@ (@ tptp.minus_minus_set_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.set_or4029947393144176647an_rat N) M))))))
% 7.27/7.61 (assert (forall ((I tptp.num) (N tptp.num) (M tptp.num)) (let ((_let_1 (@ tptp.set_or1222409239386451017an_num I))) (=> (@ (@ tptp.ord_less_eq_num I) N) (= (@ (@ tptp.minus_minus_set_num (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.set_or1222409239386451017an_num N) M))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.set_or4665077453230672383an_nat N) M))))))
% 7.27/7.61 (assert (forall ((I tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.set_or4662586982721622107an_int I))) (=> (@ (@ tptp.ord_less_eq_int I) N) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.set_or4662586982721622107an_int N) M))))))
% 7.27/7.61 (assert (forall ((I tptp.code_integer) (N tptp.code_integer) (M tptp.code_integer)) (let ((_let_1 (@ tptp.set_or8404916559141939852nteger I))) (=> (@ (@ tptp.ord_le3102999989581377725nteger I) N) (= (@ (@ tptp.minus_2355218937544613996nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.set_or8404916559141939852nteger N) M))))))
% 7.27/7.61 (assert (forall ((Y3 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) Y3)) (@ (@ tptp.nth_VEBT_VEBTi Tree_is) Y3)))) (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 Y3) 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 Y3) _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))))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 7.27/7.61 (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)))))))))
% 7.27/7.61 (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)))))))))
% 7.27/7.61 (assert (forall ((Y3 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 Y3) _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) Y3)) (@ (@ tptp.nth_VEBT_VEBTi Tree_is) Y3))) _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 Y3) 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)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (= (= (@ (@ tptp.set_or66887138388493659n_real A2) B2) (@ (@ tptp.set_or66887138388493659n_real C2) D2)) (and (= A2 C2) (= B2 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A2) B2) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (and (= A2 C2) (= B2 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_num C2) D2) (= (= (@ (@ tptp.set_or1222409239386451017an_num A2) B2) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (and (= A2 C2) (= B2 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A2) B2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (and (= A2 C2) (= B2 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (= (= (@ (@ tptp.set_or4662586982721622107an_int A2) B2) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (and (= A2 C2) (= B2 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (= (= (@ (@ tptp.set_or8404916559141939852nteger A2) B2) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (and (= A2 C2) (= B2 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.set_or66887138388493659n_real A2) B2) (@ (@ tptp.set_or66887138388493659n_real C2) D2)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (= A2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A2) B2) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (= A2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A2) B2) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_num C2) D2) (= A2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A2) B2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (= A2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A2) B2) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (= A2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A2) B2) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (= A2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.set_or66887138388493659n_real A2) B2) (@ (@ tptp.set_or66887138388493659n_real C2) D2)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real C2) D2) (= B2 D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A2) B2) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C2) D2) (= B2 D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A2) B2) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_num C2) D2) (= B2 D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A2) B2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C2) D2) (= B2 D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A2) B2) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C2) D2) (= B2 D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A2) B2) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (= B2 D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A2) B2)) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (or (@ _let_1 A2) (and (@ (@ tptp.ord_less_eq_rat C2) A2) (@ _let_1 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num B2))) (=> (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or1222409239386451017an_num A2) B2)) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (or (@ _let_1 A2) (and (@ (@ tptp.ord_less_eq_num C2) A2) (@ _let_1 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or4665077453230672383an_nat A2) B2)) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (or (@ _let_1 A2) (and (@ (@ tptp.ord_less_eq_nat C2) A2) (@ _let_1 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or4662586982721622107an_int A2) B2)) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (or (@ _let_1 A2) (and (@ (@ tptp.ord_less_eq_int C2) A2) (@ _let_1 D2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B2))) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or8404916559141939852nteger A2) B2)) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (or (@ _let_1 A2) (and (@ (@ tptp.ord_le3102999989581377725nteger C2) A2) (@ _let_1 D2)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 7.27/7.61 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A2) B2)) (@ (@ tptp.set_or633870826150836451st_rat C2) D2)) (=> (@ (@ tptp.ord_less_rat A2) B2) (and (@ (@ tptp.ord_less_eq_rat C2) A2) (@ (@ tptp.ord_less_eq_rat B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or66887138388493659n_real A2) B2)) (@ (@ tptp.set_or1222579329274155063t_real C2) D2)) (=> (@ (@ tptp.ord_less_real A2) B2) (and (@ (@ tptp.ord_less_eq_real C2) A2) (@ (@ tptp.ord_less_eq_real B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A2) B2)) (@ (@ tptp.set_or8585797421378605585et_int C2) D2)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (and (@ (@ tptp.ord_less_eq_set_int C2) A2) (@ (@ tptp.ord_less_set_int B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B2)) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (and (@ (@ tptp.ord_less_eq_rat C2) A2) (@ (@ tptp.ord_less_rat B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C2 tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B2)) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (and (@ (@ tptp.ord_less_eq_num C2) A2) (@ (@ tptp.ord_less_num B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ tptp.set_or66887138388493659n_real C2) D2)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (and (@ (@ tptp.ord_less_eq_real C2) A2) (@ (@ tptp.ord_less_real B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (and (@ (@ tptp.ord_less_eq_nat C2) A2) (@ (@ tptp.ord_less_nat B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B2)) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (and (@ (@ tptp.ord_less_eq_int C2) A2) (@ (@ tptp.ord_less_int B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger A2) B2)) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (and (@ (@ tptp.ord_le3102999989581377725nteger C2) A2) (@ (@ tptp.ord_le6747313008572928689nteger B2) D2))))))
% 7.27/7.61 (assert (= tptp.set_or66887138388493659n_real (lambda ((A5 tptp.real) (B6 tptp.real)) (@ (@ tptp.minus_minus_set_real (@ (@ tptp.set_or1222579329274155063t_real A5) B6)) (@ (@ tptp.insert_real B6) tptp.bot_bot_set_real)))))
% 7.27/7.61 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A5) B6)) (@ (@ tptp.insert_nat B6) tptp.bot_bot_set_nat)))))
% 7.27/7.61 (assert (= tptp.set_or4662586982721622107an_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ tptp.minus_minus_set_int (@ (@ tptp.set_or1266510415728281911st_int A5) B6)) (@ (@ tptp.insert_int B6) tptp.bot_bot_set_int)))))
% 7.27/7.61 (assert (= tptp.set_or8404916559141939852nteger (lambda ((A5 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.minus_2355218937544613996nteger (@ (@ tptp.set_or189985376899183464nteger A5) B6)) (@ (@ tptp.insert_Code_integer B6) tptp.bot_bo3990330152332043303nteger)))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_o) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L7489408758114837031VEBT_o A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L7489408758114837031VEBT_o A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L4595930785310033027T_VEBT A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L4595930785310033027T_VEBT A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L9060850011106065574_VEBTi A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBTi Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBTi Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L9060850011106065574_VEBTi A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.nat tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_nat) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1446010312343316929al_nat A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1446010312343316929al_nat A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real Bool tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_o) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L6234343332106409831real_o A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L6234343332106409831real_o A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.real tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_real) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1930518968523514909l_real A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1930518968523514909l_real A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_o) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (I tptp.nat) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q2 (-> tptp.vEBT_VEBTi tptp.assn)) (F4 (-> tptp.vEBT_VEBTi tptp.assn))) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1750719106661372127T_VEBT A) Xs) Xsi)) F3)) (=> (@ (@ tptp.ord_less_nat I) _let_1) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_1)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) C2) Q2) (=> (forall ((R3 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ Q2 R3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs))) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) (@ F4 R3)))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L1750719106661372127T_VEBT A) Xs) Xsi)) (@ F4 R5)))))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi tptp.vEBT_VEBT) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi tptp.nat) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_update_nat Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi Bool) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_o) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_update_o Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi tptp.real) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_update_real Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (X2 tptp.real) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (X2 tptp.real) (Xi tptp.vEBT_VEBT) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.nat tptp.assn)) (X2 tptp.real) (Xi tptp.nat) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_update_nat Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real Bool tptp.assn)) (X2 tptp.real) (Xi Bool) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_o) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_update_o Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.real tptp.assn)) (X2 tptp.real) (Xi tptp.real) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_real) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_update_real Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> Bool tptp.vEBT_VEBTi tptp.assn)) (X2 Bool) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_o) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L6286945158656146733_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L6286945158656146733_VEBTi I6) A) (@ (@ (@ tptp.list_update_o Xs) I) X2)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_VEBT_VEBT) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_nat) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_o) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_real) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_VEBT_VEBT) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_VEBT_VEBTi) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBTi Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.nat tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_nat) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real Bool tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_o) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.real tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_real) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_o) (I tptp.nat) (Xsi tptp.list_VEBT_VEBT) (I6 tptp.set_nat) (F3 tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I6) A) Xs) Xsi)) F3)) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi tptp.vEBT_VEBT) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi tptp.nat) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_update_nat Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi Bool) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_o) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_update_o Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (X2 tptp.vEBT_VEBT) (Xi tptp.real) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2)) (@ (@ (@ tptp.list_update_real Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (X2 tptp.real) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (X2 tptp.real) (Xi tptp.vEBT_VEBT) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.nat tptp.assn)) (X2 tptp.real) (Xi tptp.nat) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_update_nat Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real Bool tptp.assn)) (X2 tptp.real) (Xi Bool) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_o) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_update_o Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.real tptp.assn)) (X2 tptp.real) (Xi tptp.real) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_real) (Xsi tptp.list_real) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) (@ (@ (@ tptp.list_update_real Xs) I) X2)) (@ (@ (@ tptp.list_update_real Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> Bool tptp.vEBT_VEBTi tptp.assn)) (X2 Bool) (Xi tptp.vEBT_VEBTi) (I6 tptp.set_nat) (I tptp.nat) (Xs tptp.list_o) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A X2) Xi)) (@ (@ (@ (@ tptp.vEBT_L6286945158656146733_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L6286945158656146733_VEBTi I6) A) (@ (@ (@ tptp.list_update_o Xs) I) X2)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) Xi))) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_VEBT_VEBT) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_nat) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_o) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xs tptp.list_VEBT_VEBT) (I tptp.nat) (Xsi tptp.list_real) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_VEBT_VEBT) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_VEBT_VEBTi) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBTi Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.nat tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_nat) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real Bool tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_o) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> tptp.real tptp.real tptp.assn)) (Xs tptp.list_real) (I tptp.nat) (Xsi tptp.list_real) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_o) (I tptp.nat) (Xsi tptp.list_VEBT_VEBT) (I6 tptp.set_nat) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I6) A) Xs) Xsi)) F3)) Q) (@ _let_1 Q))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xsi tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Xsi tptp.list_o)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xsi tptp.list_real)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xsi tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (Xsi tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBTi Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real Bool tptp.assn)) (Xsi tptp.list_o)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.real tptp.assn)) (Xsi tptp.list_real)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_o) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xsi tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_nat I) I6) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I6) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT (@ (@ tptp.minus_minus_set_nat I6) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.int tptp.int tptp.assn)) (A7 (-> tptp.int tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.int) (Xi2 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_int Xi2) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L74593716426352029nt_int A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A (-> tptp.int tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.int tptp.vEBT_VEBT tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.int) (Xi2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_VEBT_VEBT Xi2) (@ tptp.set_VEBT_VEBT2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L1664421287176695555T_VEBT A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L1664421287176695555T_VEBT A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_real) (Xsi2 tptp.list_real) (A (-> tptp.int tptp.real tptp.assn)) (A7 (-> tptp.int tptp.real tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.int) (Xi2 tptp.real)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_real Xi2) (@ tptp.set_real2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L8288995350762215837t_real A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8288995350762215837t_real A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.int tptp.nat tptp.assn)) (A7 (-> tptp.int tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.int) (Xi2 tptp.nat)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_nat Xi2) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.vEBT_VEBT tptp.int tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.vEBT_VEBT) (Xi2 tptp.int)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_int Xi2) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L8294436054247626077BT_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8294436054247626077BT_int A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.vEBT_VEBT) (Xi2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_VEBT_VEBT Xi2) (@ tptp.set_VEBT_VEBT2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (Xsi2 tptp.list_real) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.real tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.vEBT_VEBT) (Xi2 tptp.real)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_real Xi2) (@ tptp.set_real2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.vEBT_VEBT) (Xi2 tptp.nat)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_nat Xi2) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.real tptp.int tptp.assn)) (A7 (-> tptp.real tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.real) (Xi2 tptp.int)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs4)) (=> (@ (@ tptp.member_int Xi2) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L1443519841834266653al_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L1443519841834266653al_int A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.real tptp.vEBT_VEBT tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X4 tptp.real) (Xi2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs4)) (=> (@ (@ tptp.member_VEBT_VEBT Xi2) (@ tptp.set_VEBT_VEBT2 Xsi2)) (= (@ (@ A X4) Xi2) (@ (@ A7 X4) Xi2))))) (= (@ (@ (@ tptp.vEBT_L4595930785310033027T_VEBT A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L4595930785310033027T_VEBT A7) Xs4) Xsi2)))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (P5 (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (L tptp.list_VEBT_VEBT) (L4 tptp.list_VEBT_VEBTi)) (=> (forall ((X4 tptp.vEBT_VEBT) (X9 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ (@ P X4) X9)) (@ (@ P5 X4) X9))) (@ (@ tptp.entails (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi P) L) L4)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi P5) L) L4)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A) Xs) Xsi)) H2) (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L4595930785310033027T_VEBT A) Xs) Xsi)) H2) (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_size_list_real Xs)))))
% 7.27/7.61 (assert (forall ((A (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_o) (Xsi tptp.list_VEBT_VEBT) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L1750719106661372127T_VEBT A) Xs) Xsi)) H2) (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_size_list_o Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.nat tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_nat) (Xsi tptp.list_VEBT_VEBT) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L8158188754432654943T_VEBT A) Xs) Xsi)) H2) (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_size_list_nat Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.vEBT_VEBTi tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_VEBT_VEBTi) (Xsi tptp.list_VEBT_VEBT) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L7265847600308530106T_VEBT A) Xs) Xsi)) H2) (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s7982070591426661849_VEBTi Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A) Xs) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.real tptp.real tptp.assn)) (Xs tptp.list_real) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L1930518968523514909l_real A) Xs) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_real Xs)))))
% 7.27/7.61 (assert (forall ((A (-> Bool tptp.real tptp.assn)) (Xs tptp.list_o) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L4725278957065240257o_real A) Xs) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_o Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.nat tptp.real tptp.assn)) (Xs tptp.list_nat) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L6102073776069194049t_real A) Xs) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_nat Xs)))))
% 7.27/7.61 (assert (forall ((A (-> tptp.vEBT_VEBTi tptp.real tptp.assn)) (Xs tptp.list_VEBT_VEBTi) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L8937798142398754470i_real A) Xs) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_s7982070591426661849_VEBTi Xs)))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBT) (Li2 tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn))) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT L) (@ tptp.size_s6755466524823107622T_VEBT Li2))) (= (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBT) (Li2 tptp.list_real) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn))) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT L) (@ tptp.size_size_list_real Li2))) (= (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBT) (Li2 tptp.list_o) (A (-> tptp.vEBT_VEBT Bool tptp.assn))) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT L) (@ tptp.size_size_list_o Li2))) (= (@ (@ (@ tptp.vEBT_L7489408758114837031VEBT_o A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBT) (Li2 tptp.list_nat) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn))) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT L) (@ tptp.size_size_list_nat Li2))) (= (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_real) (Li2 tptp.list_VEBT_VEBT) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn))) (=> (not (= (@ tptp.size_size_list_real L) (@ tptp.size_s6755466524823107622T_VEBT Li2))) (= (@ (@ (@ tptp.vEBT_L4595930785310033027T_VEBT A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_real) (Li2 tptp.list_real) (A (-> tptp.real tptp.real tptp.assn))) (=> (not (= (@ tptp.size_size_list_real L) (@ tptp.size_size_list_real Li2))) (= (@ (@ (@ tptp.vEBT_L1930518968523514909l_real A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_real) (Li2 tptp.list_o) (A (-> tptp.real Bool tptp.assn))) (=> (not (= (@ tptp.size_size_list_real L) (@ tptp.size_size_list_o Li2))) (= (@ (@ (@ tptp.vEBT_L6234343332106409831real_o A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_real) (Li2 tptp.list_nat) (A (-> tptp.real tptp.nat tptp.assn))) (=> (not (= (@ tptp.size_size_list_real L) (@ tptp.size_size_list_nat Li2))) (= (@ (@ (@ tptp.vEBT_L1446010312343316929al_nat A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_real) (Li2 tptp.list_VEBT_VEBTi) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn))) (=> (not (= (@ tptp.size_size_list_real L) (@ tptp.size_s7982070591426661849_VEBTi Li2))) (= (@ (@ (@ tptp.vEBT_L9060850011106065574_VEBTi A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((L tptp.list_o) (Li2 tptp.list_VEBT_VEBT) (A (-> Bool tptp.vEBT_VEBT tptp.assn))) (=> (not (= (@ tptp.size_size_list_o L) (@ tptp.size_s6755466524823107622T_VEBT Li2))) (= (@ (@ (@ tptp.vEBT_L1750719106661372127T_VEBT A) L) Li2) tptp.bot_bot_assn))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xsi)) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Xs4) I2)) (= (@ (@ tptp.nth_VEBT_VEBT Xsi) I2) (@ (@ tptp.nth_VEBT_VEBT Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (Xsi2 tptp.list_real)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_real Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_real Xsi)) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Xs4) I2)) (= (@ (@ tptp.nth_real Xsi) I2) (@ (@ tptp.nth_real Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (A7 (-> tptp.vEBT_VEBT Bool tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_o) (Xsi2 tptp.list_o)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_o Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Xsi)) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Xs4) I2)) (= (@ (@ tptp.nth_o Xsi) I2) (@ (@ tptp.nth_o Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Xs4) I2)) (= (@ (@ tptp.nth_nat Xsi) I2) (@ (@ tptp.nth_nat Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xsi)) (and (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Xs4) I2)) (= (@ (@ tptp.nth_VEBT_VEBT Xsi) I2) (@ (@ tptp.nth_VEBT_VEBT Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.real tptp.real tptp.assn)) (A7 (-> tptp.real tptp.real tptp.assn)) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_real) (Xsi2 tptp.list_real)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_real Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_real Xsi)) (and (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Xs4) I2)) (= (@ (@ tptp.nth_real Xsi) I2) (@ (@ tptp.nth_real Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.real Bool tptp.assn)) (A7 (-> tptp.real Bool tptp.assn)) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_o) (Xsi2 tptp.list_o)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_o Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Xsi)) (and (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Xs4) I2)) (= (@ (@ tptp.nth_o Xsi) I2) (@ (@ tptp.nth_o Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.real tptp.nat tptp.assn)) (A7 (-> tptp.real tptp.nat tptp.assn)) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Xs4) I2)) (= (@ (@ tptp.nth_nat Xsi) I2) (@ (@ tptp.nth_nat Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (A7 (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_VEBT_VEBTi) (Xsi2 tptp.list_VEBT_VEBTi)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi Xsi) (@ tptp.size_s7982070591426661849_VEBTi Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_s7982070591426661849_VEBTi Xsi)) (and (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Xs4) I2)) (= (@ (@ tptp.nth_VEBT_VEBTi Xsi) I2) (@ (@ tptp.nth_VEBT_VEBTi Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (A7 (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xs tptp.list_o) (Xs4 tptp.list_o) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT)) (=> (= I6 I7) (=> (= A A7) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Xs4)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xsi)) (and (= (@ (@ tptp.nth_o Xs) I2) (@ (@ tptp.nth_o Xs4) I2)) (= (@ (@ tptp.nth_VEBT_VEBT Xsi) I2) (@ (@ tptp.nth_VEBT_VEBT Xsi2) I2)))))))) (= (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I7) A7) Xs4) Xsi2)))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_VEBT_VEBT Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT Xs) I2))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_s6755466524823107622T_VEBT Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (Xsi2 tptp.list_real) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.real tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_real Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_real Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_real Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT Xs) I2))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_size_list_real Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_o) (Xsi2 tptp.list_o) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (A7 (-> tptp.vEBT_VEBT Bool tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_o Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_o Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT Xs) I2))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_size_list_o Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.nat tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT Xs) I2))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.real tptp.vEBT_VEBT tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_real Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_VEBT_VEBT Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_real Xs) I2))) (let ((_let_5 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_s6755466524823107622T_VEBT Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_real) (Xsi2 tptp.list_real) (A (-> tptp.real tptp.real tptp.assn)) (A7 (-> tptp.real tptp.real tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_real Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_real Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_real Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_real Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_real Xs) I2))) (let ((_let_5 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_size_list_real Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_o) (Xsi2 tptp.list_o) (A (-> tptp.real Bool tptp.assn)) (A7 (-> tptp.real Bool tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_o Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_real Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_o Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_real Xs) I2))) (let ((_let_5 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_size_list_o Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.real tptp.nat tptp.assn)) (A7 (-> tptp.real tptp.nat tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_real Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_real Xs) I2))) (let ((_let_5 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_real) (Xs4 tptp.list_real) (Xsi tptp.list_VEBT_VEBTi) (Xsi2 tptp.list_VEBT_VEBTi) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (A7 (-> tptp.real tptp.vEBT_VEBTi tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Xs4)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi Xsi) (@ tptp.size_s7982070591426661849_VEBTi Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBTi Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_real Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_VEBT_VEBTi Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_real Xs) I2))) (let ((_let_5 (@ tptp.size_size_list_real Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_s7982070591426661849_VEBTi Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I6 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_o) (Xs4 tptp.list_o) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (A7 (-> Bool tptp.vEBT_VEBT tptp.assn))) (=> (= I6 I7) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Xs4)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xsi) (@ tptp.size_s6755466524823107622T_VEBT Xsi2)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xsi2) I2))) (let ((_let_2 (@ (@ tptp.nth_o Xs4) I2))) (let ((_let_3 (@ (@ tptp.nth_VEBT_VEBT Xsi) I2))) (let ((_let_4 (@ (@ tptp.nth_o Xs) I2))) (let ((_let_5 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ (@ tptp.ord_less_nat I2) _let_5) (=> (= _let_5 (@ tptp.size_s6755466524823107622T_VEBT Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A7 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I6) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I7) A7) Xs4) Xsi2))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (X22 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_nat) (X22 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_update_nat Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_o) (X22 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_update_o Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_real) (X22 tptp.real)) (let ((_let_1 (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_update_real Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (X1 tptp.real) (Xsi tptp.list_VEBT_VEBTi) (X22 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (X1 tptp.real) (Xsi tptp.list_VEBT_VEBT) (X22 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.nat tptp.assn)) (X1 tptp.real) (Xsi tptp.list_nat) (X22 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_update_nat Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real Bool tptp.assn)) (X1 tptp.real) (Xsi tptp.list_o) (X22 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_update_o Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.real tptp.assn)) (X1 tptp.real) (Xsi tptp.list_real) (X22 tptp.real)) (let ((_let_1 (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_update_real Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_o) (A (-> Bool tptp.vEBT_VEBTi tptp.assn)) (X1 Bool) (Xsi tptp.list_VEBT_VEBTi) (X22 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.vEBT_L6286945158656146733_VEBTi I6) A))) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ _let_1 (@ (@ (@ tptp.list_update_o Xs) I) X1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) X22)) (@ (@ _let_1 Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Xsi tptp.list_VEBT_VEBTi)) (=> (= N (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi A) Xs) Xsi)))))
% 7.27/7.61 (assert (= tptp.vEBT_L6296928887356842470_VEBTi (lambda ((A6 (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Xs2 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 Xs2))) A6) Xs2) __flatten_var_0))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (Xsi tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Xsi tptp.list_o)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (Xsi tptp.list_real)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (Xsi tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (Xsi tptp.list_VEBT_VEBTi)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_VEBT_VEBTi Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real Bool tptp.assn)) (Xsi tptp.list_o)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_o Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.real tptp.assn)) (Xsi tptp.list_real)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_real Xs) I)) (@ (@ tptp.nth_real Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_o) (A (-> Bool tptp.vEBT_VEBT tptp.assn)) (Xsi tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT (@ (@ tptp.insert_nat I) I6)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L1319876754960170684T_VEBT I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Xsi tptp.list_VEBT_VEBTi) (F3 tptp.assn)) (=> (= N (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) A) Xs) Xsi)) F3) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi A) Xs) Xsi)) F3)))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (X22 tptp.vEBT_VEBT)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L3204528365124325536T_VEBT I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_nat) (X22 tptp.nat)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_update_nat Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L8650695023172932196BT_nat I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_o) (X22 Bool)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_update_o Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L7058566406413635588VEBT_o I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_VEBT_VEBT) (A (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (X1 tptp.vEBT_VEBT) (Xsi tptp.list_real) (X22 tptp.real)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X1)) (@ (@ (@ tptp.list_update_real Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L4281036506115550016T_real I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBTi tptp.assn)) (X1 tptp.real) (Xsi tptp.list_VEBT_VEBTi) (X22 tptp.vEBT_VEBTi)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L7851252805511451907_VEBTi I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.vEBT_VEBT tptp.assn)) (X1 tptp.real) (Xsi tptp.list_VEBT_VEBT) (X22 tptp.vEBT_VEBT)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L3095048238742455910T_VEBT I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.nat tptp.assn)) (X1 tptp.real) (Xsi tptp.list_nat) (X22 tptp.nat)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_update_nat Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L234762979517870878al_nat I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real Bool tptp.assn)) (X1 tptp.real) (Xsi tptp.list_o) (X22 Bool)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_update_o Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L7980206306069228746real_o I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_real) (A (-> tptp.real tptp.real tptp.assn)) (X1 tptp.real) (Xsi tptp.list_real) (X22 tptp.real)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs)) (= (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_update_real Xs) I) X1)) (@ (@ (@ tptp.list_update_real Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L5184575500739366650l_real I6) A) Xs) Xsi)))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (I6 tptp.set_nat) (Xs tptp.list_o) (A (-> Bool tptp.vEBT_VEBTi tptp.assn)) (X1 Bool) (Xsi tptp.list_VEBT_VEBTi) (X22 tptp.vEBT_VEBTi)) (=> (not (@ (@ tptp.member_nat I) I6)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6286945158656146733_VEBTi (@ (@ tptp.insert_nat I) I6)) A) (@ (@ (@ tptp.list_update_o Xs) I) X1)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xsi) I) X22)) (@ (@ tptp.times_times_assn (@ (@ A X1) X22)) (@ (@ (@ (@ tptp.vEBT_L6286945158656146733_VEBTi I6) A) Xs) Xsi)))))))
% 7.27/7.61 (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)))))))))))))
% 7.27/7.61 (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))))))))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (D2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.nth_nat Xs) I2)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.minus_minus_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Xs) D2)) D2)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Y3 tptp.real)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.set_real2 Xs))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y4) _let_1) (= X4 Y4))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (= X4 Y3))) (= (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) Xs) tptp.zero_zero_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_real Xs))) Y3))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (@ (@ (@ (@ tptp.time_htt_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_lowi X2) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_low X2) N))))) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (@ (@ (@ (@ tptp.time_htt_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_highi X2) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_high X2) N))))) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.time_TBOUND_nat (@ (@ tptp.vEBT_VEBT_lowi X2) N)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.time_TBOUND_nat (@ (@ tptp.vEBT_VEBT_highi X2) N)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (C2 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ (@ tptp.foldr_real_real tptp.plus_plus_real) Xs))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C2) D2)) (@ (@ tptp.plus_plus_real (@ _let_1 D2)) C2)))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_highi X2) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_high X2) N)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_lowi X2) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_low X2) N)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (Y3 tptp.nat)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.member_nat X4) _let_1) (=> (@ (@ tptp.member_nat Y4) _let_1) (= X4 Y4))))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (= X4 Y3))) (= (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Xs) tptp.zero_zero_nat) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) Y3))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (C2 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 Xs) _let_2) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_nat (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.nth_nat Ys) I2)))) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ _let_1 Xs) C2)) _let_2)) (@ (@ _let_1 Ys) D2)))))))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBT)) (= (@ (@ (@ tptp.foldr_VEBT_VEBT_nat (lambda ((X3 tptp.vEBT_VEBT) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT L))))
% 7.27/7.61 (assert (forall ((L tptp.list_real)) (= (@ (@ (@ tptp.foldr_real_nat (lambda ((X3 tptp.real) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_real L))))
% 7.27/7.61 (assert (forall ((L tptp.list_o)) (= (@ (@ (@ tptp.foldr_o_nat (lambda ((X3 Bool) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_o L))))
% 7.27/7.61 (assert (forall ((L tptp.list_nat)) (= (@ (@ (@ tptp.foldr_nat_nat (lambda ((X3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_nat L))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBTi)) (= (@ (@ (@ tptp.foldr_VEBT_VEBTi_nat (lambda ((X3 tptp.vEBT_VEBTi) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_s7982070591426661849_VEBTi L))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (L tptp.list_real) (K tptp.list_real) (F (-> tptp.real tptp.real tptp.real)) (G (-> tptp.real tptp.real tptp.real))) (=> (= A2 B2) (=> (= L K) (=> (forall ((A3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 L)) (= (@ (@ F X4) A3) (@ (@ G X4) A3)))) (= (@ (@ (@ tptp.foldr_real_real F) L) A2) (@ (@ (@ tptp.foldr_real_real G) K) B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (L tptp.list_nat) (K tptp.list_nat) (F (-> tptp.nat tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat tptp.nat))) (=> (= A2 B2) (=> (= L K) (=> (forall ((A3 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 L)) (= (@ (@ F X4) A3) (@ (@ G X4) A3)))) (= (@ (@ (@ tptp.foldr_nat_nat F) L) A2) (@ (@ (@ tptp.foldr_nat_nat G) K) B2)))))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBT) (A2 tptp.nat)) (= (@ (@ (@ tptp.foldr_VEBT_VEBT_nat (lambda ((X3 tptp.vEBT_VEBT) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A2) (@ (@ tptp.plus_plus_nat A2) (@ tptp.size_s6755466524823107622T_VEBT L)))))
% 7.27/7.61 (assert (forall ((L tptp.list_real) (A2 tptp.nat)) (= (@ (@ (@ tptp.foldr_real_nat (lambda ((X3 tptp.real) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A2) (@ (@ tptp.plus_plus_nat A2) (@ tptp.size_size_list_real L)))))
% 7.27/7.61 (assert (forall ((L tptp.list_o) (A2 tptp.nat)) (= (@ (@ (@ tptp.foldr_o_nat (lambda ((X3 Bool) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A2) (@ (@ tptp.plus_plus_nat A2) (@ tptp.size_size_list_o L)))))
% 7.27/7.61 (assert (forall ((L tptp.list_nat) (A2 tptp.nat)) (= (@ (@ (@ tptp.foldr_nat_nat (lambda ((X3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A2) (@ (@ tptp.plus_plus_nat A2) (@ tptp.size_size_list_nat L)))))
% 7.27/7.61 (assert (forall ((L tptp.list_VEBT_VEBTi) (A2 tptp.nat)) (= (@ (@ (@ tptp.foldr_VEBT_VEBTi_nat (lambda ((X3 tptp.vEBT_VEBTi) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A2) (@ (@ tptp.plus_plus_nat A2) (@ tptp.size_s7982070591426661849_VEBTi L)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A2) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A2)) _let_1)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A2) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.numeral_numeral_real W)))))
% 7.27/7.61 (assert (forall ((W tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A2)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A2))))))
% 7.27/7.61 (assert (forall ((W tptp.num) (A2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A2) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A2)) _let_1)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A2) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.numeral_numeral_real W)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 7.27/7.61 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 7.27/7.61 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 7.27/7.61 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 7.27/7.61 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) B2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B2) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) B2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B2) A2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y3)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y3)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A2) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A2) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A2) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A2) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (R2 tptp.real) (Y3 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y3)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y3))) (@ (@ tptp.times_times_real R2) S2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (R2 tptp.real) (Y3 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y3)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y3))) (@ (@ tptp.times_times_real R2) S2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y3))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y3))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (R2 tptp.real) (Y3 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y3)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y3))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (R2 tptp.real) (Y3 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y3)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y3))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y3))) E))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y3))) E))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y3))) E))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y3))) E))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (R2 tptp.real) (B2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A2)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A2) B2))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (R2 tptp.real) (B2 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A2)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A2) B2))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y3))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y3))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A2) B2))) C2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A2) B2))) C2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A2)) C2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y3) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y3) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y3))) E))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y3))) E))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y3) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y3) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) B2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) B2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y3)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y3))))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y3)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y3))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) B2)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.plus_plus_real C2) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) C2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (C2 tptp.complex) (D2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A2) B2)) (@ (@ tptp.plus_plus_complex C2) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) C2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B2) D2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X2) tptp.one_one_real))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X2) tptp.one_one_real))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_s6755466524823107622T_VEBT Xs))) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_real_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_real Xs))) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_o) (F (-> Bool tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_o_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_o Xs))) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_nat Xs))) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (F (-> tptp.vEBT_VEBTi tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X4) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBTi_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_s7982070591426661849_VEBTi Xs))) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (C2 tptp.real) (G (-> tptp.vEBT_VEBT tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ (@ tptp.times_times_real C2) (@ G X4))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C2) (@ (@ _let_1 (@ (@ tptp.map_VEBT_VEBT_real G) Xs)) tptp.zero_zero_real))) D2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.real)) (C2 tptp.real) (G (-> tptp.real tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ (@ tptp.times_times_real C2) (@ G X4))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_real_real F) Xs)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C2) (@ (@ _let_1 (@ (@ tptp.map_real_real G) Xs)) tptp.zero_zero_real))) D2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.real)) (C2 tptp.real) (G (-> tptp.nat tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ (@ tptp.times_times_real C2) (@ G X4))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_nat_real F) Xs)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C2) (@ (@ _let_1 (@ (@ tptp.map_nat_real G) Xs)) tptp.zero_zero_real))) D2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_real_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_o) (F (-> Bool tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_o_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_nat_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (F (-> tptp.vEBT_VEBTi tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X4) (@ tptp.set_VEBT_VEBTi2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBTi_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_s7982070591426661849_VEBTi Xs)) Bound)) I)))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (X2 tptp.nat) (T tptp.vEBT_VEBT)) (@ (@ tptp.refine_Imp_refines_o (@ (@ tptp.vEBT_vebt_memberi Ti) X2)) (@ (@ (@ tptp.vEBT_V854960066525838166emberi T) Ti) X2))))
% 7.27/7.61 (assert (forall ((F tptp.heap_Time_Heap_o) (F5 tptp.heap_Time_Heap_o) (N tptp.nat)) (let ((_let_1 (@ tptp.vEBT_V2326993469660664182atei_o N))) (=> (@ (@ tptp.refine_Imp_refines_o F) F5) (@ (@ tptp.refine5896690332125372649list_o (@ _let_1 F)) (@ _let_1 F5))))))
% 7.27/7.61 (assert (forall ((F tptp.heap_T2636463487746394924on_nat) (F5 tptp.heap_T2636463487746394924on_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.vEBT_V792416675989592002on_nat N))) (=> (@ (@ tptp.refine7594492741263601813on_nat F) F5) (@ (@ tptp.refine1935026298455697829on_nat (@ _let_1 F)) (@ _let_1 F5))))))
% 7.27/7.61 (assert (forall ((F tptp.heap_T8145700208782473153_VEBTi) (F5 tptp.heap_T8145700208782473153_VEBTi) (N tptp.nat)) (let ((_let_1 (@ tptp.vEBT_V1859673955506687831_VEBTi N))) (=> (@ (@ tptp.refine5565527176597971370_VEBTi F) F5) (@ (@ tptp.refine3700189196150522554_VEBTi (@ _let_1 F)) (@ _let_1 F5))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.real)) (Y3 tptp.real)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_int_real F) Xs)) Y3)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Y3 tptp.real)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) Y3)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.real)) (Y3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_real_real F) Xs)) Y3)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.real)) (Y3 tptp.real)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real F) Xs)) Y3)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.real tptp.vEBT_VEBT)) (Xs tptp.list_real)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_real_VEBT_VEBT F) Xs)) (@ tptp.size_size_list_real Xs))))
% 7.27/7.61 (assert (forall ((F (-> Bool tptp.vEBT_VEBT)) (Xs tptp.list_o)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_o_VEBT_VEBT F) Xs)) (@ tptp.size_size_list_o Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.nat tptp.vEBT_VEBT)) (Xs tptp.list_nat)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_nat_VEBT_VEBT F) Xs)) (@ tptp.size_size_list_nat Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBT)) (Xs tptp.list_VEBT_VEBTi)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_VE7998069337340375161T_VEBT F) Xs)) (@ tptp.size_s7982070591426661849_VEBTi Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.real tptp.real)) (Xs tptp.list_real)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_real_real F) Xs)) (@ tptp.size_size_list_real Xs))))
% 7.27/7.61 (assert (forall ((F (-> Bool tptp.real)) (Xs tptp.list_o)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_o_real F) Xs)) (@ tptp.size_size_list_o Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.nat tptp.real)) (Xs tptp.list_nat)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_nat_real F) Xs)) (@ tptp.size_size_list_nat Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.real)) (Xs tptp.list_VEBT_VEBTi)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_VEBT_VEBTi_real F) Xs)) (@ tptp.size_s7982070591426661849_VEBTi Xs))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (= (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Xs)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X3) (@ G X3)))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (= (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Xs)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X3) (@ G X3)))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (C2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) C2)) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real (lambda ((X3 tptp.vEBT_VEBT)) (@ tptp.semiri5074537144036343181t_real (@ F X3)))) Xs)) (@ tptp.semiri5074537144036343181t_real C2)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.map_VE7029150624388687525_VEBTi F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_o (@ (@ tptp.map_VEBT_VEBT_o F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_real (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (F (-> tptp.real tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_real_VEBT_VEBT F) Xs)) N) (@ F (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (F (-> tptp.real tptp.vEBT_VEBTi))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.map_real_VEBT_VEBTi F) Xs)) N) (@ F (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (F (-> tptp.real tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_real_nat F) Xs)) N) (@ F (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (F (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_o (@ (@ tptp.map_real_o F) Xs)) N) (@ F (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real (@ (@ tptp.map_real_real F) Xs)) N) (@ F (@ (@ tptp.nth_real Xs) N))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (Ti2 tptp.vEBT_VEBTi) (F1 (-> Bool Bool tptp.heap_Time_Heap_o)) (F12 (-> Bool Bool tptp.heap_Time_Heap_o)) (F22 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_Time_Heap_o)) (F23 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_Time_Heap_o))) (=> (= Ti Ti2) (=> (forall ((A3 Bool) (B3 Bool)) (@ (@ tptp.refine_Imp_refines_o (@ (@ F1 A3) B3)) (@ (@ F12 A3) B3))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (@ (@ tptp.refine_Imp_refines_o (@ (@ (@ (@ F22 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ F23 Info2) Deg2) TreeArray) Summary2))) (@ (@ tptp.refine_Imp_refines_o (@ (@ (@ tptp.vEBT_c6104975476656191286Heap_o F22) F1) Ti)) (@ (@ (@ tptp.vEBT_c6104975476656191286Heap_o F23) F12) Ti2)))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (Ti2 tptp.vEBT_VEBTi) (F1 (-> Bool Bool tptp.heap_T2636463487746394924on_nat)) (F12 (-> Bool Bool tptp.heap_T2636463487746394924on_nat)) (F22 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T2636463487746394924on_nat)) (F23 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T2636463487746394924on_nat))) (=> (= Ti Ti2) (=> (forall ((A3 Bool) (B3 Bool)) (@ (@ tptp.refine7594492741263601813on_nat (@ (@ F1 A3) B3)) (@ (@ F12 A3) B3))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (@ (@ tptp.refine7594492741263601813on_nat (@ (@ (@ (@ F22 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ F23 Info2) Deg2) TreeArray) Summary2))) (@ (@ tptp.refine7594492741263601813on_nat (@ (@ (@ tptp.vEBT_c6250501799366334488on_nat F22) F1) Ti)) (@ (@ (@ tptp.vEBT_c6250501799366334488on_nat F23) F12) Ti2)))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (Ti2 tptp.vEBT_VEBTi) (F1 (-> Bool Bool tptp.heap_T8145700208782473153_VEBTi)) (F12 (-> Bool Bool tptp.heap_T8145700208782473153_VEBTi)) (F22 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T8145700208782473153_VEBTi)) (F23 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T8145700208782473153_VEBTi))) (=> (= Ti Ti2) (=> (forall ((A3 Bool) (B3 Bool)) (@ (@ tptp.refine5565527176597971370_VEBTi (@ (@ F1 A3) B3)) (@ (@ F12 A3) B3))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (@ (@ tptp.refine5565527176597971370_VEBTi (@ (@ (@ (@ F22 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ F23 Info2) Deg2) TreeArray) Summary2))) (@ (@ tptp.refine5565527176597971370_VEBTi (@ (@ (@ tptp.vEBT_c6028912655521741485_VEBTi F22) F1) Ti)) (@ (@ (@ tptp.vEBT_c6028912655521741485_VEBTi F23) F12) Ti2)))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.real tptp.nat)) (Ys tptp.list_real)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_real_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_real Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.real tptp.real)) (Ys tptp.list_real)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_real_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_real Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> Bool tptp.nat)) (Ys tptp.list_o)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_o_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_o Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> Bool tptp.real)) (Ys tptp.list_o)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_o_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_o Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_nat_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_nat Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.nat tptp.real)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_nat_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_nat Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBTi tptp.nat)) (Ys tptp.list_VEBT_VEBTi)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBTi_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s7982070591426661849_VEBTi Ys)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBTi tptp.real)) (Ys tptp.list_VEBT_VEBTi)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBTi_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s7982070591426661849_VEBTi Ys)))))
% 7.27/7.61 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Ya tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (= X2 Ya) (=> (forall ((Z2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z2) (@ tptp.set_VEBT_VEBT2 Ya)) (= (@ F Z2) (@ G Z2)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) X2) (@ (@ tptp.map_VEBT_VEBT_nat G) Ya))))))
% 7.27/7.61 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Ya tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (= X2 Ya) (=> (forall ((Z2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z2) (@ tptp.set_VEBT_VEBT2 Ya)) (= (@ F Z2) (@ G Z2)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) X2) (@ (@ tptp.map_VEBT_VEBT_real G) Ya))))))
% 7.27/7.61 (assert (forall ((X2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((Z2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z2) (@ tptp.set_VEBT_VEBT2 X2)) (= (@ F Z2) (@ G Z2)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) X2) (@ (@ tptp.map_VEBT_VEBT_nat G) X2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((Z2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z2) (@ tptp.set_VEBT_VEBT2 X2)) (= (@ F Z2) (@ G Z2)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) X2) (@ (@ tptp.map_VEBT_VEBT_real G) X2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Xa tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (Fa (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((Z2 tptp.vEBT_VEBT) (Za tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z2) (@ tptp.set_VEBT_VEBT2 X2)) (=> (@ (@ tptp.member_VEBT_VEBT Za) (@ tptp.set_VEBT_VEBT2 Xa)) (=> (= (@ F Z2) (@ Fa Za)) (= Z2 Za))))) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) X2) (@ (@ tptp.map_VEBT_VEBT_nat Fa) Xa)) (= X2 Xa)))))
% 7.27/7.61 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Xa tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Fa (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((Z2 tptp.vEBT_VEBT) (Za tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z2) (@ tptp.set_VEBT_VEBT2 X2)) (=> (@ (@ tptp.member_VEBT_VEBT Za) (@ tptp.set_VEBT_VEBT2 Xa)) (=> (= (@ F Z2) (@ Fa Za)) (= Z2 Za))))) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) X2) (@ (@ tptp.map_VEBT_VEBT_real Fa) Xa)) (= X2 Xa)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Xs)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_int_int F) Xs) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_real_real F) Xs) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_nat_nat F) Xs) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (= Xs Ys) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (= Xs Ys) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Ys))))))
% 7.27/7.61 (assert (forall ((Ys tptp.list_real) (F (-> tptp.vEBT_VEBT tptp.real))) (= (exists ((Xs2 tptp.list_VEBT_VEBT)) (= Ys (@ (@ tptp.map_VEBT_VEBT_real F) Xs2))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Ys)) (exists ((Y tptp.vEBT_VEBT)) (= X3 (@ F Y))))))))
% 7.27/7.61 (assert (forall ((Ys tptp.list_nat) (F (-> tptp.vEBT_VEBT tptp.nat))) (= (exists ((Xs2 tptp.list_VEBT_VEBT)) (= Ys (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Ys)) (exists ((Y tptp.vEBT_VEBT)) (= X3 (@ F Y))))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (L tptp.list_VEBT_VEBT) (L4 tptp.list_VEBT_VEBT) (I tptp.nat)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_nat F))) (=> (= (@ _let_1 L) (@ _let_1 L4)) (= (@ F (@ (@ tptp.nth_VEBT_VEBT L) I)) (@ F (@ (@ tptp.nth_VEBT_VEBT L4) I)))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (L tptp.list_VEBT_VEBT) (L4 tptp.list_VEBT_VEBT) (I tptp.nat)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_real F))) (=> (= (@ _let_1 L) (@ _let_1 L4)) (= (@ F (@ (@ tptp.nth_VEBT_VEBT L) I)) (@ F (@ (@ tptp.nth_VEBT_VEBT L4) I)))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBTi)) (Xs tptp.list_VEBT_VEBTi) (K tptp.nat) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VE483055756984248624_VEBTi F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) K) Y3)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBT)) (Xs tptp.list_VEBT_VEBTi) (K tptp.nat) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VE7998069337340375161T_VEBT F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) K) Y3)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.nat)) (Xs tptp.list_VEBT_VEBTi) (K tptp.nat) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VEBT_VEBTi_nat F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) K) Y3)) (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi Bool)) (Xs tptp.list_VEBT_VEBTi) (K tptp.nat) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VEBT_VEBTi_o F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) K) Y3)) (@ (@ (@ tptp.list_update_o (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.real)) (Xs tptp.list_VEBT_VEBTi) (K tptp.nat) (Y3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VEBT_VEBTi_real F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) K) Y3)) (@ (@ (@ tptp.list_update_real (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi)) (Xs tptp.list_VEBT_VEBT) (K tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VE7029150624388687525_VEBTi F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) K) Y3)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (Xs tptp.list_VEBT_VEBT) (K tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VE8901447254227204932T_VEBT F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) K) Y3)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (K tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_nat F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) K) Y3)) (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT) (K tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_o F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) K) Y3)) (@ (@ (@ tptp.list_update_o (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (K tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_real F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) K) Y3)) (@ (@ (@ tptp.list_update_real (@ _let_1 Xs)) K) (@ F Y3))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (X2 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 X2))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X2)) (@ _let_1 L))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (X2 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 X2))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X2)) (@ _let_1 L))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_cnt2 X2) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 tptp.one_one_nat))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y3 (@ (@ 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)))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X2) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 tptp.one_one_real))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y3 (@ (@ 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)))))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X2) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 (@ 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)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y3 (@ (@ 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)))))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X2) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 (@ 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)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y3 (@ (@ 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)))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 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 Y3))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X2) _let_1)) (= (@ tptp.archim8280529875227126926d_real X2) Y3)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.rat) (Y3 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 Y3))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X2) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X2) Y3)))))))
% 7.27/7.61 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y3) Z)) (@ (@ tptp.ord_less_eq_real X2) Y3)))))
% 7.27/7.61 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y3) Z)) (@ (@ tptp.ord_less_eq_rat X2) Y3)))))
% 7.27/7.61 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y3) Z)) (@ (@ tptp.ord_less_eq_int X2) Y3)))))
% 7.27/7.61 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))))
% 7.27/7.61 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_rat X2) Y3))))))
% 7.27/7.61 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_int X2) Y3))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (X2 tptp.nat) (T tptp.vEBT_VEBT)) (@ (@ tptp.refine7594492741263601813on_nat (@ (@ tptp.vEBT_vebt_succi Ti) X2)) (@ (@ (@ tptp.vEBT_VEBT_vebt_succi T) Ti) X2))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (X2 tptp.nat) (T tptp.vEBT_VEBT)) (@ (@ tptp.refine7594492741263601813on_nat (@ (@ tptp.vEBT_vebt_predi Ti) X2)) (@ (@ (@ tptp.vEBT_VEBT_vebt_predi T) Ti) X2))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.refine5565527176597971370_VEBTi (@ tptp.vEBT_vebt_buildupi N)) (@ tptp.vEBT_V739175172307565963ildupi N))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (X2 tptp.nat) (T tptp.vEBT_VEBT)) (@ (@ tptp.refine5565527176597971370_VEBTi (@ (@ tptp.vEBT_vebt_inserti Ti) X2)) (@ (@ (@ tptp.vEBT_V3964819847710782039nserti T) Ti) X2))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 7.27/7.61 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 7.27/7.61 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 7.27/7.61 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.61 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 7.27/7.61 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (F (-> Bool Bool tptp.heap_T8145700208782473153_VEBTi)) (Bnd (-> Bool Bool tptp.nat)) (F5 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T8145700208782473153_VEBTi)) (Bnd2 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.nat))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= Ti (@ (@ tptp.vEBT_Leafi A3) B3)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ F A3) B3)) (@ (@ Bnd A3) B3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (=> (= Ti (@ (@ (@ (@ tptp.vEBT_Nodei Info2) Deg2) TreeArray) Summary2)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ (@ (@ F5 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ Bnd2 Info2) Deg2) TreeArray) Summary2)))) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ (@ tptp.vEBT_c6028912655521741485_VEBTi F5) F) Ti)) (@ (@ (@ tptp.vEBT_case_VEBTi_nat Bnd2) Bnd) Ti))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (F (-> Bool Bool tptp.heap_Time_Heap_o)) (Bnd (-> Bool Bool tptp.nat)) (F5 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_Time_Heap_o)) (Bnd2 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.nat))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= Ti (@ (@ tptp.vEBT_Leafi A3) B3)) (@ (@ tptp.time_TBOUND_o (@ (@ F A3) B3)) (@ (@ Bnd A3) B3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (=> (= Ti (@ (@ (@ (@ tptp.vEBT_Nodei Info2) Deg2) TreeArray) Summary2)) (@ (@ tptp.time_TBOUND_o (@ (@ (@ (@ F5 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ Bnd2 Info2) Deg2) TreeArray) Summary2)))) (@ (@ tptp.time_TBOUND_o (@ (@ (@ tptp.vEBT_c6104975476656191286Heap_o F5) F) Ti)) (@ (@ (@ tptp.vEBT_case_VEBTi_nat Bnd2) Bnd) Ti))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (F (-> Bool Bool tptp.heap_T2636463487746394924on_nat)) (Bnd (-> Bool Bool tptp.nat)) (F5 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_T2636463487746394924on_nat)) (Bnd2 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.nat))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= Ti (@ (@ tptp.vEBT_Leafi A3) B3)) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ F A3) B3)) (@ (@ Bnd A3) B3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (=> (= Ti (@ (@ (@ (@ tptp.vEBT_Nodei Info2) Deg2) TreeArray) Summary2)) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ (@ (@ F5 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ Bnd2 Info2) Deg2) TreeArray) Summary2)))) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ (@ tptp.vEBT_c6250501799366334488on_nat F5) F) Ti)) (@ (@ (@ tptp.vEBT_case_VEBTi_nat Bnd2) Bnd) Ti))))))
% 7.27/7.61 (assert (forall ((Ti tptp.vEBT_VEBTi) (F (-> Bool Bool tptp.heap_Time_Heap_nat)) (Bnd (-> Bool Bool tptp.nat)) (F5 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.heap_Time_Heap_nat)) (Bnd2 (-> tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi tptp.nat))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= Ti (@ (@ tptp.vEBT_Leafi A3) B3)) (@ (@ tptp.time_TBOUND_nat (@ (@ F A3) B3)) (@ (@ Bnd A3) B3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeArray tptp.array_VEBT_VEBTi) (Summary2 tptp.vEBT_VEBTi)) (=> (= Ti (@ (@ (@ (@ tptp.vEBT_Nodei Info2) Deg2) TreeArray) Summary2)) (@ (@ tptp.time_TBOUND_nat (@ (@ (@ (@ F5 Info2) Deg2) TreeArray) Summary2)) (@ (@ (@ (@ Bnd2 Info2) Deg2) TreeArray) Summary2)))) (@ (@ tptp.time_TBOUND_nat (@ (@ (@ tptp.vEBT_c1335663792808957512ap_nat F5) F) Ti)) (@ (@ (@ tptp.vEBT_case_VEBTi_nat Bnd2) Bnd) Ti))))))
% 7.27/7.61 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X2)) (@ tptp.archim7778729529865785530nd_rat Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X2)) (@ tptp.archim7802044766580827645g_real X2))))
% 7.27/7.61 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N4)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N4) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N4)))))))
% 7.27/7.61 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N4)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N4) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N4)))))))
% 7.27/7.61 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N4)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N4) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N4)))))))
% 7.27/7.61 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y3) Z)) (@ (@ tptp.ord_less_real X2) Y3)))))
% 7.27/7.61 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y3) Z)) (@ (@ tptp.ord_less_rat X2) Y3)))))
% 7.27/7.61 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y3) Z)) (@ (@ tptp.ord_less_int X2) Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 7.27/7.61 (assert (forall ((Q3 tptp.code_integer) (R2 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q3) R2)) (= R2 tptp.zero_z3403309356797280102nteger))))
% 7.27/7.61 (assert (forall ((Q3 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R2)) (= R2 tptp.zero_zero_nat))))
% 7.27/7.61 (assert (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R2)) (= R2 tptp.zero_zero_int))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.int)) (let ((_let_1 (not (= Y3 tptp.one_one_int)))) (=> (= (@ tptp.vEBT_V9176841429113362141ildupi X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((N3 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 N3) _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_5 (@ (@ tptp.power_power_int _let_4) _let_3))) (let ((_let_6 (@ tptp.suc _let_3))) (let ((_let_7 (@ tptp.vEBT_V9176841429113362141ildupi _let_6))) (let ((_let_8 (@ (@ tptp.times_times_int _let_7) _let_5))) (let ((_let_9 (@ tptp.bit0 _let_1))) (let ((_let_10 (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_9)))) (let ((_let_11 (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))) (let ((_let_12 (@ (@ tptp.dvd_dvd_nat _let_2) N3))) (=> (= X2 (@ tptp.suc (@ tptp.suc N3))) (not (and (=> _let_12 (= Y3 (@ _let_11 (@ (@ tptp.plus_plus_int _let_7) (@ (@ tptp.plus_plus_int (@ _let_10 _let_5)) (@ (@ tptp.times_times_int _let_4) _let_8)))))) (=> (not _let_12) (= Y3 (@ _let_11 (@ (@ tptp.plus_plus_int (@ tptp.vEBT_V9176841429113362141ildupi (@ tptp.suc _let_6))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 _let_9))) _let_5)) (@ _let_10 _let_8)))))))))))))))))))))))))))))
% 7.27/7.61 (assert (= tptp.vEBT_VEBT_highi (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ tptp.heap_Time_return_nat (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBTi) (A2 tptp.array_VEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ (@ tptp.array_nth_VEBT_VEBTi A2) I)) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_VEBT_VEBTi Xs) I)))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (A2 tptp.array_o)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.snga_assn_o A2) Xs)) (@ (@ tptp.array_nth_o A2) I)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_o A2) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_o Xs) I)))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (Xs tptp.list_option_nat) (A2 tptp.array_option_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6086282163384603972on_nat Xs)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.snga_assn_option_nat A2) Xs)) (@ (@ tptp.array_nth_option_nat A2) I)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_option_nat A2) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_option_nat Xs) I)))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (A2 tptp.array_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_nat A2) Xs)) (@ (@ tptp.array_nth_nat A2) I)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_nat A2) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_nat Xs) I)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A2) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A2) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A2) _let_1))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (Ps tptp.assn) (F3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F3)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi Ps) C2) (lambda ((X3 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ Q X3)) F3)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (Ps tptp.assn) (F3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F3)) (@ (@ (@ tptp.hoare_hoare_triple_o Ps) C2) (lambda ((X3 Bool)) (@ (@ tptp.times_times_assn (@ Q X3)) F3)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (Ps tptp.assn) (F3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F3)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat Ps) C2) (lambda ((X3 tptp.option_nat)) (@ (@ tptp.times_times_assn (@ Q X3)) F3)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (Ps tptp.assn) (F3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F3)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat Ps) C2) (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_assn (@ Q X3)) F3)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ tptp.heap_Time_return_nat (@ (@ tptp.vEBT_VEBT_high X2) N)) (@ (@ tptp.vEBT_VEBT_highi X2) N))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ tptp.heap_Time_return_nat (@ (@ tptp.vEBT_VEBT_low X2) N)) (@ (@ tptp.vEBT_VEBT_lowi X2) N))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) A2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) A2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) A2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) A2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B2) A2)) (@ (@ tptp.divide_divide_nat C2) A2)) (@ (@ tptp.dvd_dvd_nat B2) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B2) A2)) (@ (@ tptp.divide_divide_int C2) A2)) (@ (@ tptp.dvd_dvd_int B2) C2)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 7.27/7.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B2) A2)) (@ (@ tptp.times_times_nat C2) A2)) (@ (@ tptp.dvd_dvd_nat B2) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B2) A2)) (@ (@ tptp.times_times_int C2) A2)) (@ (@ tptp.dvd_dvd_int B2) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B2)) (@ _let_1 C2)) (@ (@ tptp.dvd_dvd_nat B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B2)) (@ _let_1 C2)) (@ (@ tptp.dvd_dvd_int B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (C2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A2) C2)) (@ (@ tptp.times_times_complex B2) C2)) (or (= C2 tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) C2)) (or (= C2 tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) C2)) (or (= C2 tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (or (= C2 tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A2) B2)))))
% 7.27/7.61 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C2))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A2)) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A2) B2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C2))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A2)) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A2) B2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A2)) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A2) B2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B2)) (or (= C2 tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A2) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.times_times_real C2) A2))) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.times_times_rat C2) A2))) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.times_times_nat C2) A2))) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.times_times_int C2) A2))) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C2) A2)) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C2) A2)) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) A2)) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) A2)) B2)) (@ _let_1 B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.one_one_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B2)) tptp.one_one_int)))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) C2)) (@ (@ tptp.divide_divide_nat B2) C2))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) C2)) (@ (@ tptp.divide_divide_int B2) C2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A2) B2)) tptp.one_one_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A2) B2)) tptp.one_one_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A2)) tptp.one_one_nat))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A2)) tptp.one_one_int))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A2)) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A2)) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A2)) A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A2)) A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) B2) (= (@ (@ tptp.times_times_nat A2) (@ (@ tptp.divide_divide_nat B2) A2)) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) B2) (= (@ (@ tptp.times_times_int A2) (@ (@ tptp.divide_divide_int B2) A2)) B2))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A2) B2)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A2) C2)) (@ (@ tptp.divide_divide_int B2) C2))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 7.27/7.61 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A2)) (@ (@ tptp.divide_divide_nat B2) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int tptp.one_one_int) A2)) (@ (@ tptp.divide_divide_int B2) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A2)) A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A2)) A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2))) (not (= (not (@ _let_1 A2)) (not (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2))) (not (= (not (@ _let_1 A2)) (not (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)) (= (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)) (= (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 7.27/7.61 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) (not (@ _let_1 A2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) (not (@ _let_1 A2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A2) B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A2)) _let_1) (@ (@ tptp.divide_divide_nat A2) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A2)) _let_1) (@ (@ tptp.divide_divide_int A2) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A2)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) _let_1)) tptp.one_one_nat))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A2)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) _let_1)) tptp.one_one_int))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A2) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A2) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) tptp.zero_z3403309356797280102nteger) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real)))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) _let_1)) tptp.zero_z3403309356797280102nteger) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) _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 A2) tptp.zero_zero_real))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) _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 A2) tptp.zero_zero_rat))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) _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 A2) tptp.zero_zero_int))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A2) _let_1))) tptp.one_one_nat) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A2) _let_1))) tptp.one_one_int) A2)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A2 tptp.zero_z3403309356797280102nteger))) (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A2 tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A2 tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A2 tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A2)))))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _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 A2) tptp.zero_zero_real)) (and _let_2 (= A2 tptp.zero_zero_real)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_1)) tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger)) (and _let_2 (= A2 tptp.zero_z3403309356797280102nteger)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _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 A2) tptp.zero_zero_rat)) (and _let_2 (= A2 tptp.zero_zero_rat)))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _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 A2) tptp.zero_zero_int)) (and _let_2 (= A2 tptp.zero_zero_int)))))))))
% 7.27/7.61 (assert (forall ((A2 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) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A2)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A2) _let_2))))))))
% 7.27/7.61 (assert (forall ((A2 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) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A2)) _let_2) (@ (@ tptp.divide_divide_nat A2) _let_2))))))))
% 7.27/7.61 (assert (forall ((A2 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) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A2)) _let_2) (@ (@ tptp.divide_divide_int A2) _let_2))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B2))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B2))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.dvd_dvd_assn tptp.one_one_assn) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A2)))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A2) (not (forall ((K2 tptp.real)) (not (= A2 (@ (@ tptp.times_times_real B2) K2))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B2) A2) (not (forall ((K2 tptp.rat)) (not (= A2 (@ (@ tptp.times_times_rat B2) K2))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (not (forall ((K2 tptp.nat)) (not (= A2 (@ (@ tptp.times_times_nat B2) K2))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (not (forall ((K2 tptp.int)) (not (= A2 (@ (@ tptp.times_times_int B2) K2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (K tptp.real)) (=> (= A2 (@ (@ tptp.times_times_real B2) K)) (@ (@ tptp.dvd_dvd_real B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (K tptp.rat)) (=> (= A2 (@ (@ tptp.times_times_rat B2) K)) (@ (@ tptp.dvd_dvd_rat B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (K tptp.nat)) (=> (= A2 (@ (@ tptp.times_times_nat B2) K)) (@ (@ tptp.dvd_dvd_nat B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (K tptp.int)) (=> (= A2 (@ (@ tptp.times_times_int B2) K)) (@ (@ tptp.dvd_dvd_int B2) A2))))
% 7.27/7.61 (assert (= tptp.dvd_dvd_real (lambda ((B6 tptp.real) (A5 tptp.real)) (exists ((K3 tptp.real)) (= A5 (@ (@ tptp.times_times_real B6) K3))))))
% 7.27/7.61 (assert (= tptp.dvd_dvd_rat (lambda ((B6 tptp.rat) (A5 tptp.rat)) (exists ((K3 tptp.rat)) (= A5 (@ (@ tptp.times_times_rat B6) K3))))))
% 7.27/7.61 (assert (= tptp.dvd_dvd_nat (lambda ((B6 tptp.nat) (A5 tptp.nat)) (exists ((K3 tptp.nat)) (= A5 (@ (@ tptp.times_times_nat B6) K3))))))
% 7.27/7.61 (assert (= tptp.dvd_dvd_int (lambda ((B6 tptp.int) (A5 tptp.int)) (exists ((K3 tptp.int)) (= A5 (@ (@ tptp.times_times_int B6) K3))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_nat B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A2) B2)) C2) (@ (@ tptp.dvd_dvd_real A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) B2)) C2) (@ (@ tptp.dvd_dvd_rat A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B2)) C2) (@ (@ tptp.dvd_dvd_nat A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B2)) C2) (@ (@ tptp.dvd_dvd_int A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A2) (@ (@ tptp.times_times_real A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.dvd_dvd_rat A2) (@ (@ tptp.times_times_rat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A2) B2) (=> (@ (@ tptp.dvd_dvd_real C2) D2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A2) C2)) (@ (@ tptp.times_times_real B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A2) B2) (=> (@ (@ tptp.dvd_dvd_rat C2) D2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) C2)) (@ (@ tptp.times_times_rat B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) B2) (=> (@ (@ tptp.dvd_dvd_nat C2) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) B2) (=> (@ (@ tptp.dvd_dvd_int C2) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A2) B2)) C2) (@ (@ tptp.dvd_dvd_real B2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) B2)) C2) (@ (@ tptp.dvd_dvd_rat B2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B2)) C2) (@ (@ tptp.dvd_dvd_nat B2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B2)) C2) (@ (@ tptp.dvd_dvd_int B2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A2) (@ (@ tptp.times_times_real B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.dvd_dvd_rat A2) (@ (@ tptp.times_times_rat B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int B2) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C2) B2)) (@ _let_1 (@ (@ tptp.minus_minus_int B2) C2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y3) Z)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y3) Z)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y3) Z)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.complex) (A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) C2) (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_real A2) C2) (@ (@ tptp.divide_divide_real B2) C2)) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_rat A2) C2) (@ (@ tptp.divide_divide_rat B2) C2)) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_nat A2) C2) (@ (@ tptp.divide_divide_nat B2) C2)) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_int A2) C2) (@ (@ tptp.divide_divide_int B2) C2)) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (C2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C2))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A2) C2) (@ (@ tptp.divide1717551699836669952omplex B2) C2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C2))) (=> (= (@ (@ tptp.divide_divide_real A2) C2) (@ (@ tptp.divide_divide_real B2) C2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (C2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C2))) (=> (= (@ (@ tptp.divide_divide_rat A2) C2) (@ (@ tptp.divide_divide_rat B2) C2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (= (@ (@ tptp.divide_divide_nat A2) C2) (@ (@ tptp.divide_divide_nat B2) C2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (= (@ (@ tptp.divide_divide_int A2) C2) (@ (@ tptp.divide_divide_int B2) C2)) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= A2 B2)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat D2) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D2)) (@ (@ tptp.divide_divide_nat B2) D2)) (@ _let_1 B2)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.dvd_dvd_int D2) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (= (@ (@ tptp.divide_divide_int (@ _let_1 D2)) (@ (@ tptp.divide_divide_int B2) D2)) (@ _let_1 B2)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y3) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y3) N)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y3) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y3) N)))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y3) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y3) N)))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y3) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y3) N)))))
% 7.27/7.61 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y3) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y3) N)))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) A2)))) (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) B2)))) (@ (@ tptp.dvd_dvd_complex A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A2)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B2)))) (@ (@ tptp.dvd_dvd_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A2)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B2)))) (@ (@ tptp.dvd_dvd_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) A2)))) (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) B2)))) (and (@ (@ tptp.dvd_dvd_complex A2) B2) (not (@ (@ tptp.dvd_dvd_complex B2) A2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A2)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B2)))) (and (@ (@ tptp.dvd_dvd_nat A2) B2) (not (@ (@ tptp.dvd_dvd_nat B2) A2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A2)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B2)))) (and (@ (@ tptp.dvd_dvd_int A2) B2) (not (@ (@ tptp.dvd_dvd_int B2) A2))))))
% 7.27/7.61 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.27/7.61 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 7.27/7.61 (assert (forall ((D2 tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X8) S2)))) (=> (@ (@ tptp.ord_less_real Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X8) S2)))) (=> (@ (@ tptp.ord_less_rat Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X8) S2)))) (=> (@ (@ tptp.ord_less_nat Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X8) S2)))) (=> (@ (@ tptp.ord_less_int Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X8) S2))))) (=> (@ (@ tptp.ord_less_real Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X8) S2))))) (=> (@ (@ tptp.ord_less_rat Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X8) S2))))) (=> (@ (@ tptp.ord_less_nat Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X8) S2))))) (=> (@ (@ tptp.ord_less_int Z2) X8) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X8) S2)))) (=> (@ (@ tptp.ord_less_real X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X8) S2)))) (=> (@ (@ tptp.ord_less_rat X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X8) S2)))) (=> (@ (@ tptp.ord_less_nat X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X8) S2)))) (=> (@ (@ tptp.ord_less_int X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X8 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X8) S2))))) (=> (@ (@ tptp.ord_less_real X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X8 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X8) S2))))) (=> (@ (@ tptp.ord_less_rat X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X8 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X8) S2))))) (=> (@ (@ tptp.ord_less_nat X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X8 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X8) S2))))) (=> (@ (@ tptp.ord_less_int X8) Z2) (= _let_1 _let_1)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A2) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B2) tptp.zero_zero_complex) (= A2 tptp.zero_zero_complex)))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A2) (= (= (@ (@ tptp.divide_divide_real A2) B2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real)))))
% 7.27/7.61 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B2) A2) (= (= (@ (@ tptp.divide_divide_rat A2) B2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (= (= (@ (@ tptp.divide_divide_nat A2) B2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (= (= (@ (@ tptp.divide_divide_int A2) B2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B2) A2) (@ (@ tptp.times_times_nat C2) A2)) (= B2 C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B2) A2) (@ (@ tptp.times_times_int C2) A2)) (= B2 C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (= (@ _let_1 B2) (@ _let_1 C2)) (= B2 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B2)) C2) (@ (@ tptp.dvd_dvd_nat B2) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B2)) C2) (@ (@ tptp.dvd_dvd_int B2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B2)) C2) (@ (@ tptp.dvd_dvd_nat A2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B2)) C2) (@ (@ tptp.dvd_dvd_int A2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C2) B2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C2) B2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B2)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int)))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) C2)) (@ (@ tptp.divide_divide_nat B2) C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) C2)) (@ (@ tptp.divide_divide_int B2) C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) A2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) C2)) (@ (@ tptp.divide_divide_nat B2) C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) A2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) C2)) (@ (@ tptp.divide_divide_int B2) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B2) A2) (@ (@ tptp.divide_divide_nat C2) A2)) (= B2 C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B2) A2) (@ (@ tptp.divide_divide_int C2) A2)) (= B2 C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A2) B2)) C2) (@ (@ tptp.dvd_dvd_nat A2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A2) B2)) C2) (@ (@ tptp.dvd_dvd_int A2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C2) B2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C2) B2)) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) C2)) A2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B2) A2)) C2)))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) C2)) A2) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B2) A2)) C2)))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat C2) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (=> (@ (@ tptp.dvd_dvd_int C2) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat C2) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C2)) (@ (@ tptp.times_times_nat (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.dvd_dvd_int C2) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C2)) (@ (@ tptp.times_times_int (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (let ((_let_2 (@ (@ tptp.times_times_nat B2) C2))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A2) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (let ((_let_2 (@ (@ tptp.times_times_int B2) C2))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A2) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) C2)) B2) (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.divide_divide_nat B2) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) C2)) B2) (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.divide_divide_int B2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (D2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (=> (@ (@ tptp.dvd_dvd_nat D2) C2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) (@ (@ tptp.divide_divide_nat C2) D2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) D2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (D2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (=> (@ (@ tptp.dvd_dvd_int D2) C2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) (@ (@ tptp.divide_divide_int C2) D2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) D2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A2) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A2) B2)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A2) B2)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (N tptp.nat) (B2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (N tptp.nat) (B2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.complex) (N tptp.nat) (B2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A2))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y3) M))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y3) M))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y3) M))))))
% 7.27/7.61 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y3) M))))))
% 7.27/7.61 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y3) M))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.entails P) (@ Q X2)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) (@ tptp.heap_T3630416162098727440_VEBTi X2)) Q))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Q (-> Bool tptp.assn)) (X2 Bool)) (=> (@ (@ tptp.entails P) (@ Q X2)) (@ (@ (@ tptp.hoare_hoare_triple_o P) (@ tptp.heap_Time_return_o X2)) Q))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Q (-> tptp.option_nat tptp.assn)) (X2 tptp.option_nat)) (=> (@ (@ tptp.entails P) (@ Q X2)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) (@ tptp.heap_T3487192422709364219on_nat X2)) Q))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Q (-> tptp.nat tptp.assn)) (X2 tptp.nat)) (=> (@ (@ tptp.entails P) (@ Q X2)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) (@ tptp.heap_Time_return_nat X2)) Q))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A2)) (or (@ _let_1 A2) (= M tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A2)) (or (@ _let_1 A2) (= M tptp.zero_zero_nat))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 7.27/7.61 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X3 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X3))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X3) tptp.zero_zero_complex)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X3 tptp.real)) (@ P (@ (@ tptp.times_times_real L) X3))) (exists ((X3 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X3) tptp.zero_zero_real)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X3 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X3))) (exists ((X3 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X3) tptp.zero_zero_rat)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X3 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X3) tptp.zero_zero_nat)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X3 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X3) tptp.zero_zero_int)) (@ P X3))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (not (=> (not (= A2 tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B2 (@ (@ tptp.times_times_nat A2) C3)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (not (=> (not (= A2 tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B2 (@ (@ tptp.times_times_int A2) C3)))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A2) B2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A2) B2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) B2) (= (= (@ (@ tptp.divide_divide_nat B2) A2) C2) (= B2 (@ (@ tptp.times_times_nat C2) A2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A2) B2) (= (= (@ (@ tptp.divide_divide_int B2) A2) C2) (= B2 (@ (@ tptp.times_times_int C2) A2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A2) B2)) C2) (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat C2) B2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A2) B2)) C2) (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int C2) B2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (not (= C2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B2) (= (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.divide_divide_nat B2) C2)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) C2)) B2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (not (= C2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C2) B2) (= (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.divide_divide_int B2) C2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) C2)) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (not (= C2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) B2) (=> (@ (@ tptp.dvd_dvd_nat C2) D2) (= (= (@ (@ tptp.divide_divide_nat B2) A2) (@ (@ tptp.divide_divide_nat D2) C2)) (= (@ (@ tptp.times_times_nat B2) C2) (@ (@ tptp.times_times_nat A2) D2)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (not (= C2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A2) B2) (=> (@ (@ tptp.dvd_dvd_int C2) D2) (= (= (@ (@ tptp.divide_divide_int B2) A2) (@ (@ tptp.divide_divide_int D2) C2)) (= (@ (@ tptp.times_times_int B2) C2) (@ (@ tptp.times_times_int A2) D2)))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.real) (D tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D) (forall ((X8 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X8) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X8) (@ (@ tptp.times_times_real K5) D))) T))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.rat) (D tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D) (forall ((X8 tptp.rat) (K5 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X8) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X8) (@ (@ tptp.times_times_rat K5) D))) T))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (D tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X8 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X8) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X8) (@ (@ tptp.times_times_int K5) D))) T))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.real) (D tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D) (forall ((X8 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X8) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X8) (@ (@ tptp.times_times_real K5) D))) T)))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.rat) (D tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D) (forall ((X8 tptp.rat) (K5 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X8) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X8) (@ (@ tptp.times_times_rat K5) D))) T)))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (D tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X8 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X8) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X8) (@ (@ tptp.times_times_int K5) D))) T)))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A2) B2) C2) (= A2 (@ (@ tptp.times_times_nat C2) B2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A2) B2) C2) (= A2 (@ (@ tptp.times_times_int C2) B2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= A2 (@ (@ tptp.divide_divide_nat C2) B2)) (= (@ (@ tptp.times_times_nat A2) B2) C2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= A2 (@ (@ tptp.divide_divide_int C2) B2)) (= (@ (@ tptp.times_times_int A2) B2) C2)))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) A2) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) A2) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) C2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) C2)) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) C2) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) C2)) B2)))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A2) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A2) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A2) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.time_TBOUND_nat (@ tptp.heap_Time_return_nat X2)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 Bool)) (@ (@ tptp.time_TBOUND_o (@ tptp.heap_Time_return_o X2)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBTi)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ tptp.heap_T3630416162098727440_VEBTi X2)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.option_nat)) (@ (@ tptp.time_T8353473612707095248on_nat (@ tptp.heap_T3487192422709364219on_nat X2)) tptp.one_one_nat)))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.time_time_nat (@ tptp.heap_Time_return_nat X2)) H2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 Bool) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.time_time_o (@ tptp.heap_Time_return_o X2)) H2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBTi) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.time_time_VEBT_VEBTi (@ tptp.heap_T3630416162098727440_VEBTi X2)) H2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((X2 tptp.option_nat) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.time_time_option_nat (@ tptp.heap_T3487192422709364219on_nat X2)) H2) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C2) (@ (@ tptp.times_times_assn (@ _let_1 C2)) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (let ((_let_2 (@ tptp.times_times_assn B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.27/7.61 (assert (= tptp.times_times_assn (lambda ((A5 tptp.assn) (B6 tptp.assn)) (@ (@ tptp.times_times_assn B6) A5))))
% 7.27/7.61 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.times_times_assn B2) C2))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ (@ tptp.entails P) Q))) (=> _let_1 _let_1))))
% 7.27/7.61 (assert (forall ((Xs tptp.array_VEBT_VEBTi) (I tptp.nat)) (@ (@ tptp.time_T5737551269749752165_VEBTi (@ (@ tptp.array_nth_VEBT_VEBTi Xs) I)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Xs tptp.array_o) (I tptp.nat)) (@ (@ tptp.time_TBOUND_o (@ (@ tptp.array_nth_o Xs) I)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Xs tptp.array_option_nat) (I tptp.nat)) (@ (@ tptp.time_T8353473612707095248on_nat (@ (@ tptp.array_nth_option_nat Xs) I)) tptp.one_one_nat)))
% 7.27/7.61 (assert (forall ((Xs tptp.array_nat) (I tptp.nat)) (@ (@ tptp.time_TBOUND_nat (@ (@ tptp.array_nth_nat Xs) I)) tptp.one_one_nat)))
% 7.27/7.61 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.27/7.61 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A2)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A2)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 7.27/7.61 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 7.27/7.61 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A2) (not (forall ((B3 tptp.nat)) (not (= A2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A2) (not (forall ((B3 tptp.int)) (not (= A2 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))))
% 7.27/7.61 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A5 tptp.nat) (B6 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A5) (@ _let_2 B6)) (= (@ (@ tptp.divide_divide_nat A5) _let_1) (@ (@ tptp.divide_divide_nat B6) _let_1))))))))
% 7.27/7.61 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A5 tptp.int) (B6 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A5) (@ _let_2 B6)) (= (@ (@ tptp.divide_divide_int A5) _let_1) (@ (@ tptp.divide_divide_int B6) _let_1))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A2) (@ (@ tptp.times_times_nat B2) A2)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A2) (@ (@ tptp.times_times_int B2) A2)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A2) (@ (@ tptp.times_times_nat A2) B2)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A2) (@ (@ tptp.times_times_int A2) B2)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (not (=> (not (= A2 tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A2) B3) (=> (= (@ _let_1 B3) A2) (=> (= (@ (@ tptp.times_times_nat A2) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C2) A2) (@ (@ tptp.times_times_nat C2) B3)))))))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (not (=> (not (= A2 tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A2) B3) (=> (= (@ _let_1 B3) A2) (=> (= (@ (@ tptp.times_times_int A2) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C2) A2) (@ (@ tptp.times_times_int C2) B3)))))))))))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X2))) (=> (not (= X2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (not (= X2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X2) (@ (@ tptp.power_power_rat X2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X2) (@ (@ tptp.power_power_nat X2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X2) (@ (@ tptp.power_power_real X2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X2) (@ (@ tptp.power_power_int X2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X2) (@ (@ tptp.power_power_complex X2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X2) (@ (@ tptp.power_8256067586552552935nteger X2) N)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A2) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A2) _let_1)) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A2) _let_1)) A2)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B2) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N))))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A2)) (and (@ _let_1 A2) (not (= M tptp.zero_zero_nat)))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A2)) (and (@ _let_1 A2) (not (= M tptp.zero_zero_nat)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (X2 tptp.vEBT_VEBTi)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) (@ tptp.heap_T3630416162098727440_VEBTi X2)) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn (= R5 X2)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (X2 Bool)) (@ (@ (@ tptp.hoare_hoare_triple_o P) (@ tptp.heap_Time_return_o X2)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn (= R5 X2)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (X2 tptp.option_nat)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) (@ tptp.heap_T3487192422709364219on_nat X2)) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn (= R5 X2)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (X2 tptp.nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) (@ tptp.heap_Time_return_nat X2)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn (= R5 X2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A2)) (not (forall ((B3 tptp.nat)) (not (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A2)) (not (forall ((B3 tptp.int)) (not (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or _let_2 (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or _let_2 (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or _let_2 (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or _let_2 (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)) (@ _let_1 A2))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)) (@ _let_1 A2))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)) (@ _let_1 A2))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)) (@ _let_1 A2))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 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 A2) N)))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A2 tptp.zero_z3403309356797280102nteger))) (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A2 tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A2 tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A2 tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A2))))))))
% 7.27/7.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.entails (@ (@ tptp.times_times_assn B) A)) C))))
% 7.27/7.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.entails A) B) (@ (@ tptp.entails (@ (@ tptp.times_times_assn A) C)) (@ (@ tptp.times_times_assn B) C)))))
% 7.27/7.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 (@ (@ tptp.times_times_assn B) C)) (@ _let_1 (@ (@ tptp.times_times_assn C) B))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (R tptp.assn) (Ps tptp.assn) (F3 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails Ps))) (=> (@ (@ tptp.entails P) R) (=> (@ _let_1 (@ (@ tptp.times_times_assn P) F3)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn R) F3)) Q) (@ _let_1 Q)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) 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 A2) tptp.zero_zero_real)) (and _let_1 (= A2 tptp.zero_zero_real))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) N)) tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger)) (and _let_1 (= A2 tptp.zero_z3403309356797280102nteger))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) 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 A2) tptp.zero_zero_rat)) (and _let_1 (= A2 tptp.zero_zero_rat))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) 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 A2) tptp.zero_zero_int)) (and _let_1 (= A2 tptp.zero_zero_int))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2) Q) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn R) P)) C2) (lambda ((X3 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn R) (@ Q X3)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_hoare_triple_o P) C2) Q) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.times_times_assn R) P)) C2) (lambda ((X3 Bool)) (@ (@ tptp.times_times_assn R) (@ Q X3)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat P) C2) Q) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ (@ tptp.times_times_assn R) P)) C2) (lambda ((X3 tptp.option_nat)) (@ (@ tptp.times_times_assn R) (@ Q X3)))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (R tptp.assn)) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat P) C2) Q) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.times_times_assn R) P)) C2) (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_assn R) (@ Q X3)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 7.27/7.61 (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))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) (@ _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 A2) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) (@ _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 A2) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) (@ _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 A2) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (not (= Y3 _let_1)))) (=> (= (@ tptp.vEBT_V441764108873111860ildupi X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_2) (=> (=> (= X2 _let_1) _let_2) (not (forall ((N3 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 N3) _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) N3))) (=> (= X2 (@ tptp.suc (@ tptp.suc N3))) (not (and (=> _let_10 (= Y3 (@ 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) (= Y3 (@ 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))))))))))))))))))))))))))))))
% 7.27/7.61 (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.divide_divide_nat N) _let_2)))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.power_power_nat _let_2))) (let ((_let_6 (@ tptp.vEBT_VEBT_Tb2 _let_3))) (let ((_let_7 (@ tptp.times_times_nat _let_6))) (let ((_let_8 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_1))))) (let ((_let_9 (@ tptp.vEBT_VEBT_Tb2 (@ tptp.suc (@ tptp.suc N))))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_2) N))) (and (=> _let_10 (= _let_9 (@ (@ tptp.plus_plus_nat (@ _let_8 _let_6)) (@ _let_7 (@ _let_5 _let_3))))) (=> (not _let_10) (= _let_9 (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_VEBT_Tb2 _let_4))) (@ _let_7 (@ _let_5 _let_4))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))) (=> (= (@ tptp.vEBT_VEBT_Tb2 X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ (@ tptp.divide_divide_nat N3) _let_2)))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.power_power_nat _let_2))) (let ((_let_6 (@ tptp.vEBT_VEBT_Tb2 _let_3))) (let ((_let_7 (@ tptp.times_times_nat _let_6))) (let ((_let_8 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_1))))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_2) N3))) (=> (= X2 (@ tptp.suc (@ tptp.suc N3))) (not (and (=> _let_9 (= Y3 (@ (@ tptp.plus_plus_nat (@ _let_8 _let_6)) (@ _let_7 (@ _let_5 _let_3))))) (=> (not _let_9) (= Y3 (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_VEBT_Tb2 _let_4))) (@ _let_7 (@ _let_5 _let_4)))))))))))))))))))))))))
% 7.27/7.61 (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.divide_divide_nat N) _let_2)))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.power_power_int (@ tptp.numeral_numeral_int _let_1)))) (let ((_let_6 (@ tptp.vEBT_VEBT_Tb _let_3))) (let ((_let_7 (@ tptp.times_times_int _let_6))) (let ((_let_8 (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 _let_1))))) (let ((_let_9 (@ tptp.vEBT_VEBT_Tb (@ tptp.suc (@ tptp.suc N))))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_2) N))) (and (=> _let_10 (= _let_9 (@ (@ tptp.plus_plus_int (@ _let_8 _let_6)) (@ _let_7 (@ _let_5 _let_3))))) (=> (not _let_10) (= _let_9 (@ (@ tptp.plus_plus_int (@ _let_8 (@ tptp.vEBT_VEBT_Tb _let_4))) (@ _let_7 (@ _let_5 _let_4))))))))))))))))))
% 7.27/7.61 (assert (forall ((Ps tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (P tptp.assn) (R tptp.assn) (F3 tptp.assn)) (=> (@ (@ tptp.rep_assn Ps) H2) (=> (@ (@ tptp.entails P) R) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F3)) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn R) F3)) H2))))))
% 7.27/7.61 (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.numeral_numeral_int _let_1))) (let ((_let_5 (@ (@ tptp.power_power_int _let_4) _let_3))) (let ((_let_6 (@ tptp.suc _let_3))) (let ((_let_7 (@ tptp.vEBT_V9176841429113362141ildupi _let_6))) (let ((_let_8 (@ (@ tptp.times_times_int _let_7) _let_5))) (let ((_let_9 (@ tptp.bit0 _let_1))) (let ((_let_10 (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_9)))) (let ((_let_11 (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))) (let ((_let_12 (@ tptp.vEBT_V9176841429113362141ildupi (@ tptp.suc (@ tptp.suc N))))) (let ((_let_13 (@ (@ tptp.dvd_dvd_nat _let_2) N))) (and (=> _let_13 (= _let_12 (@ _let_11 (@ (@ tptp.plus_plus_int _let_7) (@ (@ tptp.plus_plus_int (@ _let_10 _let_5)) (@ (@ tptp.times_times_int _let_4) _let_8)))))) (=> (not _let_13) (= _let_12 (@ _let_11 (@ (@ tptp.plus_plus_int (@ tptp.vEBT_V9176841429113362141ildupi (@ tptp.suc _let_6))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 _let_9))) _let_5)) (@ _let_10 _let_8))))))))))))))))))))))
% 7.27/7.61 (assert (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.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)))))))))))))))))
% 7.27/7.61 (assert (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.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))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.int)) (let ((_let_1 (not (= Y3 (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))) (=> (= (@ tptp.vEBT_VEBT_Tb X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ (@ tptp.divide_divide_nat N3) _let_2)))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.power_power_int (@ tptp.numeral_numeral_int _let_1)))) (let ((_let_6 (@ tptp.vEBT_VEBT_Tb _let_3))) (let ((_let_7 (@ tptp.times_times_int _let_6))) (let ((_let_8 (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 _let_1))))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_2) N3))) (=> (= X2 (@ tptp.suc (@ tptp.suc N3))) (not (and (=> _let_9 (= Y3 (@ (@ tptp.plus_plus_int (@ _let_8 _let_6)) (@ _let_7 (@ _let_5 _let_3))))) (=> (not _let_9) (= Y3 (@ (@ tptp.plus_plus_int (@ _let_8 (@ tptp.vEBT_VEBT_Tb _let_4))) (@ _let_7 (@ _let_5 _let_4)))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))) (=> (= (@ tptp.vEBT_V8346862874174094_d_u_p X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va3)))) (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))) (=> (= X2 _let_3) (not (and (=> _let_9 (= Y3 (@ (@ 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) (= Y3 (@ (@ 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))))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (not (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))) (=> (= (@ tptp.vEBT_V8646137997579335489_i_l_d X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va3)))) (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))) (=> (= X2 _let_3) (not (and (=> _let_8 (= Y3 (@ (@ 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) (= Y3 (@ (@ 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)))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)) (@ (@ tptp.dvd_dvd_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)) (@ (@ tptp.dvd_dvd_int A2) B2)))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X2) _let_1) (@ (@ tptp.divide_divide_nat Y3) _let_1)) (=> (= (@ _let_2 X2) (@ _let_2 Y3)) (= X2 Y3)))))))
% 7.27/7.61 (assert (= tptp.vEBT_VEBT_lowi (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ tptp.heap_Time_return_nat (@ (@ tptp.modulo_modulo_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (exists ((D4 tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D4))) (and (@ _let_1 A2) (@ _let_1 B2) (= (@ (@ tptp.times_times_nat A2) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) Y4)) D4))))))))
% 7.27/7.61 (assert (= tptp.vEBT_VEBT_low (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 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 B2) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) B2) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A2))) (@ _let_1 B2)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A2) B2))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B2) _let_1))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) B2))) (= (@ (@ tptp.modulo_modulo_int _let_1) B2) _let_1))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A2) B2))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B2) _let_1))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A2) B2)) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) N) (= (@ (@ tptp.modulo_modulo_nat A2) N) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A2) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) tptp.one_one_int) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A2) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A2) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) tptp.one_one_int) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A2) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B2) A2)) B2) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B2) A2)) B2) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) B2) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) B2) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) B2) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) B2) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) B2) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A2) B2)) B2) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) B2) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) B2) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A2) B2)) B2) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) B2) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat C2) B2))) B2) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int C2) B2))) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.times_3573771949741848930nteger C2) B2))) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat B2) C2))) B2) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int B2) C2))) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.times_3573771949741848930nteger B2) C2))) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B2)) A2)) B2) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B2)) A2)) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((C2 tptp.code_integer) (B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C2) B2)) A2)) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (C2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C2)) A2)) B2) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (C2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C2)) A2)) B2) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (C2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) C2)) A2)) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 7.27/7.61 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 7.27/7.61 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.27/7.61 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 7.27/7.61 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 7.27/7.61 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_1)) (@ _let_2 A2))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_1)) (@ _let_2 A2))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_1)) (@ _let_2 A2))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 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) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A2)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A2) _let_2))))))))))
% 7.27/7.61 (assert (forall ((A2 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) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A2)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A2) _let_2))))))))))
% 7.27/7.61 (assert (forall ((A2 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) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A2)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A2) _let_2))))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) C2)) B2)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) C2)) B2)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) B2)) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (A4 tptp.nat) (B2 tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A2) C2) (@ (@ tptp.modulo_modulo_nat A4) C2)) (=> (= (@ (@ tptp.modulo_modulo_nat B2) C2) (@ (@ tptp.modulo_modulo_nat B4) C2)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (A4 tptp.int) (B2 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A2) C2) (@ (@ tptp.modulo_modulo_int A4) C2)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C2) (@ (@ tptp.modulo_modulo_int B4) C2)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (A4 tptp.code_integer) (B2 tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A2) C2) (@ (@ tptp.modulo364778990260209775nteger A4) C2)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B2) C2) (@ (@ tptp.modulo364778990260209775nteger B4) C2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) C2)) (@ (@ tptp.modulo_modulo_nat B2) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) C2)) (@ (@ tptp.modulo_modulo_int B2) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A2) C2)) B2)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A2) C2)) B2)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) B2)) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A2) B2)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A2) B2)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A2) B2)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) C2)) (@ (@ tptp.times_times_nat B2) C2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) C2)) (@ (@ tptp.times_times_int B2) C2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) C2)) (@ (@ tptp.times_3573771949741848930nteger B2) C2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (A4 tptp.nat) (B2 tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A2) C2) (@ (@ tptp.modulo_modulo_nat A4) C2)) (=> (= (@ (@ tptp.modulo_modulo_nat B2) C2) (@ (@ tptp.modulo_modulo_nat B4) C2)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (A4 tptp.int) (B2 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A2) C2) (@ (@ tptp.modulo_modulo_int A4) C2)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C2) (@ (@ tptp.modulo_modulo_int B4) C2)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (A4 tptp.code_integer) (B2 tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A2) C2) (@ (@ tptp.modulo364778990260209775nteger A4) C2)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B2) C2) (@ (@ tptp.modulo364778990260209775nteger B4) C2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A2) C2)) (@ (@ tptp.modulo_modulo_nat B2) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A2) C2)) (@ (@ tptp.modulo_modulo_int B2) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A2) C2)) B2)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) B2)) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (A4 tptp.int) (B2 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A2) C2) (@ (@ tptp.modulo_modulo_int A4) C2)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C2) (@ (@ tptp.modulo_modulo_int B4) C2)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A2) B2)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (A4 tptp.code_integer) (B2 tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A2) C2) (@ (@ tptp.modulo364778990260209775nteger A4) C2)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B2) C2) (@ (@ tptp.modulo364778990260209775nteger B4) C2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B4)) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A2) C2)) (@ (@ tptp.modulo_modulo_int B2) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) N)) B2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A2) N)) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A2) B2)) N)) B2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A2) N)) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) N)) B2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) B2))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat C2) B2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C2) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (=> (@ (@ tptp.dvd_dvd_int C2) B2) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C2) (@ _let_1 C2))))))
% 7.27/7.61 (assert (forall ((C2 tptp.code_integer) (B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A2))) (=> (@ (@ tptp.dvd_dvd_Code_integer C2) B2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C2) (@ _let_1 C2))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A2) N))) (=> (@ (@ tptp.ord_less_nat B2) N) (=> (= _let_1 (@ (@ tptp.modulo_modulo_nat B2) N)) (= _let_1 B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (X2 tptp.nat) (M tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) X2)) M) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B2) X2)) M)) (= (@ (@ tptp.modulo_modulo_nat A2) M) (@ (@ tptp.modulo_modulo_nat B2) M)))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 7.27/7.61 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M5) N3)) (@ (@ P M5) N3)))) (@ (@ P M) N)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) A2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A2) B2)) A2))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A2) B2)) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) B2))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A2) B2) A2) (= (@ (@ tptp.divide_divide_nat A2) B2) tptp.zero_zero_nat))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A2) B2) A2) (= (@ (@ tptp.divide_divide_int A2) B2) tptp.zero_zero_int))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A2) B2) A2) (= (@ (@ tptp.divide6298287555418463151nteger A2) B2) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A2) C2) (@ (@ tptp.modulo_modulo_int B2) C2)) (not (forall ((D4 tptp.int)) (not (= B2 (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int C2) D4)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A2) C2) (@ (@ tptp.modulo364778990260209775nteger B2) C2)) (not (forall ((D4 tptp.code_integer)) (not (= B2 (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.times_3573771949741848930nteger C2) D4)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) C2)) (@ (@ tptp.divide_divide_nat B2) C2))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) C2)) (@ (@ tptp.modulo_modulo_nat B2) C2))) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) B2)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) C2)) (@ (@ tptp.divide_divide_int B2) C2))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) C2)) (@ (@ tptp.modulo_modulo_int B2) C2))) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A2) C2)) (@ (@ tptp.divide6298287555418463151nteger B2) C2))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) C2)) (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A2) C2) (@ (@ tptp.modulo_modulo_int B2) C2)) (@ (@ tptp.dvd_dvd_int C2) (@ (@ tptp.minus_minus_int A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (C2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A2) C2) (@ (@ tptp.modulo364778990260209775nteger B2) C2)) (@ (@ tptp.dvd_dvd_Code_integer C2) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.modulo_modulo_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.modulo_modulo_int A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B2) (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.modulo364778990260209775nteger A2) B2)))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P6 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P6) (=> (@ (@ tptp.ord_less_nat M) P6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P6) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P6))))) (@ P M)))))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_nat B2) N) (= (@ (@ tptp.modulo_modulo_nat B2) N) B2)))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))
% 7.27/7.61 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N4)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N4)) N4)))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat X2) Y3))) (=> (@ (@ tptp.ord_less_nat X2) Z) (= (@ (@ tptp.modulo_modulo_nat _let_1) Z) _let_1)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D2) tptp.zero_zero_nat) (exists ((Q4 tptp.nat)) (= M (@ (@ tptp.times_times_nat D2) Q4))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) X2)) (@ (@ tptp.modulo_modulo_nat N) M))) M) (@ (@ tptp.modulo_modulo_nat X2) M))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y3) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X2) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y3) (@ _let_1 Q22))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (D2 tptp.int) (X2 tptp.int) (T tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (let ((_let_2 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_2 D2) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C2) D2))) T))))))))
% 7.27/7.61 (assert (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (= (@ (@ tptp.modulo364778990260209775nteger A2) B2) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.modulo_modulo_nat A2) B2) A2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.modulo_modulo_int A2) B2) A2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A2) B2)))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 7.27/7.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A2) B2))) (@ (@ tptp.modulo_modulo_nat A2) B2)) A2)))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A2) B2))) (@ (@ tptp.modulo_modulo_int A2) B2)) A2)))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A2) B2))) (@ (@ tptp.modulo364778990260209775nteger A2) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A2) B2))) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A2) B2))) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A2) B2))) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A2) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2)) (@ (@ tptp.modulo_modulo_int A2) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A2) B2)) A2)))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2)) (@ (@ tptp.modulo_modulo_int A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= A2 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A2) B2))) C2) (@ (@ tptp.plus_plus_nat A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2)) (@ (@ tptp.modulo_modulo_int A2) B2))) C2) (@ (@ tptp.plus_plus_int A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A2) B2))) C2) (@ (@ tptp.plus_p5714425477246183910nteger A2) C2))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A2) B2))) (@ (@ tptp.modulo_modulo_nat A2) B2))) C2) (@ (@ tptp.plus_plus_nat A2) C2))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A2) B2))) (@ (@ tptp.modulo_modulo_int A2) B2))) C2) (@ (@ tptp.plus_plus_int A2) C2))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A2) B2))) (@ (@ tptp.modulo364778990260209775nteger A2) B2))) C2) (@ (@ tptp.plus_p5714425477246183910nteger A2) C2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C2))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C2))) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B2) C2))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C2))) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C2) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B2) C2))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C2))) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A2) B2))) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A2) B2))) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A2) B2))) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.modulo_modulo_nat A2) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.modulo_modulo_int A2) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.modulo364778990260209775nteger A2) B2)) (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.modulo_modulo_nat A2) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.modulo_modulo_int A2) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.modulo364778990260209775nteger A2) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2)) (@ (@ tptp.modulo_modulo_int A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A2) B2))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A2) B2)) (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.modulo_modulo_int A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A2) B2)) (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.modulo364778990260209775nteger A2) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A2) B2) tptp.zero_zero_nat))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A2) B2) tptp.zero_zero_int))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A2) B2) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A) N)) (@ (@ tptp.divide_divide_nat B) N))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat X2) Y3))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat _let_1) Z))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_1) Z))) (=> (@ (@ tptp.ord_less_nat X2) Z) (=> (@ (@ tptp.ord_less_nat Y3) Z) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) Z)))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y3) N)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (exists ((Q4 tptp.nat)) (= X2 (@ (@ tptp.plus_plus_nat Y3) (@ (@ tptp.times_times_nat N) Q4))))))))
% 7.27/7.61 (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 ((S3 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q3) S3))))))))))
% 7.27/7.61 (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 ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q3) S3))))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 7.27/7.61 (assert (forall ((A tptp.nat) (N tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) N)) N)) (@ (@ tptp.modulo_modulo_nat A) N)))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N4)) N4)))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.array_VEBT_VEBTi) (Vc tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_VEBT_minNulli (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)) (@ tptp.heap_Time_return_o false))))
% 7.27/7.61 (assert (forall ((Uw tptp.nat) (Ux tptp.array_VEBT_VEBTi) (Uy tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_VEBT_minNulli (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)) (@ tptp.heap_Time_return_o true))))
% 7.27/7.61 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M5 tptp.nat)) (not (= X2 (@ (@ tptp.product_Pair_nat_nat K2) M5)))))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A2))) (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 A2) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A2))) (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 A2) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A2))) (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 A2) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 7.27/7.61 (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)))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (R2 tptp.nat) (B2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (=> (@ (@ tptp.ord_less_nat R2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat Q3) C2))) R2)) (@ _let_1 C2)))))))
% 7.27/7.61 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 7.27/7.61 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 7.27/7.61 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (D2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) D2) (=> (@ (@ tptp.dvd_dvd_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.modulo_modulo_nat A2) B2))) (@ (@ tptp.minus_minus_nat D2) B2))))))
% 7.27/7.61 (assert (= (@ tptp.vEBT_V739175172307565963ildupi (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.heap_T3630416162098727440_VEBTi (@ (@ tptp.vEBT_Leafi false) false))))
% 7.27/7.61 (assert (= (@ tptp.vEBT_vebt_buildupi (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.heap_T3630416162098727440_VEBTi (@ (@ tptp.vEBT_Leafi false) false))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X2) D2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X2) D2))) _let_1))))))
% 7.27/7.61 (assert (forall ((Uu tptp.nat) (Uv tptp.array_VEBT_VEBTi) (Uw tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_vebt_minti (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat))))
% 7.27/7.61 (assert (forall ((Uu tptp.nat) (Uv tptp.array_VEBT_VEBTi) (Uw tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_vebt_maxti (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat))))
% 7.27/7.61 (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)))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X8) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X8) D)) T)))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X8 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X8) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X8) D)) T))))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X8))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T))))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.int) (D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X8 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X8))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X8 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T)))))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A2) B2)) C2))) (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A2) B2)) C2))) (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A2) B2)) C2))) (@ _let_1 B2))))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A2) (= (@ (@ tptp.modulo_modulo_nat A2) _let_1) tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A2) (= (@ (@ tptp.modulo_modulo_int A2) _let_1) tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) A2) (= (@ (@ tptp.modulo364778990260209775nteger A2) _let_1) tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A2)) (= (@ (@ tptp.modulo_modulo_nat A2) _let_1) tptp.one_one_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A2)) (= (@ (@ tptp.modulo_modulo_int A2) _let_1) tptp.one_one_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A2)) (= (@ (@ tptp.modulo364778990260209775nteger A2) _let_1) tptp.one_one_Code_integer)))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBTi) (Y3 tptp.heap_Time_Heap_o)) (let ((_let_1 (not (= Y3 (@ tptp.heap_Time_return_o false))))) (let ((_let_2 (not (= Y3 (@ tptp.heap_Time_return_o true))))) (=> (= (@ tptp.vEBT_VEBT_minNulli X2) Y3) (=> (=> (= X2 (@ (@ tptp.vEBT_Leafi false) false)) _let_2) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leafi true) Uv2))) _let_1) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leafi Uu2) true))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.array_VEBT_VEBTi) (Uy2 tptp.vEBT_VEBTi)) (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_2) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.array_VEBT_VEBTi) (Vc2 tptp.vEBT_VEBTi)) (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) _let_1)))))))))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.array_VEBT_VEBTi) (Uz tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_vebt_minti (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat Mi)))))
% 7.27/7.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.array_VEBT_VEBTi) (Uz tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_vebt_maxti (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat Ma)))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A2) _let_1) A2) (= (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.modulo_modulo_nat A2) _let_1)) tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A2) _let_1) A2) (= (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.modulo_modulo_int A2) _let_1)) tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A2) _let_1) A2) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.modulo364778990260209775nteger A2) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A2) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A2))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A2) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A2))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A2) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A2))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A2) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A2) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A2) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A2))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat X2) (@ _let_1 N))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat X2) _let_2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))
% 7.27/7.61 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B) N))))))
% 7.27/7.61 (assert (forall ((B2 Bool) (A2 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxti (@ (@ tptp.vEBT_Leafi A2) B2)))) (and (=> B2 (= _let_1 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.one_one_nat)))) (=> (not B2) (and (=> A2 (= _let_1 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.zero_zero_nat)))) (=> (not A2) (= _let_1 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)))))))))
% 7.27/7.61 (assert (forall ((A2 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_minti (@ (@ tptp.vEBT_Leafi A2) B2)))) (and (=> A2 (= _let_1 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.zero_zero_nat)))) (=> (not A2) (and (=> B2 (= _let_1 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.one_one_nat)))) (=> (not B2) (= _let_1 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)))))))))
% 7.27/7.61 (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)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A2) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A2) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A2) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 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 A2) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 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 A2) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (N tptp.nat) (A2 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 A2) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A2) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X2 (@ tptp.suc N3))))))))
% 7.27/7.61 (assert (forall ((P6 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P6) (@ (@ tptp.times_times_nat A2) B2)) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= P6 (@ (@ tptp.times_times_nat X4) Y4)) (=> (@ (@ tptp.dvd_dvd_nat X4) A2) (not (@ (@ tptp.dvd_dvd_nat Y4) B2)))))))))
% 7.27/7.61 (assert (forall ((P6 tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P6) (@ (@ tptp.times_times_int A2) B2)) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P6 (@ (@ tptp.times_times_int X4) Y4)) (=> (@ (@ tptp.dvd_dvd_int X4) A2) (not (@ (@ tptp.dvd_dvd_int Y4) B2)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat B2) C2)) (exists ((B7 tptp.nat) (C5 tptp.nat)) (and (= A2 (@ (@ tptp.times_times_nat B7) C5)) (@ (@ tptp.dvd_dvd_nat B7) B2) (@ (@ tptp.dvd_dvd_nat C5) C2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int B2) C2)) (exists ((B7 tptp.int) (C5 tptp.int)) (and (= A2 (@ (@ tptp.times_times_int B7) C5)) (@ (@ tptp.dvd_dvd_int B7) B2) (@ (@ tptp.dvd_dvd_int C5) C2))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A3) B3) (@ (@ P B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P A2) B2))))))
% 7.27/7.61 (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)))))))))))
% 7.27/7.61 (assert (forall ((M tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X2))) (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) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 7.27/7.61 (assert (forall ((M tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B2) (@ _let_1 B2)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B2) (@ _let_1 B2)))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B2) (@ _let_1 B2)))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A2) _let_1))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) (@ (@ tptp.modulo364778990260209775nteger A2) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B2))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.modulo_modulo_nat A2) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B2))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.modulo_modulo_int A2) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B2))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBTi) (Y3 tptp.heap_T2636463487746394924on_nat)) (=> (= (@ tptp.vEBT_vebt_minti X2) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leafi A3) B3)) (not (and (=> A3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.zero_zero_nat)))) (=> (not A3) (and (=> B3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.one_one_nat)))) (=> (not B3) (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.array_VEBT_VEBTi) (Uw2 tptp.vEBT_VEBTi)) (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.array_VEBT_VEBTi) (Uz2 tptp.vEBT_VEBTi)) (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat Mi2))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBTi) (Y3 tptp.heap_T2636463487746394924on_nat)) (=> (= (@ tptp.vEBT_vebt_maxti X2) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leafi A3) B3)) (not (and (=> B3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.one_one_nat)))) (=> (not B3) (and (=> A3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.zero_zero_nat)))) (=> (not A3) (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.array_VEBT_VEBTi) (Uw2 tptp.vEBT_VEBTi)) (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.array_VEBT_VEBTi) (Uz2 tptp.vEBT_VEBTi)) (= X2 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat Ma2))))))))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (exists ((D4 tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D4))) (and (@ _let_3 A2) (@ _let_3 B2) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) D4)) (= (@ _let_2 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D4))))))))))
% 7.27/7.61 (assert (forall ((D2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (=> (@ _let_3 A2) (=> (@ _let_3 B2) (=> (or (= (@ _let_1 X2) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D2)) (= (@ _let_2 X2) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D2))) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A2) B2))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_4 A2) (@ _let_4 _let_2) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_3 Y4)) D2)) (= (@ _let_3 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D2)))))))))))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (exists ((D4 tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D4))) (and (@ _let_3 A2) (@ _let_3 B2) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X4)) (@ _let_2 Y4)) D4) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X4)) (@ _let_1 Y4)) D4)))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 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) B2) (=> (@ (@ (@ tptp.eucl_rel_int A2) B2) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A2))) (@ _let_1 B2)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 7.27/7.61 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.divide_divide_nat X2))) (let ((_let_3 (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat (@ _let_2 _let_1)) Y3)))) (let ((_let_4 (@ (@ tptp.minus_minus_nat X2) (@ (@ tptp.times_times_nat _let_3) Y3)))) (=> (not (= Y3 tptp.zero_zero_nat)) (= (@ (@ tptp.product_Pair_nat_nat (@ _let_2 Y3)) (@ (@ tptp.modulo_modulo_nat X2) Y3)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat Y3) _let_4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_3) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat _let_4) Y3))) (@ (@ tptp.product_Pair_nat_nat _let_3) _let_4))))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A2) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A2) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A2) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.size_s3445333598471063425nteger Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs)) _let_1)) (= (@ (@ tptp.nth_Pr2304437835452373666nteger (@ (@ tptp.produc8792966785426426881nteger Xs) Ys)) N) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.nth_Code_integer Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_Code_integer Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs) Ys)) N) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_real)) (let ((_let_1 (@ tptp.size_size_list_real Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6842391030413306568T_real (@ (@ tptp.produc4908677263432625371T_real Xs) Ys)) N) (@ (@ tptp.produc8117437818029410057T_real (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_real Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ tptp.size_s7982070591426661849_VEBTi Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr316670251186196177_VEBTi (@ (@ tptp.produc316462671093861988_VEBTi Xs) Ys)) N) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBTi Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5429231388385915574T_VEBT (@ (@ tptp.produc3722688996059531265T_VEBT Xs) Ys)) N) (@ (@ tptp.produc6931449550656315951T_VEBT (@ (@ tptp.nth_real Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (Ys tptp.list_real)) (let ((_let_1 (@ tptp.size_size_list_real Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7489471911767062336l_real (@ (@ tptp.product_real_real Xs) Ys)) N) (@ (@ tptp.produc4511245868158468465l_real (@ (@ tptp.nth_real Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_real Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.vEBT_VEBTi) (Y3 tptp.assn)) (let ((_let_1 (not (= Y3 tptp.bot_bot_assn)))) (=> (= (@ (@ tptp.vEBT_vebt_assn_raw X2) Xa) Y3) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Ai2 Bool) (Bi2 Bool)) (=> (= Xa (@ (@ tptp.vEBT_Leafi Ai2) Bi2)) (not (= Y3 (@ tptp.pure_assn (and (= Ai2 A3) (= Bi2 B3))))))))) (=> (forall ((Mmo tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (Tree_list tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mmo) Deg2) Tree_list) Summary2)) (forall ((Mmoi tptp.option4927543243414619207at_nat) (Degi tptp.nat) (Tree_array tptp.array_VEBT_VEBTi) (Summaryi tptp.vEBT_VEBTi)) (=> (= Xa (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi) Degi) Tree_array) Summaryi)) (not (= Y3 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ tptp.pure_assn (and (= Mmoi Mmo) (= Degi Deg2)))) (@ (@ tptp.vEBT_vebt_assn_raw Summary2) 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))))))))))) (=> (=> (exists ((V2 tptp.option4927543243414619207at_nat) (Va3 tptp.nat) (Vb3 tptp.list_VEBT_VEBT) (Vc3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node V2) Va3) Vb3) Vc3))) (=> (exists ((Vd Bool) (Ve Bool)) (= Xa (@ (@ tptp.vEBT_Leafi Vd) Ve))) _let_1)) (not (=> (exists ((Vd Bool) (Ve Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Vd) Ve))) (=> (exists ((V2 tptp.option4927543243414619207at_nat) (Va3 tptp.nat) (Vb3 tptp.array_VEBT_VEBTi) (Vc3 tptp.vEBT_VEBTi)) (= Xa (@ (@ (@ (@ tptp.vEBT_Nodei V2) Va3) Vb3) Vc3))) _let_1))))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.assn)) (= (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) C2)) C2)))
% 7.27/7.61 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 7.27/7.61 (assert (forall ((R tptp.assn) (Q (-> tptp.list_VEBT_VEBTi tptp.assn))) (= (@ (@ tptp.times_times_assn R) (@ tptp.ex_ass463751140784270563_VEBTi Q)) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn R) (@ Q X3)))))))
% 7.27/7.61 (assert (forall ((Q (-> tptp.list_VEBT_VEBTi tptp.assn)) (R tptp.assn)) (= (@ (@ tptp.times_times_assn (@ tptp.ex_ass463751140784270563_VEBTi Q)) R) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ Q X3)) R))))))
% 7.27/7.61 (assert (forall ((Q (-> tptp.list_VEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi)) (@ (@ tptp.entails (@ Q X2)) (@ tptp.ex_ass463751140784270563_VEBTi Q))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.ex_ass463751140784270563_VEBTi P)) H2) (exists ((X3 tptp.list_VEBT_VEBTi)) (@ (@ tptp.rep_assn (@ P X3)) H2)))))
% 7.27/7.61 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 7.27/7.61 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_real)) (= (@ tptp.size_s5035110155006384947T_real (@ (@ tptp.produc4908677263432625371T_real Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_real Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBTi)) (= (@ tptp.size_s3387956428969716412_VEBTi (@ (@ tptp.produc316462671093861988_VEBTi Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s7982070591426661849_VEBTi Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s3289364478449617953T_VEBT (@ (@ tptp.produc3722688996059531265T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_real)) (= (@ tptp.size_s3932428310213730859l_real (@ (@ tptp.product_real_real Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) (@ tptp.size_size_list_real Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_o)) (= (@ tptp.size_s987546567493390085real_o (@ (@ tptp.product_real_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) (@ tptp.size_size_list_o Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_nat)) (= (@ tptp.size_s1877336372972134351al_nat (@ (@ tptp.product_real_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) (@ tptp.size_size_list_nat Ys)))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_VEBT_VEBTi)) (= (@ tptp.size_s6963394564282275252_VEBTi (@ (@ tptp.produc5599769701989005224_VEBTi Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs)) (@ tptp.size_s7982070591426661849_VEBTi Ys)))))
% 7.27/7.61 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 7.27/7.61 (assert (forall ((R (-> tptp.list_VEBT_VEBTi tptp.assn)) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.rep_assn (@ tptp.ex_ass463751140784270563_VEBTi R)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) (exists ((X3 tptp.list_VEBT_VEBTi)) (@ (@ tptp.rep_assn (@ R X3)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))))
% 7.27/7.61 (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))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (B4 tptp.int) (X2 tptp.int) (X5 tptp.int) (Y3 tptp.int) (Y7 tptp.int) (Z6 tptp.int)) (=> (= B2 B4) (=> (= (@ (@ tptp.modulo_modulo_int X2) B4) (@ (@ tptp.modulo_modulo_int X5) B4)) (=> (= (@ (@ tptp.modulo_modulo_int Y3) B4) (@ (@ tptp.modulo_modulo_int Y7) B4)) (=> (= (@ (@ tptp.plus_plus_int X5) Y7) Z6) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int X2) Y3)) B2) (@ (@ tptp.modulo_modulo_int Z6) B4))))))))
% 7.27/7.61 (assert (forall ((N tptp.int) (M tptp.int) (K tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int N) M) K) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int N) A2)) M) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int K) A2)) M)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (B4 tptp.int) (X2 tptp.int) (X5 tptp.int) (Y3 tptp.int) (Y7 tptp.int) (Z6 tptp.int)) (=> (= B2 B4) (=> (= (@ (@ tptp.modulo_modulo_int X2) B4) (@ (@ tptp.modulo_modulo_int X5) B4)) (=> (= (@ (@ tptp.modulo_modulo_int Y3) B4) (@ (@ tptp.modulo_modulo_int Y7) B4)) (=> (= (@ (@ tptp.minus_minus_int X5) Y7) Z6) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int X2) Y3)) B2) (@ (@ tptp.modulo_modulo_int Z6) B4))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (Q tptp.assn)) (= (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ P X3)) Q))) (@ (@ tptp.times_times_assn (@ tptp.ex_ass463751140784270563_VEBTi P)) Q))))
% 7.27/7.61 (assert (forall ((Z7 (-> tptp.list_VEBT_VEBTi Bool)) (P tptp.assn) (Q (-> tptp.list_VEBT_VEBTi tptp.assn))) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (=> (@ Z7 X4) (@ (@ tptp.entails P) (@ Q X4)))) (=> (exists ((X_12 tptp.list_VEBT_VEBTi)) (@ Z7 X_12)) (@ (@ tptp.entails P) (@ tptp.ex_ass463751140784270563_VEBTi Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (Q tptp.assn)) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ tptp.entails (@ P X4)) Q)) (@ (@ tptp.entails (@ tptp.ex_ass463751140784270563_VEBTi P)) Q))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (Q (-> tptp.list_VEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ Q X2)) (@ _let_1 (@ tptp.ex_ass463751140784270563_VEBTi Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn))) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ P X4)) F) Q)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn))) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ P X4)) F) Q)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn))) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ P X4)) F) Q)) (@ (@ (@ tptp.hoare_7629718768684598413on_nat (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn))) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ P X4)) F) Q)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.list_VEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.hoare_1429296392585015714_VEBTi P) C2))) (=> (@ _let_1 (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ Q R5) X2))) (@ _let_1 (lambda ((R5 tptp.vEBT_VEBTi)) (@ tptp.ex_ass463751140784270563_VEBTi (@ Q R5))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_o) (Q (-> Bool tptp.list_VEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.hoare_hoare_triple_o P) C2))) (=> (@ _let_1 (lambda ((R5 Bool)) (@ (@ Q R5) X2))) (@ _let_1 (lambda ((R5 Bool)) (@ tptp.ex_ass463751140784270563_VEBTi (@ Q R5))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.list_VEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.hoare_7629718768684598413on_nat P) C2))) (=> (@ _let_1 (lambda ((R5 tptp.option_nat)) (@ (@ Q R5) X2))) (@ _let_1 (lambda ((R5 tptp.option_nat)) (@ tptp.ex_ass463751140784270563_VEBTi (@ Q R5))))))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (C2 tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.list_VEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.hoare_3067605981109127869le_nat P) C2))) (=> (@ _let_1 (lambda ((R5 tptp.nat)) (@ (@ Q R5) X2))) (@ _let_1 (lambda ((R5 tptp.nat)) (@ tptp.ex_ass463751140784270563_VEBTi (@ Q R5))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ tptp.ex_ass463751140784270563_VEBTi P)) H2) (not (forall ((X4 tptp.list_VEBT_VEBTi)) (not (@ (@ tptp.rep_assn (@ P X4)) H2)))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (H2 tptp.produc3658429121746597890et_nat)) (=> (exists ((X8 tptp.list_VEBT_VEBTi)) (@ (@ tptp.rep_assn (@ P X8)) H2)) (@ (@ tptp.rep_assn (@ tptp.ex_ass463751140784270563_VEBTi P)) H2))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (V tptp.list_VEBT_VEBTi)) (=> (forall ((H3 tptp.produc3658429121746597890et_nat) (X4 tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.rep_assn (@ P X4)) H3) (= X4 V))) (= (@ tptp.ex_ass463751140784270563_VEBTi P) (@ P V)))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.list_VEBT_VEBTi tptp.vEBT_VEBTi tptp.assn)) (X2 tptp.list_VEBT_VEBTi) (T tptp.nat)) (let ((_let_1 (@ (@ tptp.time_htt_VEBT_VEBTi P) F))) (=> (@ (@ _let_1 (@ Q X2)) T) (@ (@ _let_1 (lambda ((R5 tptp.vEBT_VEBTi)) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ Q X3) R5))))) T)))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (F tptp.heap_Time_Heap_o) (Q (-> tptp.list_VEBT_VEBTi Bool tptp.assn)) (X2 tptp.list_VEBT_VEBTi) (T tptp.nat)) (let ((_let_1 (@ (@ tptp.time_htt_o P) F))) (=> (@ (@ _let_1 (@ Q X2)) T) (@ (@ _let_1 (lambda ((R5 Bool)) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ Q X3) R5))))) T)))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.list_VEBT_VEBTi tptp.option_nat tptp.assn)) (X2 tptp.list_VEBT_VEBTi) (T tptp.nat)) (let ((_let_1 (@ (@ tptp.time_htt_option_nat P) F))) (=> (@ (@ _let_1 (@ Q X2)) T) (@ (@ _let_1 (lambda ((R5 tptp.option_nat)) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ Q X3) R5))))) T)))))
% 7.27/7.61 (assert (forall ((P tptp.assn) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.list_VEBT_VEBTi tptp.nat tptp.assn)) (X2 tptp.list_VEBT_VEBTi) (T tptp.nat)) (let ((_let_1 (@ (@ tptp.time_htt_nat P) F))) (=> (@ (@ _let_1 (@ Q X2)) T) (@ (@ _let_1 (lambda ((R5 tptp.nat)) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((X3 tptp.list_VEBT_VEBTi)) (@ (@ Q X3) R5))))) T)))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_T8145700208782473153_VEBTi) (Q (-> tptp.vEBT_VEBTi tptp.assn)) (T tptp.nat)) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ P X4)) F) Q) T)) (@ (@ (@ (@ tptp.time_htt_VEBT_VEBTi (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q) T))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_Time_Heap_o) (Q (-> Bool tptp.assn)) (T tptp.nat)) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_o (@ P X4)) F) Q) T)) (@ (@ (@ (@ tptp.time_htt_o (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q) T))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_T2636463487746394924on_nat) (Q (-> tptp.option_nat tptp.assn)) (T tptp.nat)) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_option_nat (@ P X4)) F) Q) T)) (@ (@ (@ (@ tptp.time_htt_option_nat (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q) T))))
% 7.27/7.61 (assert (forall ((P (-> tptp.list_VEBT_VEBTi tptp.assn)) (F tptp.heap_Time_Heap_nat) (Q (-> tptp.nat tptp.assn)) (T tptp.nat)) (=> (forall ((X4 tptp.list_VEBT_VEBTi)) (@ (@ (@ (@ tptp.time_htt_nat (@ P X4)) F) Q) T)) (@ (@ (@ (@ tptp.time_htt_nat (@ tptp.ex_ass463751140784270563_VEBTi P)) F) Q) T))))
% 7.27/7.61 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 7.27/7.61 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))))
% 7.27/7.61 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.modulo_modulo_int A2) N))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) B2))) (let ((_let_2 (@ tptp.ord_less_int B2))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B2))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 7.27/7.61 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))))
% 7.27/7.61 (assert (forall ((N tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int B2) N)) (= (@ (@ tptp.modulo_modulo_int B2) N) B2)))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (N tptp.int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) N) (=> (= _let_1 (@ (@ tptp.modulo_modulo_int B2) N)) (= _let_1 B2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int B2) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int B2) N)) _let_1)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (and (@ _let_1 (@ (@ tptp.modulo_modulo_int A2) B2)) (@ _let_1 (@ (@ tptp.divide_divide_int A2) B2))))))))
% 7.27/7.61 (assert (forall ((A tptp.int) (N tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) N)) N)) (@ (@ tptp.modulo_modulo_int A) N)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) B2)) B2) (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.modulo_modulo_int A2) B2)))))
% 7.27/7.61 (assert (= tptp.modulo_modulo_nat (lambda ((A5 tptp.nat) (B6 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B6))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A2) _let_1)) _let_1))))
% 7.27/7.61 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L) _let_1))))))
% 7.27/7.61 (assert (forall ((B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) N)) (@ (@ tptp.modulo_modulo_int B2) N))))))
% 7.27/7.61 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))))
% 7.27/7.61 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X2) Y3)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y3))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X2) D2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X2) D2))) _let_1))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 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 A2) _let_1)) _let_1))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (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) A2) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) R2) (= (@ (@ tptp.modulo_modulo_int A2) B2) R2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B2) (= (@ (@ tptp.modulo_modulo_int A2) B2) R2))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Z tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X2) Y3))) (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 X2) Z) (=> (@ (@ tptp.ord_less_int Y3) Z) (=> (@ _let_4 Y3) (=> (@ _let_4 X2) (=> (@ _let_4 Z) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) Z)))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (Z tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X2) Y3))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int _let_1) Z))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int Y3) X2))) (let ((_let_4 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X2) Z) (=> (@ (@ tptp.ord_less_int Y3) Z) (=> (@ _let_4 Y3) (=> (@ _let_4 X2) (=> (@ _let_4 Z) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) Z)))))))))))))))
% 7.27/7.61 (assert (forall ((C2 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A2) B2)) C2))) (@ _let_1 B2))))))))
% 7.27/7.61 (assert (forall ((X2 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) X2)) X2)) _let_1) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) X2)) X2)) _let_1) tptp.zero_zero_int)))))
% 7.27/7.61 (assert (forall ((B2 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) B2)) tptp.one_one_int)) _let_1) tptp.one_one_int))))
% 7.27/7.61 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B) N))))))
% 7.27/7.61 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 7.27/7.61 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 7.27/7.61 (assert (forall ((B2 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 B2)) tptp.one_one_int)) (@ _let_3 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ (@ tptp.modulo_modulo_int B2) _let_2))) tptp.one_one_int)))))))
% 7.27/7.61 (assert (forall ((B2 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 B2))) (@ _let_3 _let_2)) (@ _let_4 (@ _let_3 (@ (@ tptp.modulo_modulo_int B2) _let_2))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (= (= X2 (@ (@ tptp.minus_minus_real Y3) Z)) (= Y3 (@ (@ tptp.plus_plus_real X2) Z)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 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) A2) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B2))) (@ _let_1 A2)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) A2)))))))))
% 7.27/7.61 (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))))))))))
% 7.27/7.61 (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))))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A2)) (not (= (@ _let_1 A2) (= M tptp.zero_zero_nat)))))))
% 7.27/7.61 (assert (forall ((M tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A2)) (not (= (@ _let_1 A2) (= M tptp.zero_zero_nat)))))))
% 7.27/7.61 (assert (forall ((A2 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 A2) (@ _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))))))))
% 7.27/7.61 (assert (forall ((Mmo2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (Tree_list2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Mmoi2 tptp.option4927543243414619207at_nat) (Degi2 tptp.nat) (Tree_array2 tptp.array_VEBT_VEBTi) (Summaryi2 tptp.vEBT_VEBTi)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node Mmo2) Deg) Tree_list2) Summary)) (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi2) Degi2) Tree_array2) Summaryi2)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ tptp.pure_assn (and (= Mmoi2 Mmo2) (= Degi2 Deg)))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) 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))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B2))) (@ _let_1 A2)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)) A2))) tptp.one_one_int))))))
% 7.27/7.61 (assert (= tptp.nat_triangle (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N4) (@ tptp.suc N4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.27/7.61 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A) Z) (=> (@ tptp.finite_finite_nat A) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A) X2) X_1)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A) Z) (=> (@ tptp.finite_finite_nat B) (=> (= A B) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A) X2) X_1))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y3 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X2 _let_2) (not (and (=> _let_8 (= Y3 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y3 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (B2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B2) X2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X2) (@ (@ tptp.ord_less_eq_real X2) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBTi Bool)) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.replicate_VEBT_VEBTi N) X2)) I))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> Bool Bool)) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_o (@ (@ tptp.replicate_o N) X2)) I))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.real Bool)) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_real (@ (@ tptp.replicate_real N) X2)) I))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((Xs tptp.set_nat) (A2 tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs) A2) X_1))) (=> (@ tptp.finite_finite_nat Xs) (not (exists ((X8 tptp.nat)) (and (@ (@ tptp.member_nat X8) Xs) (@ (@ tptp.ord_less_nat A2) X8))))))))
% 7.27/7.61 (assert (forall ((Xs tptp.set_nat) (A2 tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs) A2) X_1))) (=> (@ tptp.finite_finite_nat Xs) (not (exists ((X8 tptp.nat)) (and (@ (@ tptp.member_nat X8) Xs) (@ (@ tptp.ord_less_nat X8) A2))))))))
% 7.27/7.61 (assert (forall ((Q tptp.assn) (X2 tptp.heap_T8145700208782473153_VEBTi) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi Q) X2) (lambda ((R5 tptp.vEBT_VEBTi)) (@ (@ tptp.times_times_assn Q) (@ (@ A Y3) R5)))) (@ (@ (@ tptp.hoare_3904069481286416050_VEBTi Q) (@ (@ tptp.vEBT_V1859673955506687831_VEBTi N) X2)) (lambda ((R5 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn Q) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3)) R5)))))))
% 7.27/7.61 (assert (forall ((Q tptp.assn) (X2 tptp.heap_Time_Heap_o) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_o Q) X2) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn Q) (@ (@ A Y3) R5)))) (@ (@ (@ tptp.hoare_9089481587091695345list_o Q) (@ (@ tptp.vEBT_V2326993469660664182atei_o N) X2)) (lambda ((R5 tptp.list_o)) (@ (@ tptp.times_times_assn Q) (@ (@ (@ tptp.vEBT_L7489408758114837031VEBT_o A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3)) R5)))))))
% 7.27/7.61 (assert (forall ((Q tptp.assn) (X2 tptp.heap_T2636463487746394924on_nat) (A (-> tptp.vEBT_VEBT tptp.option_nat tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat Q) X2) (lambda ((R5 tptp.option_nat)) (@ (@ tptp.times_times_assn Q) (@ (@ A Y3) R5)))) (@ (@ (@ tptp.hoare_6480275734082232733on_nat Q) (@ (@ tptp.vEBT_V792416675989592002on_nat N) X2)) (lambda ((R5 tptp.list_option_nat)) (@ (@ tptp.times_times_assn Q) (@ (@ (@ tptp.vEBT_L8010285020845282001on_nat A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3)) R5)))))))
% 7.27/7.61 (assert (forall ((Q tptp.assn) (X2 tptp.heap_Time_Heap_nat) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat Q) X2) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn Q) (@ (@ A Y3) R5)))) (@ (@ (@ tptp.hoare_7964568885773372237st_nat Q) (@ (@ tptp.vEBT_V7726092123322077554ei_nat N) X2)) (lambda ((R5 tptp.list_nat)) (@ (@ tptp.times_times_assn Q) (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3)) R5)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.heap_T8145700208782473153_VEBTi) (A (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) X2) (@ A Y3)) (@ (@ (@ tptp.hoare_3904069481286416050_VEBTi tptp.one_one_assn) (@ (@ tptp.vEBT_V1859673955506687831_VEBTi N) X2)) (@ (@ tptp.vEBT_L6296928887356842470_VEBTi A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3))))))
% 7.27/7.61 (assert (forall ((X2 tptp.heap_Time_Heap_o) (A (-> tptp.vEBT_VEBT Bool tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_o tptp.one_one_assn) X2) (@ A Y3)) (@ (@ (@ tptp.hoare_9089481587091695345list_o tptp.one_one_assn) (@ (@ tptp.vEBT_V2326993469660664182atei_o N) X2)) (@ (@ tptp.vEBT_L7489408758114837031VEBT_o A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3))))))
% 7.27/7.61 (assert (forall ((X2 tptp.heap_T2636463487746394924on_nat) (A (-> tptp.vEBT_VEBT tptp.option_nat tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_7629718768684598413on_nat tptp.one_one_assn) X2) (@ A Y3)) (@ (@ (@ tptp.hoare_6480275734082232733on_nat tptp.one_one_assn) (@ (@ tptp.vEBT_V792416675989592002on_nat N) X2)) (@ (@ tptp.vEBT_L8010285020845282001on_nat A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3))))))
% 7.27/7.61 (assert (forall ((X2 tptp.heap_Time_Heap_nat) (A (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (Y3 tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) X2) (@ A Y3)) (@ (@ (@ tptp.hoare_7964568885773372237st_nat tptp.one_one_assn) (@ (@ tptp.vEBT_V7726092123322077554ei_nat N) X2)) (@ (@ tptp.vEBT_L8296926524756676353BT_nat A) (@ (@ tptp.replicate_VEBT_VEBT N) Y3))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real)) (@ tptp.finite_finite_real (@ tptp.set_real2 Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_Code_integer)) (@ tptp.finite6017078050557962740nteger (@ tptp.set_Code_integer2 Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs))))
% 7.27/7.61 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A2) tptp.one_one_real)))
% 7.27/7.61 (assert (forall ((M tptp.nat) (X2 tptp.vEBT_VEBT) (N tptp.nat) (Y3 tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X2) (@ (@ tptp.replicate_VEBT_VEBT N) Y3)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X2 Y3))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) N)))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.size_size_list_real (@ (@ tptp.replicate_real N) X2)) N)))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X2)) N)))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X2)) N)))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBTi)) (= (@ tptp.size_s7982070591426661849_VEBTi (@ (@ tptp.replicate_VEBT_VEBTi N) X2)) N)))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_nat F) (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.replicate_nat N) (@ F X2)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_real F) (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.replicate_real N) (@ F X2)))))
% 7.27/7.61 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.replicate_VEBT_VEBT N))) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT F) (@ _let_1 X2)) (@ _let_1 (@ F X2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B2))) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2))) (@ (@ tptp.ord_less_real A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or66887138388493659n_real A2) B2))) (@ (@ tptp.ord_less_real A2) B2))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or4029947393144176647an_rat A2) B2))) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X2) tptp.zero_zero_real))) (let ((_let_2 (= X2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.real) (P (-> tptp.real Bool))) (= (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) A2))) (@ P X3))) (or (@ P A2) (= N tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A2))) (@ P X3))) (or (@ P A2) (= N tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A2))) (@ P X3))) (or (@ P A2) (= N tptp.zero_zero_nat)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.real) (P (-> tptp.real Bool))) (= (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) A2))) (@ P X3))) (and (@ P A2) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A2))) (@ P X3))) (and (@ P A2) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (A2 tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A2))) (@ P X3))) (and (@ P A2) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y3 tptp.int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y3))) (and (= X2 Y3) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y3 tptp.real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y3))) (and (= X2 Y3) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y3))) (and (= X2 Y3) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((X2 tptp.vEBT_VEBT) (N tptp.nat) (Y3 tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y3))) (and (= X2 Y3) (not (= N tptp.zero_zero_nat))))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.replicate_VEBT_VEBTi N) X2)) I) X2))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I) X2))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_o (@ (@ tptp.replicate_o N) X2)) I) X2))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_real (@ (@ tptp.replicate_real N) X2)) I) X2))))
% 7.27/7.61 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I) X2))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A2) X2)) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A2) B2))))))
% 7.27/7.61 (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)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (= (= (@ (@ tptp.powr_real A2) X2) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.27/7.61 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A2) B2))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (not (= A2 tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.powr_real A2) (@ (@ tptp.log A2) X2)) X2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (not (= A2 tptp.one_one_real)) (= (@ (@ tptp.log A2) (@ (@ tptp.powr_real A2) Y3)) Y3)))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N))))))
% 7.27/7.61 (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))))
% 7.27/7.61 (assert (forall ((S tptp.set_int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((S5 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int S5) S) (@ (@ tptp.minus_minus_set_int S4) S))))))))
% 7.27/7.61 (assert (forall ((S tptp.set_Code_integer) (S4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (@ tptp.finite6931041176100689706nteger (@ tptp.collec574505750873337192nteger (lambda ((S5 tptp.set_Code_integer)) (= (@ (@ tptp.minus_2355218937544613996nteger S5) S) (@ (@ tptp.minus_2355218937544613996nteger S4) S))))))))
% 7.27/7.61 (assert (forall ((S tptp.set_complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((S5 tptp.set_complex)) (= (@ (@ tptp.minus_811609699411566653omplex S5) S) (@ (@ tptp.minus_811609699411566653omplex S4) S))))))))
% 7.27/7.61 (assert (forall ((S tptp.set_nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((S5 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat S5) S) (@ (@ tptp.minus_minus_set_nat S4) S))))))))
% 7.27/7.61 (assert (forall ((N7 tptp.set_nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N7) (@ (@ tptp.ord_less_nat X4) N))) (@ tptp.finite_finite_nat N7))))
% 7.27/7.61 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N8) (@ (@ tptp.ord_less_nat X3) M6)))))))
% 7.27/7.61 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N8) (@ (@ tptp.ord_less_eq_nat X3) M6)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A)))))
% 7.27/7.61 (assert (forall ((A tptp.set_real)) (=> (@ tptp.finite_finite_real A) (exists ((Xs3 tptp.list_real)) (= (@ tptp.set_real2 Xs3) A)))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A)))))
% 7.27/7.61 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A)))))
% 7.27/7.61 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (exists ((Xs3 tptp.list_Code_integer)) (= (@ tptp.set_Code_integer2 Xs3) A)))))
% 7.27/7.61 (assert (forall ((A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A)))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I)))))))
% 7.27/7.61 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) U)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_Code_integer) (N tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger A) (@ tptp.finite1283093830868386564nteger (@ tptp.collec3483841146883906114nteger (lambda ((Xs2 tptp.list_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.set_Code_integer2 Xs2)) A) (= (@ tptp.size_s3445333598471063425nteger Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A) (= (@ tptp.size_s3451745648224563538omplex Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_real) (N tptp.nat)) (=> (@ tptp.finite_finite_real A) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs2 tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A) (= (@ tptp.size_size_list_real Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs2 tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) A) (= (@ tptp.size_size_list_o Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A) (= (@ tptp.size_size_list_nat Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBTi) (N tptp.nat)) (=> (@ tptp.finite6580341952239402572_VEBTi A) (@ tptp.finite5722435864697464412_VEBTi (@ tptp.collec1288327022334394266_VEBTi (lambda ((Xs2 tptp.list_VEBT_VEBTi)) (and (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 Xs2)) A) (= (@ tptp.size_s7982070591426661849_VEBTi Xs2) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A) (= (@ tptp.size_size_list_int Xs2) N))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) Y3))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A2)) (@ (@ tptp.powr_real Y3) A2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A2) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_int) (N tptp.nat) (X2 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) (@ tptp.set_int2 Xs)) (= Y4 X2))) (= Xs (@ (@ tptp.replicate_int N) X2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y4 X2))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N) X2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (N tptp.nat) (X2 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) (@ tptp.set_real2 Xs)) (= Y4 X2))) (= Xs (@ (@ tptp.replicate_real N) X2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_o) (N tptp.nat) (X2 Bool)) (=> (= (@ tptp.size_size_list_o Xs) N) (=> (forall ((Y4 Bool)) (=> (@ (@ tptp.member_o Y4) (@ tptp.set_o2 Xs)) (= Y4 X2))) (= Xs (@ (@ tptp.replicate_o N) X2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (N tptp.nat) (X2 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) (@ tptp.set_nat2 Xs)) (= Y4 X2))) (= Xs (@ (@ tptp.replicate_nat N) X2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (N tptp.nat) (X2 tptp.vEBT_VEBTi)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi Xs) N) (=> (forall ((Y4 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi Y4) (@ tptp.set_VEBT_VEBTi2 Xs)) (= Y4 X2))) (= Xs (@ (@ tptp.replicate_VEBT_VEBTi N) X2))))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= X4 X2))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X2) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_real) (X2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (= X4 X2))) (= (@ (@ tptp.replicate_real (@ tptp.size_size_list_real Xs)) X2) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_o) (X2 Bool)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (= X4 X2))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X2) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_nat) (X2 tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (= X4 X2))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X2) Xs))))
% 7.27/7.61 (assert (forall ((Xs tptp.list_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (=> (forall ((X4 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X4) (@ tptp.set_VEBT_VEBTi2 Xs)) (= X4 X2))) (= (@ (@ tptp.replicate_VEBT_VEBTi (@ tptp.size_s7982070591426661849_VEBTi Xs)) X2) Xs))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or66887138388493659n_real A2) B2))))))
% 7.27/7.61 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or4029947393144176647an_rat A2) B2))))))
% 7.27/7.61 (assert (forall ((A tptp.set_Code_integer) (N tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger A) (@ tptp.finite1283093830868386564nteger (@ tptp.collec3483841146883906114nteger (lambda ((Xs2 tptp.list_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.set_Code_integer2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3445333598471063425nteger Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_real) (N tptp.nat)) (=> (@ tptp.finite_finite_real A) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs2 tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_real Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs2 tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBTi) (N tptp.nat)) (=> (@ tptp.finite6580341952239402572_VEBTi A) (@ tptp.finite5722435864697464412_VEBTi (@ tptp.collec1288327022334394266_VEBTi (lambda ((Xs2 tptp.list_VEBT_VEBTi)) (and (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s7982070591426661849_VEBTi Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) N))))))))
% 7.27/7.61 (assert (forall ((K tptp.nat) (Lst tptp.list_VEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_nat (lambda ((X3 tptp.vEBT_VEBT)) K)) Lst) (@ (@ tptp.replicate_nat (@ tptp.size_s6755466524823107622T_VEBT Lst)) K))))
% 7.27/7.61 (assert (forall ((K tptp.real) (Lst tptp.list_VEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_real (lambda ((X3 tptp.vEBT_VEBT)) K)) Lst) (@ (@ tptp.replicate_real (@ tptp.size_s6755466524823107622T_VEBT Lst)) K))))
% 7.27/7.61 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_VEBT_VEBT)) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((X3 tptp.vEBT_VEBT)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Lst)) K))))
% 7.27/7.61 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_real)) (= (@ (@ tptp.map_real_VEBT_VEBT (lambda ((X3 tptp.real)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_real Lst)) K))))
% 7.27/7.61 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_o)) (= (@ (@ tptp.map_o_VEBT_VEBT (lambda ((X3 Bool)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_o Lst)) K))))
% 7.27/7.61 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_nat)) (= (@ (@ tptp.map_nat_VEBT_VEBT (lambda ((X3 tptp.nat)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_nat Lst)) K))))
% 7.27/7.61 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_VEBT_VEBTi)) (= (@ (@ tptp.map_VE7998069337340375161T_VEBT (lambda ((X3 tptp.vEBT_VEBTi)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s7982070591426661849_VEBTi Lst)) K))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y3) A2)) (@ (@ tptp.powr_real X2) A2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X2) A2)) (@ (@ tptp.powr_real Y3) A2)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ _let_1 (@ (@ tptp.powr_real X2) Y3)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.powr_real A2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (not (= A2 tptp.one_one_real)) (= (= (@ _let_1 X2) (@ _let_1 Y3)) (= X2 Y3)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (@ _let_1 (@ (@ tptp.powr_real X2) A2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A2)) (@ (@ tptp.powr_real Y3) B2))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A2)) tptp.one_one_real)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X2) Y3)) A2) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A2)) (@ (@ tptp.powr_real Y3) A2))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X2) Y3)) A2) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X2) A2)) (@ (@ tptp.powr_real Y3) A2))))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.times_times_real (@ _let_1 A2)) (@ _let_1 B2))))))
% 7.27/7.61 (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))))))
% 7.27/7.61 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D3) M)))))))
% 7.27/7.61 (assert (forall ((N7 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N7) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N7))))
% 7.27/7.61 (assert (forall ((N7 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N7) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N7))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X2)))) (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 X2) tptp.bot_bot_set_real))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X2)))) (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 X2) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X2)))) (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 X2) tptp.bot_bot_set_nat))))))))
% 7.27/7.61 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X2)))) (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 X2) tptp.bot_bot_set_int))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B2) Y3)) X2) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.log B2) X2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B2) Y3)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) X2)) Y3))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) X2)) Y3) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B2) Y3)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.log B2) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B2) Y3)) X2))))))
% 7.27/7.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real)))))))
% 7.27/7.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 7.27/7.61 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real X2) (@ _let_1 Y3)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y3)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B2) Y3)) X2) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.log B2) X2)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B2) Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) X2)) Y3))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) X2)) Y3) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B2) Y3)))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.log B2) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B2) Y3)) X2))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real (@ _let_1 X2)) Y3) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B2) Y3)))))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y3) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B2) Y3)) X2))))))))))
% 7.27/7.61 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y3) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B2) Y3)) X2))))))))))
% 7.27/7.61 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 7.27/7.61 (assert (forall ((A tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.minus_5127226145743854075T_VEBT A))) (= (@ tptp.finite5795047828879050333T_VEBT (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT A2) B))) (@ tptp.finite5795047828879050333T_VEBT (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A2) B))) (@ tptp.finite_finite_int (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer) (B tptp.set_Code_integer)) (let ((_let_1 (@ tptp.minus_2355218937544613996nteger A))) (= (@ tptp.finite6017078050557962740nteger (@ _let_1 (@ (@ tptp.insert_Code_integer A2) B))) (@ tptp.finite6017078050557962740nteger (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_complex) (A2 tptp.complex) (B tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A2) B))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B))) (@ tptp.finite_finite_nat (@ _let_1 B))))))
% 7.27/7.61 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) K))))))
% 7.27/7.61 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat N4) K))))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (@ tptp.finite6931041176100689706nteger (@ tptp.collec574505750873337192nteger (lambda ((B5 tptp.set_Code_integer)) (@ (@ tptp.ord_le7084787975880047091nteger B5) A)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A)))))))
% 7.27/7.61 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A)))))))
% 7.27/7.61 (assert (forall ((S tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((T4 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT T4) S) (=> (@ P T4) (exists ((X8 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X8) (@ (@ tptp.minus_5127226145743854075T_VEBT S) T4)) (@ P (@ (@ tptp.insert_VEBT_VEBT X8) T4))))))) (@ P S))))))
% 7.27/7.61 (assert (forall ((S tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((T4 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger T4) S) (=> (@ P T4) (exists ((X8 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X8) (@ (@ tptp.minus_2355218937544613996nteger S) T4)) (@ P (@ (@ tptp.insert_Code_integer X8) T4))))))) (@ P S))))))
% 7.27/7.61 (assert (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T4) S) (=> (@ P T4) (exists ((X8 tptp.complex)) (and (@ (@ tptp.member_complex X8) (@ (@ tptp.minus_811609699411566653omplex S) T4)) (@ P (@ (@ tptp.insert_complex X8) T4))))))) (@ P S))))))
% 7.27/7.61 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T4) S) (=> (@ P T4) (exists ((X8 tptp.int)) (and (@ (@ tptp.member_int X8) (@ (@ tptp.minus_minus_set_int S) T4)) (@ P (@ (@ tptp.insert_int X8) T4))))))) (@ P S))))))
% 7.27/7.61 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T4) S) (=> (@ P T4) (exists ((X8 tptp.nat)) (and (@ (@ tptp.member_nat X8) (@ (@ tptp.minus_minus_set_nat S) T4)) (@ P (@ (@ tptp.insert_nat X8) T4))))))) (@ P S))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool))) (= (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P)) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (or (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (@ P X3) (@ Q X3))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ P X3) (@ Q X3))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ P X3) (@ Q X3))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool))) (=> (or (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P)) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer Q))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ P X3) (@ Q X3))))))))
% 7.27/7.61 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (or (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ P X3) (@ Q X3))))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A2) I4) (@ (@ tptp.ord_less_eq_int I4) B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A2) I4) (@ (@ tptp.ord_less_int I4) B2)))))))
% 7.27/7.61 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 7.27/7.61 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 7.27/7.61 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ tptp.finite_finite_int A) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A) B)))))
% 7.27/7.61 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.minus_2355218937544613996nteger A) B)))))
% 7.27/7.61 (assert (forall ((A tptp.set_complex) (B tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A) B)))))
% 7.27/7.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A) B)))))
% 7.27/7.61 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ tptp.finite_finite_int B) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A) B)) (@ tptp.finite_finite_int A)))))
% 7.27/7.61 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B) (= (@ tptp.finite6017078050557962740nteger (@ (@ tptp.minus_2355218937544613996nteger A) B)) (@ tptp.finite6017078050557962740nteger A)))))
% 7.27/7.61 (assert (forall ((B tptp.set_complex) (A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A) B)) (@ tptp.finite3207457112153483333omplex A)))))
% 7.27/7.61 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A) B)) (@ tptp.finite_finite_nat A)))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A2) I4) (@ (@ tptp.ord_less_int I4) B2)))))))
% 7.27/7.61 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A2) I4) (@ (@ tptp.ord_less_eq_int I4) B2)))))))
% 7.27/7.61 (assert (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))))
% 7.27/7.61 (assert (forall ((M8 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M8) (exists ((N3 tptp.nat)) (forall ((X8 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X8) M8) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X8)) N3)))))))
% 7.27/7.62 (assert (forall ((M8 tptp.set_list_real)) (=> (@ tptp.finite306553202115118035t_real M8) (exists ((N3 tptp.nat)) (forall ((X8 tptp.list_real)) (=> (@ (@ tptp.member_list_real X8) M8) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_real X8)) N3)))))))
% 7.27/7.62 (assert (forall ((M8 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M8) (exists ((N3 tptp.nat)) (forall ((X8 tptp.list_o)) (=> (@ (@ tptp.member_list_o X8) M8) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X8)) N3)))))))
% 7.27/7.62 (assert (forall ((M8 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M8) (exists ((N3 tptp.nat)) (forall ((X8 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X8) M8) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X8)) N3)))))))
% 7.27/7.62 (assert (forall ((M8 tptp.set_list_VEBT_VEBTi)) (=> (@ tptp.finite5722435864697464412_VEBTi M8) (exists ((N3 tptp.nat)) (forall ((X8 tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.member8117914210271334748_VEBTi X8) M8) (@ (@ tptp.ord_less_nat (@ tptp.size_s7982070591426661849_VEBTi X8)) N3)))))))
% 7.27/7.62 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D3 tptp.int)) (@ (@ tptp.dvd_dvd_int D3) I)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_nat) (R (-> tptp.vEBT_VEBT tptp.nat Bool))) (=> (not (@ tptp.finite5795047828879050333T_VEBT A)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B) (not (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((A5 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A5 tptp.real)) (and (@ (@ tptp.member_real A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_int) (R (-> tptp.vEBT_VEBT tptp.int Bool))) (=> (not (@ tptp.finite5795047828879050333T_VEBT A)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B) (not (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((A5 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A5 tptp.real)) (and (@ (@ tptp.member_real A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_Code_integer) (R (-> tptp.vEBT_VEBT tptp.code_integer Bool))) (=> (not (@ tptp.finite5795047828879050333T_VEBT A)) (=> (@ tptp.finite6017078050557962740nteger B) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) B) (not (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((A5 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_Code_integer) (R (-> tptp.real tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_real A)) (=> (@ tptp.finite6017078050557962740nteger B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A5 tptp.real)) (and (@ (@ tptp.member_real A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_complex) (R (-> tptp.vEBT_VEBT tptp.complex Bool))) (=> (not (@ tptp.finite5795047828879050333T_VEBT A)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (exists ((Xa2 tptp.complex)) (and (@ (@ tptp.member_complex Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) B) (not (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((A5 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_complex) (R (-> tptp.real tptp.complex Bool))) (=> (not (@ tptp.finite_finite_real A)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (exists ((Xa2 tptp.complex)) (and (@ (@ tptp.member_complex Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A5 tptp.real)) (and (@ (@ tptp.member_real A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (B tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) B) (@ (@ R X4) Xa2))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A) (@ (@ R A5) X4)))))))))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (=> (not (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P))) (exists ((X_1 tptp.product_prod_int_int)) (@ P X_1)))))
% 7.27/7.62 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 7.27/7.62 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 7.27/7.62 (assert (forall ((P (-> tptp.code_integer Bool))) (=> (not (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P))) (exists ((X_1 tptp.code_integer)) (@ P X_1)))))
% 7.27/7.62 (assert (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_1 tptp.complex)) (@ P X_1)))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (A2 tptp.real)) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real A2) A) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real X4) A2) (forall ((Xa2 tptp.real)) (=> (@ (@ tptp.member_real Xa2) A) (=> (@ (@ tptp.ord_less_eq_real Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer A2) A) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_le3102999989581377725nteger X4) A2) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_set_int) (A2 tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A) (=> (@ (@ tptp.member_set_int A2) A) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A) (@ (@ tptp.ord_less_eq_set_int X4) A2) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_set_int Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_rat) (A2 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (@ (@ tptp.member_rat A2) A) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A) (@ (@ tptp.ord_less_eq_rat X4) A2) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A) (=> (@ (@ tptp.ord_less_eq_rat Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_num) (A2 tptp.num)) (=> (@ tptp.finite_finite_num A) (=> (@ (@ tptp.member_num A2) A) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A) (@ (@ tptp.ord_less_eq_num X4) A2) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A) (=> (@ (@ tptp.ord_less_eq_num Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat A2) A) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_nat X4) A2) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_nat Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int A2) A) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_int X4) A2) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_int Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (A2 tptp.real)) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real A2) A) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real A2) X4) (forall ((Xa2 tptp.real)) (=> (@ (@ tptp.member_real Xa2) A) (=> (@ (@ tptp.ord_less_eq_real X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer A2) A) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_le3102999989581377725nteger A2) X4) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_set_int) (A2 tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A) (=> (@ (@ tptp.member_set_int A2) A) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A) (@ (@ tptp.ord_less_eq_set_int A2) X4) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_set_int X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_rat) (A2 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (@ (@ tptp.member_rat A2) A) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A) (@ (@ tptp.ord_less_eq_rat A2) X4) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_num) (A2 tptp.num)) (=> (@ tptp.finite_finite_num A) (=> (@ (@ tptp.member_num A2) A) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A) (@ (@ tptp.ord_less_eq_num A2) X4) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A) (=> (@ (@ tptp.ord_less_eq_num X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat A2) A) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_nat A2) X4) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int A2) A) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_int A2) X4) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_int X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite_finite_nat A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (@ tptp.finite6017078050557962740nteger B) (@ tptp.finite6017078050557962740nteger A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (@ tptp.finite3207457112153483333omplex B) (@ tptp.finite3207457112153483333omplex A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ tptp.finite_finite_int B) (@ tptp.finite_finite_int A)))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (T5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T5) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T5))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (T5 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger T5))))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (T5 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex T5))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (T5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S) T5) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T5))))))
% 7.27/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ tptp.finite_finite_nat A)))))
% 7.27/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (@ tptp.finite6017078050557962740nteger A)))))
% 7.27/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (@ tptp.finite3207457112153483333omplex A)))))
% 7.27/7.62 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ tptp.finite_finite_int A)))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_int) (S tptp.set_int)) (=> (@ tptp.finite_finite_int T5) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S) T5)))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.minus_2355218937544613996nteger S) T5)))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S) T5)))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_nat) (S tptp.set_nat)) (=> (@ tptp.finite_finite_nat T5) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S) T5)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A) (=> (not (= A tptp.bot_bot_set_set_int)) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_set_int X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_num)) (=> (@ tptp.finite_finite_num A) (=> (not (= A tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A) (=> (@ (@ tptp.ord_less_eq_num X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_int X4) Xa2) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A) (=> (not (= A tptp.bot_bot_set_set_int)) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_set_int Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A) (=> (@ (@ tptp.ord_less_eq_rat Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_num)) (=> (@ tptp.finite_finite_num A) (=> (not (= A tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A) (=> (@ (@ tptp.ord_less_eq_num Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_nat Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_int Xa2) X4) (= X4 Xa2))))))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT F3) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT F3) A) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((A3 tptp.vEBT_VEBT) (F6 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT A3))) (=> (@ tptp.finite5795047828879050333T_VEBT F6) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT F6) A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_VEBT_VEBT A3) F6))))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_real) (A tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.real) (F6 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A3))) (=> (@ tptp.finite_finite_real F6) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_set_real F6) A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_real A3) F6))))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_Code_integer) (A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (@ (@ tptp.ord_le7084787975880047091nteger F3) A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((A3 tptp.code_integer) (F6 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.member_Code_integer A3))) (=> (@ tptp.finite6017078050557962740nteger F6) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le7084787975880047091nteger F6) A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_Code_integer A3) F6))))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_complex) (A tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.complex) (F6 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A3))) (=> (@ tptp.finite3207457112153483333omplex F6) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le211207098394363844omplex F6) A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_complex A3) F6))))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_nat) (A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F6 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F6) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_set_nat F6) A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_nat A3) F6))))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_int) (A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F6 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F6) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_set_int F6) A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_int A3) F6))))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT F3) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT F3) A) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((A3 tptp.vEBT_VEBT) (F6 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT A3))) (=> (@ tptp.finite5795047828879050333T_VEBT F6) (=> (@ _let_1 A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_VEBT_VEBT A3) F6)))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_real) (A tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.real) (F6 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A3))) (=> (@ tptp.finite_finite_real F6) (=> (@ _let_1 A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_real A3) F6)))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_Code_integer) (A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (@ (@ tptp.ord_le7084787975880047091nteger F3) A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((A3 tptp.code_integer) (F6 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.member_Code_integer A3))) (=> (@ tptp.finite6017078050557962740nteger F6) (=> (@ _let_1 A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_Code_integer A3) F6)))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_complex) (A tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.complex) (F6 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A3))) (=> (@ tptp.finite3207457112153483333omplex F6) (=> (@ _let_1 A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_complex A3) F6)))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_nat) (A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F6 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F6) (=> (@ _let_1 A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_nat A3) F6)))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((F3 tptp.set_int) (A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F6 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F6) (=> (@ _let_1 A) (=> (not (@ _let_1 F6)) (=> (@ P F6) (@ P (@ (@ tptp.insert_int A3) F6)))))))) (@ P F3)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT)) (=> (not (@ tptp.finite5795047828879050333T_VEBT S)) (not (@ tptp.finite5795047828879050333T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex)) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int)) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)))))))
% 7.27/7.62 (assert (forall ((X (-> tptp.set_VEBT_VEBT Bool)) (A tptp.set_VEBT_VEBT)) (=> (@ X A) (=> (forall ((A8 tptp.set_VEBT_VEBT)) (=> (@ X A8) (exists ((X8 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A8) (@ (@ tptp.insert_VEBT_VEBT X8) tptp.bot_bo8194388402131092736T_VEBT)))) (and (@ (@ tptp.member_VEBT_VEBT X8) A8) (or (@ X _let_1) (not (@ tptp.finite5795047828879050333T_VEBT _let_1)))))))) (not (@ tptp.finite5795047828879050333T_VEBT A))))))
% 7.27/7.62 (assert (forall ((X (-> tptp.set_Code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ X A) (=> (forall ((A8 tptp.set_Code_integer)) (=> (@ X A8) (exists ((X8 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_2355218937544613996nteger A8) (@ (@ tptp.insert_Code_integer X8) tptp.bot_bo3990330152332043303nteger)))) (and (@ (@ tptp.member_Code_integer X8) A8) (or (@ X _let_1) (not (@ tptp.finite6017078050557962740nteger _let_1)))))))) (not (@ tptp.finite6017078050557962740nteger A))))))
% 7.27/7.62 (assert (forall ((X (-> tptp.set_complex Bool)) (A tptp.set_complex)) (=> (@ X A) (=> (forall ((A8 tptp.set_complex)) (=> (@ X A8) (exists ((X8 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A8) (@ (@ tptp.insert_complex X8) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X8) A8) (or (@ X _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A))))))
% 7.27/7.62 (assert (forall ((X (-> tptp.set_int Bool)) (A tptp.set_int)) (=> (@ X A) (=> (forall ((A8 tptp.set_int)) (=> (@ X A8) (exists ((X8 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A8) (@ (@ tptp.insert_int X8) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X8) A8) (or (@ X _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A))))))
% 7.27/7.62 (assert (forall ((X (-> tptp.set_nat Bool)) (A tptp.set_nat)) (=> (@ X A) (=> (forall ((A8 tptp.set_nat)) (=> (@ X A8) (exists ((X8 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A8) (@ (@ tptp.insert_nat X8) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X8) A8) (or (@ X _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ P A) (=> (forall ((A3 tptp.vEBT_VEBT) (A8 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A8) (=> (@ (@ tptp.member_VEBT_VEBT A3) A8) (=> (@ P A8) (@ P (@ (@ tptp.minus_5127226145743854075T_VEBT A8) (@ (@ tptp.insert_VEBT_VEBT A3) tptp.bot_bo8194388402131092736T_VEBT))))))) (@ P tptp.bot_bo8194388402131092736T_VEBT))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ P A) (=> (forall ((A3 tptp.real) (A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (@ (@ tptp.member_real A3) A8) (=> (@ P A8) (@ P (@ (@ tptp.minus_minus_set_real A8) (@ (@ tptp.insert_real A3) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ P A) (=> (forall ((A3 tptp.code_integer) (A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (@ (@ tptp.member_Code_integer A3) A8) (=> (@ P A8) (@ P (@ (@ tptp.minus_2355218937544613996nteger A8) (@ (@ tptp.insert_Code_integer A3) tptp.bot_bo3990330152332043303nteger))))))) (@ P tptp.bot_bo3990330152332043303nteger))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ P A) (=> (forall ((A3 tptp.complex) (A8 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A8) (=> (@ (@ tptp.member_complex A3) A8) (=> (@ P A8) (@ P (@ (@ tptp.minus_811609699411566653omplex A8) (@ (@ tptp.insert_complex A3) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ P A) (=> (forall ((A3 tptp.int) (A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (@ (@ tptp.member_int A3) A8) (=> (@ P A8) (@ P (@ (@ tptp.minus_minus_set_int A8) (@ (@ tptp.insert_int A3) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ P A) (=> (forall ((A3 tptp.nat) (A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (@ (@ tptp.member_nat A3) A8) (=> (@ P A8) (@ P (@ (@ tptp.minus_minus_set_nat A8) (@ (@ tptp.insert_nat A3) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 7.27/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((A8 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A8) (=> (not (= A8 tptp.bot_bo8194388402131092736T_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A8) B) (=> (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) A8) (@ P (@ (@ tptp.minus_5127226145743854075T_VEBT A8) (@ (@ tptp.insert_VEBT_VEBT X8) tptp.bot_bo8194388402131092736T_VEBT))))) (@ P A8)))))) (@ P B))))))
% 7.27/7.62 (assert (forall ((B tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (not (= A8 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A8) B) (=> (forall ((X8 tptp.real)) (=> (@ (@ tptp.member_real X8) A8) (@ P (@ (@ tptp.minus_minus_set_real A8) (@ (@ tptp.insert_real X8) tptp.bot_bot_set_real))))) (@ P A8)))))) (@ P B))))))
% 7.27/7.62 (assert (forall ((B tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (not (= A8 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A8) B) (=> (forall ((X8 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X8) A8) (@ P (@ (@ tptp.minus_2355218937544613996nteger A8) (@ (@ tptp.insert_Code_integer X8) tptp.bot_bo3990330152332043303nteger))))) (@ P A8)))))) (@ P B))))))
% 7.27/7.62 (assert (forall ((B tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A8 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A8) (=> (not (= A8 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A8) B) (=> (forall ((X8 tptp.complex)) (=> (@ (@ tptp.member_complex X8) A8) (@ P (@ (@ tptp.minus_811609699411566653omplex A8) (@ (@ tptp.insert_complex X8) tptp.bot_bot_set_complex))))) (@ P A8)))))) (@ P B))))))
% 7.27/7.62 (assert (forall ((B tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (not (= A8 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A8) B) (=> (forall ((X8 tptp.nat)) (=> (@ (@ tptp.member_nat X8) A8) (@ P (@ (@ tptp.minus_minus_set_nat A8) (@ (@ tptp.insert_nat X8) tptp.bot_bot_set_nat))))) (@ P A8)))))) (@ P B))))))
% 7.27/7.62 (assert (forall ((B tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (not (= A8 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A8) B) (=> (forall ((X8 tptp.int)) (=> (@ (@ tptp.member_int X8) A8) (@ P (@ (@ tptp.minus_minus_set_int A8) (@ (@ tptp.insert_int X8) tptp.bot_bot_set_int))))) (@ P A8)))))) (@ P B))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.set_VEBT_VEBT Bool)) (B tptp.set_VEBT_VEBT)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (=> (not (@ tptp.finite5795047828879050333T_VEBT B)) _let_1) (=> (forall ((A8 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A8) (=> (not (= A8 tptp.bot_bo8194388402131092736T_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A8) B) (=> (forall ((X8 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X8) A8) (@ P (@ (@ tptp.minus_5127226145743854075T_VEBT A8) (@ (@ tptp.insert_VEBT_VEBT X8) tptp.bot_bo8194388402131092736T_VEBT))))) (@ P A8)))))) _let_1))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.set_real Bool)) (B tptp.set_real)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B)) _let_1) (=> (forall ((A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (not (= A8 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A8) B) (=> (forall ((X8 tptp.real)) (=> (@ (@ tptp.member_real X8) A8) (@ P (@ (@ tptp.minus_minus_set_real A8) (@ (@ tptp.insert_real X8) tptp.bot_bot_set_real))))) (@ P A8)))))) _let_1))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.set_Code_integer Bool)) (B tptp.set_Code_integer)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (=> (not (@ tptp.finite6017078050557962740nteger B)) _let_1) (=> (forall ((A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (not (= A8 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A8) B) (=> (forall ((X8 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X8) A8) (@ P (@ (@ tptp.minus_2355218937544613996nteger A8) (@ (@ tptp.insert_Code_integer X8) tptp.bot_bo3990330152332043303nteger))))) (@ P A8)))))) _let_1))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.set_complex Bool)) (B tptp.set_complex)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B)) _let_1) (=> (forall ((A8 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A8) (=> (not (= A8 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A8) B) (=> (forall ((X8 tptp.complex)) (=> (@ (@ tptp.member_complex X8) A8) (@ P (@ (@ tptp.minus_811609699411566653omplex A8) (@ (@ tptp.insert_complex X8) tptp.bot_bot_set_complex))))) (@ P A8)))))) _let_1))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.set_nat Bool)) (B tptp.set_nat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B)) _let_1) (=> (forall ((A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (not (= A8 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A8) B) (=> (forall ((X8 tptp.nat)) (=> (@ (@ tptp.member_nat X8) A8) (@ P (@ (@ tptp.minus_minus_set_nat A8) (@ (@ tptp.insert_nat X8) tptp.bot_bot_set_nat))))) (@ P A8)))))) _let_1))))))
% 7.27/7.62 (assert (forall ((P (-> tptp.set_int Bool)) (B tptp.set_int)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B)) _let_1) (=> (forall ((A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (not (= A8 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A8) B) (=> (forall ((X8 tptp.int)) (=> (@ (@ tptp.member_int X8) A8) (@ P (@ (@ tptp.minus_minus_set_int A8) (@ (@ tptp.insert_int X8) tptp.bot_bot_set_int))))) (@ P A8)))))) _let_1))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (C2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat N) A)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A)))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.product_prod_int_int tptp.nat)) (N7 (-> tptp.product_prod_int_int tptp.nat))) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M8 X3)) (@ N7 X3)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.nat tptp.nat)) (N7 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M8 X3)) (@ N7 X3)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.int tptp.nat)) (N7 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M8 X3)) (@ N7 X3)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.code_integer tptp.nat)) (N7 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M8 X3)) (@ N7 X3)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.complex tptp.nat)) (N7 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M8 X3)) (@ N7 X3)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.product_prod_int_int tptp.nat)) (A2 tptp.product_prod_int_int)) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ M8 X3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X3 A2)) (@ tptp.suc _let_1)) _let_1)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.nat tptp.nat)) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (let ((_let_1 (@ M8 X3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X3 A2)) (@ tptp.suc _let_1)) _let_1)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.int tptp.nat)) (A2 tptp.int)) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (let ((_let_1 (@ M8 X3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X3 A2)) (@ tptp.suc _let_1)) _let_1)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.code_integer tptp.nat)) (A2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (let ((_let_1 (@ M8 X3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X3 A2)) (@ tptp.suc _let_1)) _let_1)))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.complex tptp.nat)) (A2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ M8 X3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X3 A2)) (@ tptp.suc _let_1)) _let_1)))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((B3 tptp.code_integer) (A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (forall ((X8 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X8) A8) (@ (@ tptp.ord_le6747313008572928689nteger X8) B3))) (=> (@ P A8) (@ P (@ (@ tptp.insert_Code_integer B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B3 tptp.real) (A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (forall ((X8 tptp.real)) (=> (@ (@ tptp.member_real X8) A8) (@ (@ tptp.ord_less_real X8) B3))) (=> (@ P A8) (@ P (@ (@ tptp.insert_real B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B3 tptp.rat) (A8 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A8) (=> (forall ((X8 tptp.rat)) (=> (@ (@ tptp.member_rat X8) A8) (@ (@ tptp.ord_less_rat X8) B3))) (=> (@ P A8) (@ P (@ (@ tptp.insert_rat B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B3 tptp.num) (A8 tptp.set_num)) (=> (@ tptp.finite_finite_num A8) (=> (forall ((X8 tptp.num)) (=> (@ (@ tptp.member_num X8) A8) (@ (@ tptp.ord_less_num X8) B3))) (=> (@ P A8) (@ P (@ (@ tptp.insert_num B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B3 tptp.nat) (A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (forall ((X8 tptp.nat)) (=> (@ (@ tptp.member_nat X8) A8) (@ (@ tptp.ord_less_nat X8) B3))) (=> (@ P A8) (@ P (@ (@ tptp.insert_nat B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B3 tptp.int) (A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (forall ((X8 tptp.int)) (=> (@ (@ tptp.member_int X8) A8) (@ (@ tptp.ord_less_int X8) B3))) (=> (@ P A8) (@ P (@ (@ tptp.insert_int B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((B2 tptp.complex) (A2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B2) A2))) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex A2))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A))))))
% 7.27/7.62 (assert (forall ((X tptp.set_Code_integer)) (=> (not (= X tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) X) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) X) (@ (@ tptp.ord_le6747313008572928689nteger X4) Xa2))))) (not (@ tptp.finite6017078050557962740nteger X))))))
% 7.27/7.62 (assert (forall ((X tptp.set_real)) (=> (not (= X tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) X) (exists ((Xa2 tptp.real)) (and (@ (@ tptp.member_real Xa2) X) (@ (@ tptp.ord_less_real X4) Xa2))))) (not (@ tptp.finite_finite_real X))))))
% 7.27/7.62 (assert (forall ((X tptp.set_rat)) (=> (not (= X tptp.bot_bot_set_rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) X) (exists ((Xa2 tptp.rat)) (and (@ (@ tptp.member_rat Xa2) X) (@ (@ tptp.ord_less_rat X4) Xa2))))) (not (@ tptp.finite_finite_rat X))))))
% 7.27/7.62 (assert (forall ((X tptp.set_num)) (=> (not (= X tptp.bot_bot_set_num)) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) X) (exists ((Xa2 tptp.num)) (and (@ (@ tptp.member_num Xa2) X) (@ (@ tptp.ord_less_num X4) Xa2))))) (not (@ tptp.finite_finite_num X))))))
% 7.27/7.62 (assert (forall ((X tptp.set_nat)) (=> (not (= X tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) X) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) X) (@ (@ tptp.ord_less_nat X4) Xa2))))) (not (@ tptp.finite_finite_nat X))))))
% 7.27/7.62 (assert (forall ((X tptp.set_int)) (=> (not (= X tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) X) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) X) (@ (@ tptp.ord_less_int X4) Xa2))))) (not (@ tptp.finite_finite_int X))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (not (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) S) (@ (@ tptp.ord_le6747313008572928689nteger Xa2) X4))))))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real)) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) S) (not (exists ((Xa2 tptp.real)) (and (@ (@ tptp.member_real Xa2) S) (@ (@ tptp.ord_less_real Xa2) X4))))))))))
% 7.27/7.62 (assert (forall ((S tptp.set_rat)) (=> (@ tptp.finite_finite_rat S) (=> (not (= S tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) S) (not (exists ((Xa2 tptp.rat)) (and (@ (@ tptp.member_rat Xa2) S) (@ (@ tptp.ord_less_rat Xa2) X4))))))))))
% 7.27/7.62 (assert (forall ((S tptp.set_num)) (=> (@ tptp.finite_finite_num S) (=> (not (= S tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) S) (not (exists ((Xa2 tptp.num)) (and (@ (@ tptp.member_num Xa2) S) (@ (@ tptp.ord_less_num Xa2) X4))))))))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (not (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) S) (@ (@ tptp.ord_less_nat Xa2) X4))))))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (not (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) S) (@ (@ tptp.ord_less_int Xa2) X4))))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.product_prod_int_int tptp.nat)) (P (-> tptp.product_prod_int_int Bool))) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X3)) (@ M8 X3)) tptp.zero_zero_nat))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.nat tptp.nat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X3)) (@ M8 X3)) tptp.zero_zero_nat))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X3)) (@ M8 X3)) tptp.zero_zero_nat))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.code_integer tptp.nat)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X3)) (@ M8 X3)) tptp.zero_zero_nat))))))))
% 7.27/7.62 (assert (forall ((M8 (-> tptp.complex tptp.nat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M8 X3))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X3)) (@ M8 X3)) tptp.zero_zero_nat))))))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X4 tptp.vEBT_VEBT) (S6 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S6) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) S6) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S6 tptp.set_real)) (=> (@ tptp.finite_finite_real S6) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) S6) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_real X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((X4 tptp.code_integer) (S6 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S6) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S6) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_Code_integer X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S6) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) S6) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_complex X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (S6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S6) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S6) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_nat X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (S6 tptp.set_int)) (=> (@ tptp.finite_finite_int S6) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S6) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_int X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.num))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X4 tptp.vEBT_VEBT) (S6 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S6) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) S6) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S6 tptp.set_real)) (=> (@ tptp.finite_finite_real S6) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) S6) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_real X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.num))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((X4 tptp.code_integer) (S6 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S6) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S6) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_Code_integer X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S6) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) S6) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S6) (@ P (@ (@ tptp.insert_complex X4) S6)))))) (@ P S))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((B3 tptp.code_integer) (A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (forall ((X8 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X8) A8) (@ (@ tptp.ord_le6747313008572928689nteger B3) X8))) (=> (@ P A8) (@ P (@ (@ tptp.insert_Code_integer B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B3 tptp.real) (A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (forall ((X8 tptp.real)) (=> (@ (@ tptp.member_real X8) A8) (@ (@ tptp.ord_less_real B3) X8))) (=> (@ P A8) (@ P (@ (@ tptp.insert_real B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B3 tptp.rat) (A8 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A8) (=> (forall ((X8 tptp.rat)) (=> (@ (@ tptp.member_rat X8) A8) (@ (@ tptp.ord_less_rat B3) X8))) (=> (@ P A8) (@ P (@ (@ tptp.insert_rat B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B3 tptp.num) (A8 tptp.set_num)) (=> (@ tptp.finite_finite_num A8) (=> (forall ((X8 tptp.num)) (=> (@ (@ tptp.member_num X8) A8) (@ (@ tptp.ord_less_num B3) X8))) (=> (@ P A8) (@ P (@ (@ tptp.insert_num B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B3 tptp.nat) (A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (forall ((X8 tptp.nat)) (=> (@ (@ tptp.member_nat X8) A8) (@ (@ tptp.ord_less_nat B3) X8))) (=> (@ P A8) (@ P (@ (@ tptp.insert_nat B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B3 tptp.int) (A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (forall ((X8 tptp.int)) (=> (@ (@ tptp.member_int X8) A8) (@ (@ tptp.ord_less_int B3) X8))) (=> (@ P A8) (@ P (@ (@ tptp.insert_int B3) A8)))))) (@ P A))))))
% 7.27/7.62 (assert (forall ((A2 tptp.array_VEBT_VEBTi) (Xs tptp.list_VEBT_VEBTi)) (@ (@ (@ tptp.hoare_3904069481286416050_VEBTi (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ tptp.array_8141364883501958055_VEBTi A2)) (lambda ((R5 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ tptp.pure_assn (= R5 Xs)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X2 (-> tptp.vEBT_VEBT tptp.assn)) (Y3 (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ X2 I4) tptp.one_one_assn)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ Y3 I4) tptp.one_one_assn)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ (@ tptp.times_times_assn (@ X2 I4)) (@ Y3 I4)) tptp.one_one_assn))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.assn)) (Y3 (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ X2 I4) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ Y3 I4) tptp.one_one_assn)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ (@ tptp.times_times_assn (@ X2 I4)) (@ Y3 I4)) tptp.one_one_assn))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_nat) (X2 (-> tptp.nat tptp.assn)) (Y3 (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ X2 I4) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ Y3 I4) tptp.one_one_assn)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ (@ tptp.times_times_assn (@ X2 I4)) (@ Y3 I4)) tptp.one_one_assn))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (X2 (-> tptp.int tptp.assn)) (Y3 (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ X2 I4) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ Y3 I4) tptp.one_one_assn)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ (@ tptp.times_times_assn (@ X2 I4)) (@ Y3 I4)) tptp.one_one_assn))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_Code_integer) (X2 (-> tptp.code_integer tptp.assn)) (Y3 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I6) (not (= (@ X2 I4) tptp.one_one_assn)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I6) (not (= (@ Y3 I4) tptp.one_one_assn)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I6) (not (= (@ (@ tptp.times_times_assn (@ X2 I4)) (@ Y3 I4)) tptp.one_one_assn))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_complex) (X2 (-> tptp.complex tptp.assn)) (Y3 (-> tptp.complex tptp.assn))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I6) (not (= (@ X2 I4) tptp.one_one_assn)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I6) (not (= (@ Y3 I4) tptp.one_one_assn)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I6) (not (= (@ (@ tptp.times_times_assn (@ X2 I4)) (@ Y3 I4)) tptp.one_one_assn))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X2 (-> tptp.vEBT_VEBT tptp.real)) (Y3 (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y3 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y3 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y3 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X2 (-> tptp.vEBT_VEBT tptp.complex)) (Y3 (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_complex)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_complex))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y3 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_complex))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y3 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_complex))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y3 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_complex))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_Code_integer) (X2 (-> tptp.code_integer tptp.complex)) (Y3 (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I6) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_complex)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_complex))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y3 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I6) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_complex))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X2 (-> tptp.vEBT_VEBT tptp.real)) (Y3 (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I4) I6) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y3 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I6) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y3 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I6) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y3 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I6) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)))))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)))))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A) tptp.zero_zero_nat)))
% 7.27/7.62 (assert (forall ((A tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A) tptp.zero_zero_complex)))
% 7.27/7.62 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A) tptp.zero_zero_real)))
% 7.27/7.62 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A) tptp.zero_zero_int)))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.nat)) (A tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.int)) (A tptp.set_complex)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.groups5690904116761175830ex_int F) A)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) (@ tptp.ring_17405671764205052669omplex (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups3539618377306564664at_int F) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X3 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups4538972089207619220nt_int F) A)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X3 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups4538972089207619220nt_int F) A)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X3 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X3)))) A))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.complex))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups8024822376189712711omplex (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8024822376189712711omplex (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_complex (= A2 K3)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups1270011288395367621r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1270011288395367621r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.complex))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups8024822376189712711omplex (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8024822376189712711omplex (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_complex (= K3 A2)) (@ B2 K3)) tptp.zero_zero_complex))) S) tptp.zero_zero_complex)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups1270011288395367621r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1270011288395367621r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X2) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X2) A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (@ (@ tptp.member_complex X2) A)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X2) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X2) A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A))))))))
% 7.27/7.62 (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.groups2073611262835488442omplex 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.zero_zero_complex)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 7.27/7.62 (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.groups2906978787729119204at_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.zero_zero_rat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 7.27/7.62 (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.groups3539618377306564664at_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.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 7.27/7.62 (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.groups3542108847815614940at_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.zero_zero_nat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 7.27/7.62 (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.groups6591440286371151544t_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.zero_zero_real)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.27/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (C2 (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat tptp.zero_zero_nat) A)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A) tptp.zero_zero_complex))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat tptp.zero_zero_nat) A)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A) tptp.zero_zero_rat))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (C2 (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat tptp.zero_zero_nat) A)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A) tptp.zero_zero_real))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (C2 (-> tptp.nat tptp.complex)) (D2 (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat tptp.zero_zero_nat) A)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D2 I4)))) A) (@ (@ tptp.divide1717551699836669952omplex (@ C2 tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D2 I4)))) A) tptp.zero_zero_complex))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (C2 (-> tptp.nat tptp.rat)) (D2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat tptp.zero_zero_nat) A)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A) (@ (@ tptp.divide_divide_rat (@ C2 tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A) tptp.zero_zero_rat))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (C2 (-> tptp.nat tptp.real)) (D2 (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat tptp.zero_zero_nat) A)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D2 I4)))) A) (@ (@ tptp.divide_divide_real (@ C2 tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D2 I4)))) A) tptp.zero_zero_real))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_nat) (G (-> tptp.vEBT_VEBT tptp.nat tptp.nat)) (R (-> tptp.vEBT_VEBT tptp.nat Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups771621172384141258BT_nat (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ G X3) Y))) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X3 tptp.real)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X3 tptp.real)) (@ (@ G X3) Y))) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (B tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ G X3) Y))) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.nat)) (R (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X3 tptp.code_integer)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X3 tptp.code_integer)) (@ (@ G X3) Y))) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X3 tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X3 tptp.complex)) (@ (@ G X3) Y))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_complex) (G (-> tptp.vEBT_VEBT tptp.complex tptp.complex)) (R (-> tptp.vEBT_VEBT tptp.complex Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.groups7754918857620584856omplex (@ G X3)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups1794756597179926696omplex (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ G X3) Y))) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_complex) (G (-> tptp.real tptp.complex tptp.complex)) (R (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((X3 tptp.real)) (@ (@ tptp.groups7754918857620584856omplex (@ G X3)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X3 tptp.real)) (@ (@ G X3) Y))) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (B tptp.set_complex) (G (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X3 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G X3)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X3 tptp.nat)) (@ (@ G X3) Y))) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (B tptp.set_complex) (G (-> tptp.int tptp.complex tptp.complex)) (R (-> tptp.int tptp.complex Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((X3 tptp.int)) (@ (@ tptp.groups7754918857620584856omplex (@ G X3)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X3 tptp.int)) (@ (@ G X3) Y))) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_complex) (G (-> tptp.code_integer tptp.complex tptp.complex)) (R (-> tptp.code_integer tptp.complex Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups8024822376189712711omplex (lambda ((X3 tptp.code_integer)) (@ (@ tptp.groups7754918857620584856omplex (@ G X3)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups8024822376189712711omplex (lambda ((X3 tptp.code_integer)) (@ (@ G X3) Y))) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex)) (A tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7754918857620584856omplex F) A)) (@ (@ tptp.groups7754918857620584856omplex G) A)))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (A tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) A)) (@ (@ tptp.groups6591440286371151544t_real G) A)))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A)) (@ (@ tptp.groups4538972089207619220nt_int G) A)))))
% 7.27/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.complex)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups1794756597179926696omplex F) S))) (@ (@ tptp.groups2240296850493347238T_real G) S)))))
% 7.27/7.62 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S))) (@ (@ tptp.groups8097168146408367636l_real G) S)))))
% 7.27/7.62 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S))) (@ (@ tptp.groups8778361861064173332t_real G) S)))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S))) (@ (@ tptp.groups6591440286371151544t_real G) S)))))
% 7.27/7.62 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S))) (@ (@ tptp.groups5808333547571424918x_real G) S)))))
% 7.27/7.62 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X4))) (@ G X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S))) (@ (@ tptp.groups6591440286371151544t_real G) S)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K6)) (@ (@ tptp.groups2906978787729119204at_rat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) K6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups136491112297645522BT_rat F) K6)) (@ (@ tptp.groups136491112297645522BT_rat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K6)) (@ (@ tptp.groups1300246762558778688al_rat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K6)) (@ (@ tptp.groups3906332499630173760nt_rat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) K6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups771621172384141258BT_nat F) K6)) (@ (@ tptp.groups771621172384141258BT_nat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K6)) (@ (@ tptp.groups1935376822645274424al_nat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K6)) (@ (@ tptp.groups4541462559716669496nt_nat G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K6) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K6)) (@ (@ tptp.groups3539618377306564664at_int G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int)) (G (-> tptp.vEBT_VEBT tptp.int))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) K6) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups769130701875090982BT_int F) K6)) (@ (@ tptp.groups769130701875090982BT_int G) K6)))))
% 7.27/7.62 (assert (forall ((K6 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K6) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K6)) (@ (@ tptp.groups1932886352136224148al_int G) K6)))))
% 7.27/7.62 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N4)))) A))))
% 7.27/7.62 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N4 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N4)))) A))))
% 7.27/7.62 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N4)))) A))))
% 7.27/7.62 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N4 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N4)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N4)) R2))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.complex)) (A tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N4 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N4)) R2))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) R2))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N4 tptp.int)) (@ (@ tptp.times_times_int (@ F N4)) R2))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3542108847815614940at_nat G) B)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I4)) (@ G J3)))) B))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.complex)) (A tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A)) (@ (@ tptp.groups7754918857620584856omplex G) B)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I4)) (@ G J3)))) B))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.set_nat) (G (-> tptp.nat tptp.real)) (B tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A)) (@ (@ tptp.groups6591440286371151544t_real G) B)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ G J3)))) B))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int) (G (-> tptp.int tptp.int)) (B tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A)) (@ (@ tptp.groups4538972089207619220nt_int G) B)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I4)) (@ G J3)))) B))) A))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G I4)) B))) A) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A))) B))))
% 7.27/7.62 (assert (forall ((G (-> tptp.complex tptp.complex tptp.complex)) (B tptp.set_complex) (A tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (@ G I4)) B))) A) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ G I4) J3))) A))) B))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ G I4)) B))) A) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A))) B))))
% 7.27/7.62 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B tptp.set_int) (A tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (@ G I4)) B))) A) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ G I4) J3))) A))) B))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.complex)) (A tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) R2))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) R2))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.complex)) (A tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I4)))) A))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A)) (@ (@ tptp.groups3542108847815614940at_nat H2) A)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A)) (@ (@ tptp.groups7754918857620584856omplex H2) A)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A)) (@ (@ tptp.groups6591440286371151544t_real H2) A)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A)) (@ (@ tptp.groups4538972089207619220nt_int H2) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2240296850493347238T_real F) A)) tptp.zero_zero_real))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A)) tptp.zero_zero_real))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A)) tptp.zero_zero_real))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A)) tptp.zero_zero_rat))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups136491112297645522BT_rat F) A)) tptp.zero_zero_rat))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A)) tptp.zero_zero_rat))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A)) tptp.zero_zero_rat))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups771621172384141258BT_nat F) A)) tptp.zero_zero_nat))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A)) tptp.zero_zero_nat))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A)) tptp.zero_zero_nat))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups2240296850493347238T_real F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups136491112297645522BT_rat F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups771621172384141258BT_nat F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A)))))
% 7.27/7.62 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.rat)) (I6 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (I tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.groups136491112297645522BT_rat F) I6) (@ (@ tptp.groups136491112297645522BT_rat G) I6)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_VEBT_VEBT I) I6) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.real tptp.rat)) (I6 tptp.set_real) (G (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I6) (@ (@ tptp.groups1300246762558778688al_rat G) I6)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I6) (@ (@ tptp.groups2906978787729119204at_rat G) I6)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_nat I) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.rat)) (I6 tptp.set_int) (G (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I6) (@ (@ tptp.groups3906332499630173760nt_rat G) I6)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.code_integer tptp.rat)) (I6 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (I tptp.code_integer)) (=> (= (@ (@ tptp.groups6602215022474089585er_rat F) I6) (@ (@ tptp.groups6602215022474089585er_rat G) I6)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_Code_integer I) I6) (=> (@ tptp.finite6017078050557962740nteger I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.complex tptp.rat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I6) (@ (@ tptp.groups5058264527183730370ex_rat G) I6)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (I6 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (I tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.groups771621172384141258BT_nat F) I6) (@ (@ tptp.groups771621172384141258BT_nat G) I6)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_VEBT_VEBT I) I6) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.real tptp.nat)) (I6 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I6) (@ (@ tptp.groups1935376822645274424al_nat G) I6)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.nat)) (I6 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I6) (@ (@ tptp.groups4541462559716669496nt_nat G) I6)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (I6 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (I tptp.code_integer)) (=> (= (@ (@ tptp.groups7237345082560585321er_nat F) I6) (@ (@ tptp.groups7237345082560585321er_nat G) I6)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_Code_integer I) I6) (=> (@ tptp.finite6017078050557962740nteger I6) (= (@ F I) (@ G I))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.suc X4))) (=> (@ (@ tptp.member_nat _let_1) A) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A) (@ (@ tptp.groups3542108847815614940at_nat G) A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.suc X4))) (=> (@ (@ tptp.member_nat _let_1) A) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A) (@ (@ tptp.groups6591440286371151544t_real G) A))))))
% 7.27/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (A tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A2))) A)) A2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A)) A2))))
% 7.27/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.int) (A tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A2))) A)) A2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A)) A2))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex)) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ (@ tptp.groups1794756597179926696omplex G) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ P X3))))) (@ (@ tptp.groups1794756597179926696omplex (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A) (= (@ (@ tptp.groups5754745047067104278omplex G) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ P X3))))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P X3))))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.groups3049146728041665814omplex G) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ P X3))))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.groups8024822376189712711omplex G) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ P X3))))) (@ (@ tptp.groups8024822376189712711omplex (lambda ((X3 tptp.code_integer)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ (@ tptp.groups2240296850493347238T_real G) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ P X3))))) (@ (@ tptp.groups2240296850493347238T_real (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A) (= (@ (@ tptp.groups8097168146408367636l_real G) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ P X3))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.groups8778361861064173332t_real G) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ P X3))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.groups1270011288395367621r_real G) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ P X3))))) (@ (@ tptp.groups1270011288395367621r_real (lambda ((X3 tptp.code_integer)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A)))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ (@ tptp.groups5808333547571424918x_real G) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ P X3))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A)))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (T tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (I (-> tptp.code_integer tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite6017078050557962740nteger T) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups1270011288395367621r_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa2 tptp.complex)) (and (@ (@ tptp.member_complex Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.code_integer)) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S2) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1270011288395367621r_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (T tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (I (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite6017078050557962740nteger T) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S2) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1270011288395367621r_real F) S2)) (@ (@ tptp.groups1270011288395367621r_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.code_integer)) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S2) (exists ((Xa2 tptp.complex)) (and (@ (@ tptp.member_complex Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1270011288395367621r_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_complex) (T tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (I (-> tptp.code_integer tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite6017078050557962740nteger T) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups1270011288395367621r_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (exists ((Xa2 tptp.complex)) (and (@ (@ tptp.member_complex Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) T) (= (@ I Xa2) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups2240296850493347238T_real F) A) tptp.zero_zero_real) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) A) (= (@ F X3) tptp.zero_zero_real))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A) tptp.zero_zero_real) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A) (= (@ F X3) tptp.zero_zero_real))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A) tptp.zero_zero_real) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (= (@ F X3) tptp.zero_zero_real))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups1270011288395367621r_real F) A) tptp.zero_zero_real) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (= (@ F X3) tptp.zero_zero_real))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A) tptp.zero_zero_real) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A) (= (@ F X3) tptp.zero_zero_real))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups136491112297645522BT_rat F) A) tptp.zero_zero_rat) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) A) (= (@ F X3) tptp.zero_zero_rat))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A) tptp.zero_zero_rat) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A) (= (@ F X3) tptp.zero_zero_rat))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A) tptp.zero_zero_rat) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (= (@ F X3) tptp.zero_zero_rat))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A) tptp.zero_zero_rat) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (= (@ F X3) tptp.zero_zero_rat))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups6602215022474089585er_rat F) A) tptp.zero_zero_rat) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (= (@ F X3) tptp.zero_zero_rat))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.int)) (and (@ (@ tptp.member_int X8) A) (@ (@ tptp.ord_less_real (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A)) (@ (@ tptp.groups8778361861064173332t_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X8) A) (@ (@ tptp.ord_less_real (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1270011288395367621r_real F) A)) (@ (@ tptp.groups1270011288395367621r_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.complex)) (and (@ (@ tptp.member_complex X8) A) (@ (@ tptp.ord_less_real (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A)) (@ (@ tptp.groups5808333547571424918x_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.nat)) (and (@ (@ tptp.member_nat X8) A) (@ (@ tptp.ord_less_rat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A)) (@ (@ tptp.groups2906978787729119204at_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.int)) (and (@ (@ tptp.member_int X8) A) (@ (@ tptp.ord_less_rat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A)) (@ (@ tptp.groups3906332499630173760nt_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X8) A) (@ (@ tptp.ord_less_rat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups6602215022474089585er_rat F) A)) (@ (@ tptp.groups6602215022474089585er_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.complex)) (and (@ (@ tptp.member_complex X8) A) (@ (@ tptp.ord_less_rat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A)) (@ (@ tptp.groups5058264527183730370ex_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.int)) (and (@ (@ tptp.member_int X8) A) (@ (@ tptp.ord_less_nat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.groups4541462559716669496nt_nat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X8) A) (@ (@ tptp.ord_less_nat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups7237345082560585321er_nat F) A)) (@ (@ tptp.groups7237345082560585321er_nat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X8 tptp.complex)) (and (@ (@ tptp.member_complex X8) A) (@ (@ tptp.ord_less_nat (@ F X8)) (@ G X8)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A)) (@ (@ tptp.groups5693394587270226106ex_nat G) A)))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_complex X15) Y1)) (@ (@ tptp.plus_plus_complex X23) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S)) (@ (@ tptp.groups2073611262835488442omplex G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_complex X15) Y1)) (@ (@ tptp.plus_plus_complex X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups3049146728041665814omplex H2) S)) (@ (@ tptp.groups3049146728041665814omplex G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.complex)) (G (-> tptp.code_integer tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_complex X15) Y1)) (@ (@ tptp.plus_plus_complex X23) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups8024822376189712711omplex H2) S)) (@ (@ tptp.groups8024822376189712711omplex G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X15) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S)) (@ (@ tptp.groups8778361861064173332t_real G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X15) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups1270011288395367621r_real H2) S)) (@ (@ tptp.groups1270011288395367621r_real G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X15) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S)) (@ (@ tptp.groups5808333547571424918x_real G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H2) S)) (@ (@ tptp.groups2906978787729119204at_rat G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H2) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups6602215022474089585er_rat H2) S)) (@ (@ tptp.groups6602215022474089585er_rat G) S))))))))
% 7.27/7.62 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H2) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) S))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (not (= A tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2240296850493347238T_real F) A)) (@ (@ tptp.groups2240296850493347238T_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A) (=> (not (= A tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A)) (@ (@ tptp.groups8097168146408367636l_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1270011288395367621r_real F) A)) (@ (@ tptp.groups1270011288395367621r_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (= A tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A)) (@ (@ tptp.groups5808333547571424918x_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A)) (@ (@ tptp.groups8778361861064173332t_real G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (not (= A tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups136491112297645522BT_rat F) A)) (@ (@ tptp.groups136491112297645522BT_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A) (=> (not (= A tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A)) (@ (@ tptp.groups1300246762558778688al_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups6602215022474089585er_rat F) A)) (@ (@ tptp.groups6602215022474089585er_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (= A tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A)) (@ (@ tptp.groups5058264527183730370ex_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A)) (@ (@ tptp.groups2906978787729119204at_rat G) A)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A)))) (let ((_let_4 (@ (@ tptp.member_real X2) A))) (=> (@ tptp.finite_finite_real A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A)))) (let ((_let_4 (@ (@ tptp.member_int X2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X2) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A))) (=> (@ tptp.finite3207457112153483333omplex A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A)))) (let ((_let_4 (@ (@ tptp.member_real X2) A))) (=> (@ tptp.finite_finite_real A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A)))) (let ((_let_4 (@ (@ tptp.member_int X2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X2) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_VEBT_VEBT) (S 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.complex)) (H2 (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT S7) (=> (@ tptp.finite5795047828879050333T_VEBT T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_VEBT_VEBT (@ J A3)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1794756597179926696omplex G) S) (@ (@ tptp.groups1794756597179926696omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_real) (S 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.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT S7) (=> (@ tptp.finite_finite_real T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T6)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1794756597179926696omplex G) S) (@ (@ tptp.groups5754745047067104278omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_VEBT_VEBT) (S tptp.set_real) (I (-> tptp.vEBT_VEBT tptp.real)) (J (-> tptp.real tptp.vEBT_VEBT)) (T5 tptp.set_VEBT_VEBT) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite_finite_real S7) (=> (@ tptp.finite5795047828879050333T_VEBT T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_VEBT_VEBT (@ J A3)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S) (@ (@ tptp.groups1794756597179926696omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_real) (S tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T5 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S7) (=> (@ tptp.finite_finite_real T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T6)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S) (@ (@ tptp.groups5754745047067104278omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_int) (S 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.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT S7) (=> (@ tptp.finite_finite_int T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T6)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1794756597179926696omplex G) S) (@ (@ tptp.groups3049146728041665814omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_int) (S tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T5 tptp.set_int) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S7) (=> (@ tptp.finite_finite_int T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T6)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S) (@ (@ tptp.groups3049146728041665814omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_Code_integer) (S 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.complex)) (H2 (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT S7) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_Code_integer (@ J A3)) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1794756597179926696omplex G) S) (@ (@ tptp.groups8024822376189712711omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_Code_integer) (S tptp.set_real) (I (-> tptp.code_integer tptp.real)) (J (-> tptp.real tptp.code_integer)) (T5 tptp.set_Code_integer) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite_finite_real S7) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_Code_integer (@ J A3)) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S) (@ (@ tptp.groups8024822376189712711omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_int) (T6 tptp.set_VEBT_VEBT) (S tptp.set_int) (I (-> tptp.vEBT_VEBT tptp.int)) (J (-> tptp.int tptp.vEBT_VEBT)) (T5 tptp.set_VEBT_VEBT) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite_finite_int S7) (=> (@ tptp.finite5795047828879050333T_VEBT T6) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S7)) (@ (@ tptp.member_VEBT_VEBT (@ J A3)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (@ (@ tptp.member_int (@ I B3)) (@ (@ tptp.minus_minus_set_int S) S7)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S) (@ (@ tptp.groups1794756597179926696omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S7 tptp.set_int) (T6 tptp.set_real) (S tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T5 tptp.set_real) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_int S7) (=> (@ tptp.finite_finite_real T6) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S7)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T6)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (@ (@ tptp.member_int (@ I B3)) (@ (@ tptp.minus_minus_set_int S) S7)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S7) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T6) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S) (@ (@ tptp.groups5754745047067104278omplex H2) T5)))))))))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (I tptp.vEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups2240296850493347238T_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_VEBT_VEBT I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (I tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups1270011288395367621r_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_Code_integer I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (I tptp.vEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups136491112297645522BT_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_VEBT_VEBT I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (I tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups6602215022474089585er_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_Code_integer I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (B tptp.real) (I tptp.vEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups2240296850493347238T_real F) S2) B) (=> (@ (@ tptp.member_VEBT_VEBT I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (B tptp.real) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) B) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (B tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) B) (=> (@ (@ tptp.member_int I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (B tptp.real) (I tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups1270011288395367621r_real F) S2) B) (=> (@ (@ tptp.member_Code_integer I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) B) (=> (@ (@ tptp.member_complex I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (B tptp.rat) (I tptp.vEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups136491112297645522BT_rat F) S2) B) (=> (@ (@ tptp.member_VEBT_VEBT I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (B tptp.rat) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) B) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B) (=> (@ (@ tptp.member_nat I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B) (=> (@ (@ tptp.member_int I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (B tptp.rat) (I tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups6602215022474089585er_rat F) S2) B) (=> (@ (@ tptp.member_Code_integer I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B)))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_complex))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ tptp.groups8024822376189712711omplex G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.zero_zero_complex))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_real))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.zero_zero_real))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G X3) tptp.zero_zero_real))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_rat))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.zero_zero_rat))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G X3) tptp.zero_zero_rat))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_nat))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.zero_zero_nat))))) (@ _let_1 A))))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.27/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.27/7.62 (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.zero_zero_real))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (@ (@ tptp.member_VEBT_VEBT I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2240296850493347238T_real F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))))
% 7.27/7.62 (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.zero_zero_real))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (@ (@ tptp.member_Code_integer I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1270011288395367621r_real F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))))
% 7.27/7.62 (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.zero_zero_rat))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (@ (@ tptp.member_VEBT_VEBT I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups136491112297645522BT_rat F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_Code_integer) (I tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (@ (@ tptp.member_Code_integer I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups6602215022474089585er_rat F) I6)))))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (not (= I6 tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups2240296850493347238T_real F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (not (= I6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups1270011288395367621r_real F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (not (= I6 tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups136491112297645522BT_rat F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (not (= I6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups6602215022474089585er_rat F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I6)))))))
% 7.27/7.62 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I6)))))))
% 7.27/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex)) (H2 (-> tptp.vEBT_VEBT tptp.complex))) (let ((_let_1 (@ tptp.groups1794756597179926696omplex H2))) (let ((_let_2 (@ tptp.groups1794756597179926696omplex G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex)) (H2 (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ tptp.groups8024822376189712711omplex H2))) (let ((_let_2 (@ tptp.groups8024822376189712711omplex G))) (=> (@ tptp.finite6017078050557962740nteger C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real H2))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real H2))) (let ((_let_2 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_complex) (A tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C) (=> (@ (@ tptp.ord_le211207098394363844omplex A) C) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (H2 (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat H2))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H2 (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat H2))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex)) (H2 (-> tptp.vEBT_VEBT tptp.complex))) (let ((_let_1 (@ tptp.groups1794756597179926696omplex H2))) (let ((_let_2 (@ tptp.groups1794756597179926696omplex G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex)) (H2 (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ tptp.groups8024822376189712711omplex H2))) (let ((_let_2 (@ tptp.groups8024822376189712711omplex G))) (=> (@ tptp.finite6017078050557962740nteger C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real H2))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real H2))) (let ((_let_2 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_complex) (A tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C) (=> (@ (@ tptp.ord_le211207098394363844omplex A) C) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C) A)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C) B)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (H2 (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat H2))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H2 (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat H2))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ tptp.groups8024822376189712711omplex G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S) T5) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex))) (let ((_let_1 (@ tptp.groups8024822376189712711omplex G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_real))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_real))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_nat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_nat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_int))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_int))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T5) (=> (@ (@ tptp.ord_less_eq_set_nat S) T5) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.complex)) (G (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ H2 X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1794756597179926696omplex G) S) (@ (@ tptp.groups1794756597179926696omplex H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ H2 X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S) (@ (@ tptp.groups5754745047067104278omplex H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.complex)) (G (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ H2 X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups8024822376189712711omplex G) S) (@ (@ tptp.groups8024822376189712711omplex H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ H2 X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2240296850493347238T_real G) S) (@ (@ tptp.groups2240296850493347238T_real H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ H2 X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S) (@ (@ tptp.groups8097168146408367636l_real H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ H2 X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1270011288395367621r_real G) S) (@ (@ tptp.groups1270011288395367621r_real H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ H2 X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S) (@ (@ tptp.groups5808333547571424918x_real H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ H2 X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups136491112297645522BT_rat G) S) (@ (@ tptp.groups136491112297645522BT_rat H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ H2 X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) S) (@ (@ tptp.groups1300246762558778688al_rat H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ H2 X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups6602215022474089585er_rat G) S) (@ (@ tptp.groups6602215022474089585er_rat H2) T5))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex)) (H2 (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1794756597179926696omplex G) T5) (@ (@ tptp.groups1794756597179926696omplex H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T5) (@ (@ tptp.groups5754745047067104278omplex H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.complex)) (H2 (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups8024822376189712711omplex G) T5) (@ (@ tptp.groups8024822376189712711omplex H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ G X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2240296850493347238T_real G) T5) (@ (@ tptp.groups2240296850493347238T_real H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ G X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T5) (@ (@ tptp.groups8097168146408367636l_real H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1270011288395367621r_real G) T5) (@ (@ tptp.groups1270011288395367621r_real H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T5) (@ (@ tptp.groups5808333547571424918x_real H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (H2 (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups136491112297645522BT_rat G) T5) (@ (@ tptp.groups136491112297645522BT_rat H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) T5) (@ (@ tptp.groups1300246762558778688al_rat H2) S))))))))
% 7.27/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H2 (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups6602215022474089585er_rat G) T5) (@ (@ tptp.groups6602215022474089585er_rat H2) S))))))))
% 7.27/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.27/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.27/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.27/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.27/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.27/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real F))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B)) (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B)) (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (B tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (B tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (= A2 C2) (=> (= B2 D2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X4) (=> (@ (@ tptp.ord_less_nat X4) D2) (= (@ G X4) (@ H2 X4))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat A2) B2)) (@ (@ tptp.groups3542108847815614940at_nat H2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (= A2 C2) (=> (= B2 D2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X4) (=> (@ (@ tptp.ord_less_nat X4) D2) (= (@ G X4) (@ H2 X4))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or4665077453230672383an_nat A2) B2)) (@ (@ tptp.groups6591440286371151544t_real H2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int))) (=> (= A2 C2) (=> (= B2 D2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) X4) (=> (@ (@ tptp.ord_less_int X4) D2) (= (@ G X4) (@ H2 X4))))) (= (@ (@ tptp.groups4538972089207619220nt_int G) (@ (@ tptp.set_or4662586982721622107an_int A2) B2)) (@ (@ tptp.groups4538972089207619220nt_int H2) (@ (@ tptp.set_or4662586982721622107an_int C2) D2))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.plus_plus_real (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.minus_minus_rat (@ _let_1 (@ _let_2 P6))) (@ _let_1 (@ _let_2 N))) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.minus_minus_int (@ _let_1 (@ _let_2 P6))) (@ _let_1 (@ _let_2 N))) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.minus_minus_real (@ _let_1 (@ _let_2 P6))) (@ _let_1 (@ _let_2 N))) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) P6)))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.plus_plus_nat M) I4)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 7.32/7.62 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ (@ tptp.plus_plus_nat M) I4)))) I6) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.groups7501900531339628137nteger _let_1) I6))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.plus_plus_nat M) I4)))) I6) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I6))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.plus_plus_nat M) I4)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.plus_plus_nat M) I4)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X2))) (let ((_let_2 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X2))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X2))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ (@ tptp.member_VEBT_VEBT X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X2) tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.member_complex X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ (@ tptp.member_VEBT_VEBT X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X2) tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.member_complex X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ (@ tptp.member_VEBT_VEBT X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real X2) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A2) A))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (A2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A))) (=> (@ tptp.finite_finite_real A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (A2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A2) A))) (=> (@ tptp.finite3207457112153483333omplex A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (A2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A2) A))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (A2 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A))) (=> (@ tptp.finite_finite_real A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (A2 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A2) A))) (=> (@ tptp.finite3207457112153483333omplex A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (A2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.real)) (C2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2240296850493347238T_real C2) (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_2 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.real)) (C2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups8097168146408367636l_real C2) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.real)) (C2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ (@ tptp.groups1270011288395367621r_real C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups1270011288395367621r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1270011288395367621r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.real)) (C2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C2) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.rat)) (C2 (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups136491112297645522BT_rat C2) (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_2 (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.rat)) (C2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1300246762558778688al_rat C2) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.rat)) (C2 (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ (@ tptp.groups6602215022474089585er_rat C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.rat)) (C2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C2) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.nat)) (C2 (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ (@ tptp.groups771621172384141258BT_nat C2) (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_2 (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_nat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.nat)) (C2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C2) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_nat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.plus_plus_real (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B2 tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (B2 tptp.code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups1270011288395367621r_real F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger B) A)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B2 tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B2)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) B) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B2)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (B2 tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger B) A)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B2)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) B) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B2)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B) A)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B2)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) B) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B2 tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))))))
% 7.32/7.62 (assert (forall ((I tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.member_VEBT_VEBT I) A) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups2240296850493347238T_real F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.real) (A tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite_finite_real A) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ (@ tptp.member_Code_integer I) A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer I) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups1270011288395367621r_real F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.complex) (A tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite3207457112153483333omplex A) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ tptp.finite_finite_int A) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups136491112297645522BT_rat F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.real) (A tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_real A) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ (@ tptp.member_Code_integer I) A) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer I) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups6602215022474089585er_rat F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.complex) (A tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite3207457112153483333omplex A) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A)))))))
% 7.32/7.62 (assert (forall ((I tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_int A) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) (@ tptp.suc I4))))) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) (@ tptp.suc I4))))) _let_1)))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A2 I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A2 I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat N) M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or4665077453230672383an_nat N) M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 N)) tptp.one_one_Code_integer) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) X2)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.62 (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 ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ 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))))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ 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))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 7.32/7.62 (assert (forall ((A2 tptp.complex) (D2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A2)) (@ (@ tptp.times_times_complex _let_1) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (D2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A2)) (@ (@ tptp.times_times_rat _let_1) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (D2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A2)) (@ (@ tptp.times_times_int _let_1) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A2)) (@ (@ tptp.times_times_nat _let_1) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (D2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A2)) (@ (@ tptp.times_times_real _let_1) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat I4) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A2)) (@ (@ tptp.times_times_nat N) D2)))) _let_1)))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ 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))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (D2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A2)) (@ (@ tptp.times_times_int _let_2) D2)))) _let_1))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A2)) (@ (@ tptp.times_times_nat _let_2) D2)))) _let_1))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.rat)) (B2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_rat (@ A2 I2)) (@ A2 J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_rat (@ B2 J2)) (@ B2 I2))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 K3)) (@ B2 K3)))) _let_1))) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat A2) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat B2) _let_1))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.int)) (B2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_int (@ A2 I2)) (@ A2 J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_int (@ B2 J2)) (@ B2 I2))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 K3)) (@ B2 K3)))) _let_1))) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int A2) _let_1)) (@ (@ tptp.groups3539618377306564664at_int B2) _let_1))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.real)) (B2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_real (@ A2 I2)) (@ A2 J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_real (@ B2 J2)) (@ B2 I2))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 K3)) (@ B2 K3)))) _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real A2) _let_1)) (@ (@ tptp.groups6591440286371151544t_real B2) _let_1))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.nat)) (B2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A2 I2)) (@ A2 J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B2 J2)) (@ B2 I2))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A2 I4)) (@ B2 I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A2) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B2) _let_1))))))))
% 7.32/7.62 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q5)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.32/7.62 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q5)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.32/7.62 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q5)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.array_o) (Xs tptp.list_o)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_o A2) Xs)) (@ tptp.array_len_o A2)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_o A2) Xs)) (@ tptp.pure_assn (= R5 (@ tptp.size_size_list_o Xs))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.array_nat) (Xs tptp.list_nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_nat A2) Xs)) (@ tptp.array_len_nat A2)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_nat A2) Xs)) (@ tptp.pure_assn (= R5 (@ tptp.size_size_list_nat Xs))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.array_VEBT_VEBTi) (Xs tptp.list_VEBT_VEBTi)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ tptp.array_len_VEBT_VEBTi A2)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ tptp.pure_assn (= R5 (@ tptp.size_s7982070591426661849_VEBTi Xs))))))))
% 7.32/7.62 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 7.32/7.62 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 7.32/7.62 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 7.32/7.62 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 7.32/7.62 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 7.32/7.62 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 7.32/7.62 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 7.32/7.62 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 7.32/7.62 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X2)) (@ tptp.set_ord_lessThan_rat Y3)) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.32/7.62 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X2)) (@ tptp.set_ord_lessThan_num Y3)) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.32/7.62 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X2)) (@ tptp.set_ord_lessThan_nat Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X2)) (@ tptp.set_ord_lessThan_int Y3)) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X2)) (@ tptp.set_or5984915006950818249n_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.32/7.62 (assert (forall ((N tptp.real) (M tptp.real)) (= (@ (@ tptp.minus_minus_set_real (@ tptp.set_or5984915006950818249n_real N)) (@ tptp.set_or5984915006950818249n_real M)) (@ (@ tptp.set_or66887138388493659n_real M) N))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))
% 7.32/7.62 (assert (forall ((N tptp.int) (M tptp.int)) (= (@ (@ tptp.minus_minus_set_int (@ tptp.set_ord_lessThan_int N)) (@ tptp.set_ord_lessThan_int M)) (@ (@ tptp.set_or4662586982721622107an_int M) N))))
% 7.32/7.62 (assert (forall ((N tptp.code_integer) (M tptp.code_integer)) (= (@ (@ tptp.minus_2355218937544613996nteger (@ tptp.set_or5754767410780653050nteger N)) (@ tptp.set_or5754767410780653050nteger M)) (@ (@ tptp.set_or8404916559141939852nteger M) N))))
% 7.32/7.62 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 7.32/7.62 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 7.32/7.62 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.32/7.62 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 7.32/7.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 7.32/7.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 7.32/7.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 7.32/7.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))))
% 7.32/7.62 (assert (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))))
% 7.32/7.62 (assert (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _let_1))))
% 7.32/7.62 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N))) (=> (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X3)) (@ Q X3)))) _let_1))))))
% 7.32/7.62 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X3)) (@ Q X3)))) _let_1))))))
% 7.32/7.62 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X3)) (@ Q X3)))) _let_1))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.32/7.62 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.ord_less_rat X3) U2))))))
% 7.32/7.62 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X3 tptp.num)) (@ (@ tptp.ord_less_num X3) U2))))))
% 7.32/7.62 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) U2))))))
% 7.32/7.62 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_int X3) U2))))))
% 7.32/7.62 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (@ (@ tptp.ord_less_real X3) U2))))))
% 7.32/7.62 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 7.32/7.62 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.32/7.62 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 7.32/7.62 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups771621172384141258BT_nat F) A)) (@ (@ tptp.groups771621172384141258BT_nat G) A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A)) (@ (@ tptp.groups1935376822645274424al_nat G) A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.groups4541462559716669496nt_nat G) A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3542108847815614940at_nat G) A))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A) (@ tptp.suc N)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (= (= (@ (@ tptp.groups7237345082560585321er_nat F) A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A) tptp.one_one_nat) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (= (@ F X3) tptp.one_one_nat) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (= (= (@ (@ tptp.groups7237345082560585321er_nat F) A) tptp.one_one_nat) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (= (@ F X3) tptp.one_one_nat) (forall ((Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A) tptp.one_one_nat) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (= (@ F X3) tptp.one_one_nat) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A) tptp.one_one_nat) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (= (@ F X3) tptp.one_one_nat) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A) (=> (not (= X3 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (C2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))) tptp.zero_zero_complex))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.vEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (A tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.32/7.62 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 7.32/7.62 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 7.32/7.62 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N4)) (@ F (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N4)) (@ F (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ F (@ tptp.suc N4))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N4))) (@ F N4)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N4))) (@ F N4)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N4))) (@ F N4)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) R2))) _let_1)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) R2))) _let_1)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) R2))) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((M6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M6) K))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N) K))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M6) K))) (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N) K))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X2)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 N)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X2) tptp.one_one_Code_integer)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.32/7.62 (assert (forall ((Z tptp.code_integer) (H2 tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger Z))) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger Z))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 P4)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.32/7.62 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P4)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P4)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.32/7.62 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y3) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y3)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.code_integer) (N tptp.nat) (Y3 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y3) N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X2) Y3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger Y3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_8256067586552552935nteger X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y3) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_rat X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y3) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_int X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y3) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y3) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.power_power_complex Y3) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y3)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) P4)) (@ (@ tptp.power_power_complex Y3) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.code_integer) (N tptp.nat) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X2) Y3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((P4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X2) P4)) (@ (@ tptp.power_8256067586552552935nteger Y3) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) P4)) (@ (@ tptp.power_power_rat Y3) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) P4)) (@ (@ tptp.power_power_int Y3) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y3 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) P4)) (@ (@ tptp.power_power_real Y3) (@ (@ tptp.minus_minus_nat N) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K6 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K6))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K6) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K6))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K6 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K6))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K6) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K6))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K6 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K6))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K6) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K6))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K6 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K6))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K6) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K6))))))
% 7.32/7.62 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.times_times_complex (@ _let_1 X2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 X2)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.times_times_rat (@ _let_1 X2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.times_times_int (@ _let_1 X2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 7.32/7.62 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ 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)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 7.32/7.62 (assert (forall ((Tree_array2 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBT)) (=> (= (@ tptp.ex_ass463751140784270563_VEBTi (@ tptp.snga_assn_VEBT_VEBTi Tree_array2)) tptp.top_top_assn) (= (@ tptp.heap_Time_return_nat (@ tptp.size_s6755466524823107622T_VEBT Tree_is)) (@ tptp.array_len_VEBT_VEBTi Tree_array2)))))
% 7.32/7.62 (assert (forall ((Tree_array2 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_real)) (=> (= (@ tptp.ex_ass463751140784270563_VEBTi (@ tptp.snga_assn_VEBT_VEBTi Tree_array2)) tptp.top_top_assn) (= (@ tptp.heap_Time_return_nat (@ tptp.size_size_list_real Tree_is)) (@ tptp.array_len_VEBT_VEBTi Tree_array2)))))
% 7.32/7.62 (assert (forall ((Tree_array2 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_o)) (=> (= (@ tptp.ex_ass463751140784270563_VEBTi (@ tptp.snga_assn_VEBT_VEBTi Tree_array2)) tptp.top_top_assn) (= (@ tptp.heap_Time_return_nat (@ tptp.size_size_list_o Tree_is)) (@ tptp.array_len_VEBT_VEBTi Tree_array2)))))
% 7.32/7.62 (assert (forall ((Tree_array2 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_nat)) (=> (= (@ tptp.ex_ass463751140784270563_VEBTi (@ tptp.snga_assn_VEBT_VEBTi Tree_array2)) tptp.top_top_assn) (= (@ tptp.heap_Time_return_nat (@ tptp.size_size_list_nat Tree_is)) (@ tptp.array_len_VEBT_VEBTi Tree_array2)))))
% 7.32/7.62 (assert (forall ((Tree_array2 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi)) (=> (= (@ tptp.ex_ass463751140784270563_VEBTi (@ tptp.snga_assn_VEBT_VEBTi Tree_array2)) tptp.top_top_assn) (= (@ tptp.heap_Time_return_nat (@ tptp.size_s7982070591426661849_VEBTi Tree_is)) (@ tptp.array_len_VEBT_VEBTi Tree_array2)))))
% 7.32/7.62 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 7.32/7.62 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.set_ord_lessThan_nat K2))))))
% 7.32/7.62 (assert (= tptp.finite_finite_nat (lambda ((S8 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S8) (@ tptp.set_ord_lessThan_nat K3))))))
% 7.32/7.62 (assert (forall ((X2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.top_to3028658606643905974d_enat) X2) tptp.top_to3028658606643905974d_enat)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_Product_unit)) (= (@ (@ tptp.ord_ma508538259134630082t_unit tptp.top_to1996260823553986621t_unit) X2) tptp.top_to1996260823553986621t_unit)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_Numeral_num1)) (= (@ (@ tptp.ord_ma2202181864719522458l_num1 tptp.top_to3689904429138878997l_num1) X2) tptp.top_to3689904429138878997l_num1)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.top_top_set_real) X2) tptp.top_top_set_real)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.ord_max_set_o tptp.top_top_set_o) X2) tptp.top_top_set_o)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.top_top_set_nat) X2) tptp.top_top_set_nat)))
% 7.32/7.62 (assert (forall ((X2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) tptp.top_to3028658606643905974d_enat) tptp.top_to3028658606643905974d_enat)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_Product_unit)) (= (@ (@ tptp.ord_ma508538259134630082t_unit X2) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_Numeral_num1)) (= (@ (@ tptp.ord_ma2202181864719522458l_num1 X2) tptp.top_to3689904429138878997l_num1) tptp.top_to3689904429138878997l_num1)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X2) tptp.top_top_set_real) tptp.top_top_set_real)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.ord_max_set_o X2) tptp.top_top_set_o) tptp.top_top_set_o)))
% 7.32/7.62 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X2) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 7.32/7.62 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 7.32/7.62 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 7.32/7.62 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Product_unit)) (not (@ (@ tptp.ord_le8056459307392131481t_unit tptp.top_to1996260823553986621t_unit) A2))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Numeral_num1)) (not (@ (@ tptp.ord_le526730876122248049l_num1 tptp.top_to3689904429138878997l_num1) A2))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real tptp.top_top_set_real) A2))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o tptp.top_top_set_o) A2))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat tptp.top_top_set_nat) A2))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Product_unit)) (= (not (= A2 tptp.top_to1996260823553986621t_unit)) (@ (@ tptp.ord_le8056459307392131481t_unit A2) tptp.top_to1996260823553986621t_unit))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Numeral_num1)) (= (not (= A2 tptp.top_to3689904429138878997l_num1)) (@ (@ tptp.ord_le526730876122248049l_num1 A2) tptp.top_to3689904429138878997l_num1))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_real)) (= (not (= A2 tptp.top_top_set_real)) (@ (@ tptp.ord_less_set_real A2) tptp.top_top_set_real))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_o)) (= (not (= A2 tptp.top_top_set_o)) (@ (@ tptp.ord_less_set_o A2) tptp.top_top_set_o))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_nat)) (= (not (= A2 tptp.top_top_set_nat)) (@ (@ tptp.ord_less_set_nat A2) tptp.top_top_set_nat))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (assert (= tptp.top_to7662761140297458691t_unit (@ tptp.some_s8043159101241848530t_unit tptp.top_to1996260823553986621t_unit)))
% 7.32/7.62 (assert (= tptp.top_to176924430543178203l_num1 (@ tptp.some_s513430669971965098l_num1 tptp.top_to3689904429138878997l_num1)))
% 7.32/7.62 (assert (= tptp.top_to1083748111577038690t_real (@ tptp.some_set_real tptp.top_top_set_real)))
% 7.32/7.62 (assert (= tptp.top_top_option_set_o (@ tptp.some_set_o tptp.top_top_set_o)))
% 7.32/7.62 (assert (= tptp.top_to4826455019444611206et_nat (@ tptp.some_set_nat tptp.top_top_set_nat)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit A2) tptp.top_to1996260823553986621t_unit)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Numeral_num1)) (@ (@ tptp.ord_le5200684355995106405l_num1 A2) tptp.top_to3689904429138878997l_num1)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A2) tptp.top_top_set_real)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o A2) tptp.top_top_set_o)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) tptp.top_top_set_nat)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) tptp.top_top_set_int)))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit tptp.top_to1996260823553986621t_unit) A2) (= A2 tptp.top_to1996260823553986621t_unit))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Numeral_num1)) (= (@ (@ tptp.ord_le5200684355995106405l_num1 tptp.top_to3689904429138878997l_num1) A2) (= A2 tptp.top_to3689904429138878997l_num1))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real tptp.top_top_set_real) A2) (= A2 tptp.top_top_set_real))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o tptp.top_top_set_o) A2) (= A2 tptp.top_top_set_o))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat tptp.top_top_set_nat) A2) (= A2 tptp.top_top_set_nat))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int tptp.top_top_set_int) A2) (= A2 tptp.top_top_set_int))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit tptp.top_to1996260823553986621t_unit) A2) (= A2 tptp.top_to1996260823553986621t_unit))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_Numeral_num1)) (=> (@ (@ tptp.ord_le5200684355995106405l_num1 tptp.top_to3689904429138878997l_num1) A2) (= A2 tptp.top_to3689904429138878997l_num1))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real tptp.top_top_set_real) A2) (= A2 tptp.top_top_set_real))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o tptp.top_top_set_o) A2) (= A2 tptp.top_top_set_o))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat tptp.top_top_set_nat) A2) (= A2 tptp.top_top_set_nat))))
% 7.32/7.62 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int tptp.top_top_set_int) A2) (= A2 tptp.top_top_set_int))))
% 7.32/7.62 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) tptp.top_top_assn)))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (assert (forall ((A tptp.assn)) (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn A) tptp.top_top_assn))))
% 7.32/7.62 (assert (forall ((A tptp.assn) (A7 tptp.assn) (B tptp.assn) (B8 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A7))) (=> (@ (@ tptp.entails A) (@ _let_1 tptp.top_top_assn)) (=> (@ (@ tptp.entails B) (@ (@ tptp.times_times_assn B8) tptp.top_top_assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) B)) tptp.top_top_assn)) (@ (@ tptp.times_times_assn (@ _let_1 B8)) tptp.top_top_assn)))))))
% 7.32/7.62 (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)))))))
% 7.32/7.62 (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))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (S tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N9) (@ (@ tptp.member_nat N9) S))))) (not (@ tptp.finite_finite_nat S)))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M6 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N4) (@ (@ tptp.member_nat N4) S)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M6 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N4) (@ (@ tptp.member_nat N4) S)))))))
% 7.32/7.62 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z) N4)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.32/7.62 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z) N4)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.vEBT_VEBTi) (Y3 tptp.assn)) (=> (= (@ (@ tptp.vEBT_vebt_assn_raw X2) Xa) Y3) (=> (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi X2) Xa)) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Ai2 Bool) (Bi2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi Ai2) Bi2))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.pure_assn (and (= Ai2 A3) (= Bi2 B3)))) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf A3) B3)) _let_1))))))))) (=> (forall ((Mmo tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (Tree_list tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mmo) Deg2) Tree_list) Summary2)) (forall ((Mmoi tptp.option4927543243414619207at_nat) (Degi tptp.nat) (Tree_array tptp.array_VEBT_VEBTi) (Summaryi tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi) Degi) Tree_array) Summaryi))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ tptp.pure_assn (and (= Mmoi Mmo) (= Degi Deg2)))) (@ (@ tptp.vEBT_vebt_assn_raw Summary2) 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)))))) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node Mmo) Deg2) Tree_list) Summary2)) _let_1))))))))) (=> (forall ((V2 tptp.option4927543243414619207at_nat) (Va3 tptp.nat) (Vb3 tptp.list_VEBT_VEBT) (Vc3 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node V2) Va3) Vb3) Vc3)) (forall ((Vd Bool) (Ve Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi Vd) Ve))) (=> (= Xa _let_1) (=> (= Y3 tptp.bot_bot_assn) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node V2) Va3) Vb3) Vc3)) _let_1))))))))) (not (forall ((Vd Bool) (Ve Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Vd) Ve)) (forall ((V2 tptp.option4927543243414619207at_nat) (Va3 tptp.nat) (Vb3 tptp.array_VEBT_VEBTi) (Vc3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei V2) Va3) Vb3) Vc3))) (=> (= Xa _let_1) (=> (= Y3 tptp.bot_bot_assn) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf Vd) Ve)) _let_1)))))))))))))))))
% 7.32/7.62 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ tptp.vEBT_VEBT_height (@ (@ tptp.vEBT_Leaf A2) B2)) tptp.zero_zero_nat)))
% 7.32/7.62 (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)))))))))
% 7.32/7.62 (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)))))))))
% 7.32/7.62 (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)))))))))
% 7.32/7.62 (assert (= (@ tptp.finite1345302120164226195on_int tptp.top_to6430115241214627170on_int) (@ tptp.finite_finite_int tptp.top_top_set_int)))
% 7.32/7.62 (assert (= (@ tptp.finite6785661671136154180nteger tptp.top_to5929521628599800467nteger) (@ tptp.finite6017078050557962740nteger tptp.top_to4645266643341252675nteger)))
% 7.32/7.62 (assert (= (@ tptp.finite2569390945932476949omplex tptp.top_to6180147692022559204omplex) (@ tptp.finite3207457112153483333omplex tptp.top_top_set_complex)))
% 7.32/7.62 (assert (= (@ tptp.finite1445617369574913404t_unit tptp.top_to2690860209552263555t_unit) (@ tptp.finite4290736615968046902t_unit tptp.top_to1996260823553986621t_unit)))
% 7.32/7.62 (assert (= (@ tptp.finite3139260975159805780l_num1 tptp.top_to4428395536652758875l_num1) (@ tptp.finite1111429032697314574l_num1 tptp.top_to3689904429138878997l_num1)))
% 7.32/7.62 (assert (= (@ tptp.finite5731380839103853331n_real tptp.top_to853713521313446370n_real) (@ tptp.finite_finite_real tptp.top_top_set_real)))
% 7.32/7.62 (assert (= (@ tptp.finite4093902646404507527tion_o tptp.top_top_set_option_o) (@ tptp.finite_finite_o tptp.top_top_set_o)))
% 7.32/7.62 (assert (= (@ tptp.finite5523153139673422903on_nat tptp.top_to8920198386146353926on_nat) (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_complex (lambda ((S5 tptp.complex)) P)) tptp.top_top_set_complex)) (=> (not P) (= (@ tptp.collect_complex (lambda ((S5 tptp.complex)) P)) tptp.bot_bot_set_complex)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collec213857154873943460nt_int (lambda ((S5 tptp.product_prod_int_int)) P)) tptp.top_to4366644338036079209nt_int)) (=> (not P) (= (@ tptp.collec213857154873943460nt_int (lambda ((S5 tptp.product_prod_int_int)) P)) tptp.bot_bo1796632182523588997nt_int)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_int (lambda ((S5 tptp.int)) P)) tptp.top_top_set_int)) (=> (not P) (= (@ tptp.collect_int (lambda ((S5 tptp.int)) P)) tptp.bot_bot_set_int)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_Product_unit (lambda ((S5 tptp.product_unit)) P)) tptp.top_to1996260823553986621t_unit)) (=> (not P) (= (@ tptp.collect_Product_unit (lambda ((S5 tptp.product_unit)) P)) tptp.bot_bo3957492148770167129t_unit)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_Numeral_num1 (lambda ((S5 tptp.numeral_num1)) P)) tptp.top_to3689904429138878997l_num1)) (=> (not P) (= (@ tptp.collect_Numeral_num1 (lambda ((S5 tptp.numeral_num1)) P)) tptp.bot_bo5651135754355059505l_num1)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_real (lambda ((S5 tptp.real)) P)) tptp.top_top_set_real)) (=> (not P) (= (@ tptp.collect_real (lambda ((S5 tptp.real)) P)) tptp.bot_bot_set_real)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_o (lambda ((S5 Bool)) P)) tptp.top_top_set_o)) (=> (not P) (= (@ tptp.collect_o (lambda ((S5 Bool)) P)) tptp.bot_bot_set_o)))))
% 7.32/7.62 (assert (forall ((P Bool)) (and (=> P (= (@ tptp.collect_nat (lambda ((S5 tptp.nat)) P)) tptp.top_top_set_nat)) (=> (not P) (= (@ tptp.collect_nat (lambda ((S5 tptp.nat)) P)) tptp.bot_bot_set_nat)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (= (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (not (@ P X3))))) (@ tptp.finite2998713641127702882nt_int tptp.top_to4366644338036079209nt_int)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int P)) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (not (@ P X3))))) (@ tptp.finite_finite_int tptp.top_top_set_int)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P)) (= (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (not (@ P X3))))) (@ tptp.finite6017078050557962740nteger tptp.top_to4645266643341252675nteger)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (not (@ P X3))))) (@ tptp.finite3207457112153483333omplex tptp.top_top_set_complex)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit (@ tptp.collect_Product_unit P)) (= (@ tptp.finite4290736615968046902t_unit (@ tptp.collect_Product_unit (lambda ((X3 tptp.product_unit)) (not (@ P X3))))) (@ tptp.finite4290736615968046902t_unit tptp.top_to1996260823553986621t_unit)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.numeral_num1 Bool))) (=> (@ tptp.finite1111429032697314574l_num1 (@ tptp.collect_Numeral_num1 P)) (= (@ tptp.finite1111429032697314574l_num1 (@ tptp.collect_Numeral_num1 (lambda ((X3 tptp.numeral_num1)) (not (@ P X3))))) (@ tptp.finite1111429032697314574l_num1 tptp.top_to3689904429138878997l_num1)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X3 tptp.real)) (not (@ P X3))))) (@ tptp.finite_finite_real tptp.top_top_set_real)))))
% 7.32/7.62 (assert (forall ((P (-> Bool Bool))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o P)) (= (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((X3 Bool)) (not (@ P X3))))) (@ tptp.finite_finite_o tptp.top_top_set_o)))))
% 7.32/7.62 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (not (@ P X3))))) (@ tptp.finite_finite_nat tptp.top_top_set_nat)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) tptp.top_top_set_int) tptp.bot_bot_set_int)))
% 7.32/7.62 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.minus_6452836326544984404t_unit A) tptp.top_to1996260823553986621t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 7.32/7.62 (assert (forall ((A tptp.set_Numeral_num1)) (= (@ (@ tptp.minus_8146479932129876780l_num1 A) tptp.top_to3689904429138878997l_num1) tptp.bot_bo5651135754355059505l_num1)))
% 7.32/7.62 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A) tptp.top_top_set_real) tptp.bot_bot_set_real)))
% 7.32/7.62 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) tptp.top_top_set_o) tptp.bot_bot_set_o)))
% 7.32/7.62 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) tptp.top_top_set_nat) tptp.bot_bot_set_nat)))
% 7.32/7.62 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A2) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.32/7.62 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A2) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.32/7.62 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.32/7.62 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) X2) (= (@ A2 tptp.zero_zero_nat) X2))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.real)) (X2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) X2) (= (@ A2 tptp.zero_zero_nat) X2))))
% 7.32/7.62 (assert (forall ((A tptp.set_Product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit A) tptp.top_to1996260823553986621t_unit)))
% 7.32/7.62 (assert (forall ((A tptp.set_Numeral_num1)) (@ (@ tptp.ord_le5200684355995106405l_num1 A) tptp.top_to3689904429138878997l_num1)))
% 7.32/7.62 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A) tptp.top_top_set_real)))
% 7.32/7.62 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o A) tptp.top_top_set_o)))
% 7.32/7.62 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) tptp.top_top_set_nat)))
% 7.32/7.62 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) tptp.top_top_set_int)))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X2) N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X2) N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X2) N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X2) N))))))
% 7.32/7.62 (assert (forall ((A2 tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A2))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A2))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A2))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 7.32/7.62 (assert (forall ((A2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A2))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A2))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A2))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 7.32/7.62 (assert (forall ((L tptp.nat) (H2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_set_nat tptp.top_top_set_nat) (@ (@ tptp.set_or1269000886237332187st_nat L) H2)))))
% 7.32/7.62 (assert (forall ((L tptp.int) (H2 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int tptp.top_top_set_int) (@ (@ tptp.set_or1266510415728281911st_int L) H2)))))
% 7.32/7.62 (assert (forall ((L tptp.real) (H2 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real tptp.top_top_set_real) (@ (@ tptp.set_or1222579329274155063t_real L) H2)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X2) N)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X2) N)))))
% 7.32/7.62 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 7.32/7.62 (assert (forall ((X2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X2) N)))))
% 7.32/7.62 (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)))))))
% 7.32/7.62 (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)))))))
% 7.32/7.62 (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)))))))
% 7.32/7.62 (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)))))))
% 7.32/7.62 (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)))))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ A2 tptp.zero_zero_nat))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ A2 tptp.zero_zero_nat))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A2) (@ tptp.suc N)) (@ (@ tptp.times_times_real A2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A2) tptp.one_one_real)) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A2) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A2) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A2) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A2) (@ tptp.suc N)) (@ (@ tptp.times_times_int A2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A2) (@ tptp.semiri681578069525770553at_rat N)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A2) (@ tptp.semiri5074537144036343181t_real N)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A2) (@ tptp.semiri1314217659103216013at_int N)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A2) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A3) B3)))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) X2))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real) (F (-> tptp.nat tptp.real)) (Y3 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (=> (@ (@ tptp.sums_real F) Y3) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ F (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X2) Y3))))))
% 7.32/7.62 (assert (forall ((C2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C2)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C2))))))
% 7.32/7.62 (assert (forall ((C2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C2)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C2))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (S2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat N4) K))) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) S2)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (K tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat N4) K))) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) S2)))))
% 7.32/7.62 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N4)))) tptp.one_one_real))
% 7.32/7.62 (assert (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 7.32/7.62 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 7.32/7.62 (assert (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 7.32/7.62 (assert (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (S tptp.real) (A tptp.set_nat) (S7 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S) (=> (@ tptp.finite_finite_nat A) (=> (= S7 (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))) A))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N4) A)) (@ F N4)) (@ G N4)))) S7))))))
% 7.32/7.62 (assert (= tptp.top_top_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) true))))
% 7.32/7.62 (assert (= tptp.top_top_set_complex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) true))))
% 7.32/7.62 (assert (= tptp.top_to4366644338036079209nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) true))))
% 7.32/7.62 (assert (= tptp.top_to1996260823553986621t_unit (@ tptp.collect_Product_unit (lambda ((X3 tptp.product_unit)) true))))
% 7.32/7.62 (assert (= tptp.top_to3689904429138878997l_num1 (@ tptp.collect_Numeral_num1 (lambda ((X3 tptp.numeral_num1)) true))))
% 7.32/7.62 (assert (= tptp.top_top_set_real (@ tptp.collect_real (lambda ((X3 tptp.real)) true))))
% 7.32/7.62 (assert (= tptp.top_top_set_o (@ tptp.collect_o (lambda ((X3 Bool)) true))))
% 7.32/7.62 (assert (= tptp.top_top_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) true))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S2 tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S2) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S2) T))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S2) T))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S2) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S2) T))))))
% 7.32/7.62 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I)) (@ F R5)) tptp.zero_zero_complex))) (@ F I))))
% 7.32/7.62 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I)) (@ F R5)) tptp.zero_zero_real))) (@ F I))))
% 7.32/7.62 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I)) (@ F R5)) tptp.zero_zero_nat))) (@ F I))))
% 7.32/7.62 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I)) (@ F R5)) tptp.zero_zero_int))) (@ F I))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (G (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ (@ tptp.sums_real F) A2) (=> (@ (@ tptp.sums_real G) B2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N4)) (@ G N4)))) (@ (@ tptp.plus_plus_real A2) B2))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (G (-> tptp.nat tptp.nat)) (B2 tptp.nat)) (=> (@ (@ tptp.sums_nat F) A2) (=> (@ (@ tptp.sums_nat G) B2) (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N4)) (@ G N4)))) (@ (@ tptp.plus_plus_nat A2) B2))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.int) (G (-> tptp.nat tptp.int)) (B2 tptp.int)) (=> (@ (@ tptp.sums_int F) A2) (=> (@ (@ tptp.sums_int G) B2) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N4)) (@ G N4)))) (@ (@ tptp.plus_plus_int A2) B2))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F) A2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F N4)))) (@ (@ tptp.times_times_real C2) A2)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F) A2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) C2))) (@ (@ tptp.times_times_real A2) C2)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (G (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ (@ tptp.sums_real F) A2) (=> (@ (@ tptp.sums_real G) B2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))) (@ (@ tptp.minus_minus_real A2) B2))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.complex) (C2 tptp.complex)) (=> (@ (@ tptp.sums_complex F) A2) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) C2))) (@ (@ tptp.divide1717551699836669952omplex A2) C2)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.sums_real F) A2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C2))) (@ (@ tptp.divide_divide_real A2) C2)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat tptp.real)) (X2 (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.sums_real (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups2240296850493347238T_real (lambda ((I4 tptp.vEBT_VEBT)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups2240296850493347238T_real X2) I6)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real)) (X2 (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.sums_real (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups8097168146408367636l_real X2) I6)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real)) (X2 (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.sums_real (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups8778361861064173332t_real X2) I6)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat)) (X2 (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.sums_nat (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups3542108847815614940at_nat X2) I6)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex)) (X2 (-> tptp.complex tptp.complex))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.sums_complex (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups7754918857620584856omplex X2) I6)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real)) (X2 (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.sums_real (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups6591440286371151544t_real X2) I6)))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int)) (X2 (-> tptp.int tptp.int))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.sums_int (@ F I2)) (@ X2 I2)))) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ F I4) N4))) I6))) (@ (@ tptp.groups4538972089207619220nt_int X2) I6)))))
% 7.32/7.62 (assert (forall ((C2 tptp.complex) (F (-> tptp.nat tptp.complex)) (D2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C2) (@ F N4)))) (@ (@ tptp.times_times_complex C2) D2)) (@ (@ tptp.sums_complex F) D2)))))
% 7.32/7.62 (assert (forall ((C2 tptp.real) (F (-> tptp.nat tptp.real)) (D2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F N4)))) (@ (@ tptp.times_times_real C2) D2)) (@ (@ tptp.sums_real F) D2)))))
% 7.32/7.62 (assert (forall ((C2 tptp.complex) (F (-> tptp.nat tptp.complex)) (D2 tptp.complex)) (=> (not (= C2 tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) C2))) (@ (@ tptp.times_times_complex D2) C2)) (@ (@ tptp.sums_complex F) D2)))))
% 7.32/7.62 (assert (forall ((C2 tptp.real) (F (-> tptp.nat tptp.real)) (D2 tptp.real)) (=> (not (= C2 tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) C2))) (@ (@ tptp.times_times_real D2) C2)) (@ (@ tptp.sums_real F) D2)))))
% 7.32/7.62 (assert (forall ((C2 tptp.complex) (F (-> tptp.nat tptp.complex)) (A2 tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C2) (@ F N4)))) A2) (=> (not (= C2 tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A2) C2))))))
% 7.32/7.62 (assert (forall ((C2 tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C2) (@ F N4)))) A2) (=> (not (= C2 tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A2) C2))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ F tptp.zero_zero_nat))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ F I2) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ F I2) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 7.32/7.62 (assert (forall ((N7 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N7) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N7)) (= (@ F N3) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N7))))))
% 7.32/7.62 (assert (forall ((N7 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N7) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N7)) (= (@ F N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F) (@ (@ tptp.groups3539618377306564664at_int F) N7))))))
% 7.32/7.62 (assert (forall ((N7 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N7) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N7)) (= (@ F N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N7))))))
% 7.32/7.62 (assert (forall ((N7 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N7) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N7)) (= (@ F N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F) (@ (@ tptp.groups6591440286371151544t_real F) N7))))))
% 7.32/7.62 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R5)) (@ F R5)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) _let_1))))))
% 7.32/7.62 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R5)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) _let_1))))))
% 7.32/7.62 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R5)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) _let_1))))))
% 7.32/7.62 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R5)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) _let_1))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R5) A)) (@ F R5)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) A)))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N4 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N4)))) (@ (@ tptp.power_power_complex Z) M))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N4 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N4)))) (@ (@ tptp.power_power_real Z) M))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N4 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N4)))) (@ (@ tptp.power_power_int Z) M))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S2))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= N4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))))
% 7.32/7.62 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))))
% 7.32/7.62 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))))
% 7.32/7.62 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))))
% 7.32/7.62 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.plus_plus_complex I4) tptp.one_one_complex))) N4) tptp.zero_zero_complex))))
% 7.32/7.62 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N4) tptp.zero_zero_rat))))
% 7.32/7.62 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N4) tptp.zero_zero_real))))
% 7.32/7.62 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N4) tptp.zero_zero_int))))
% 7.32/7.62 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N4) tptp.zero_zero_nat))))
% 7.32/7.62 (assert (forall ((B2 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ 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))))))))))
% 7.32/7.62 (assert (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))))
% 7.32/7.62 (assert (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R2) _let_1))))))
% 7.32/7.62 (assert (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A) tptp.one_one_nat)))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat F) A)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups705719431365010083at_int F) A)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X3 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups705719431365010083at_int F) A)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X3 tptp.nat)) (@ tptp.ring_1_of_int_rat (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X3 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups1705073143266064639nt_int F) A)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X3 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups1705073143266064639nt_int F) A)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X3 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X3)))) A))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.assn))) (= (@ (@ tptp.groups6906906614972039071t_assn G) tptp.bot_bot_set_nat) tptp.one_one_assn)))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.assn))) (= (@ (@ tptp.groups7882442080178216443t_assn G) tptp.bot_bot_set_int) tptp.one_one_assn)))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups705719431365010083at_int G) tptp.bot_bot_set_nat) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) tptp.bot_bot_set_int) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) tptp.bot_bot_set_nat) tptp.one_one_nat)))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.assn))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups6906906614972039071t_assn G) A) tptp.one_one_assn))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.assn))) (=> (not (@ tptp.finite_finite_int A)) (= (@ (@ tptp.groups7882442080178216443t_assn G) A) tptp.one_one_assn))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups1304777262505850412r_assn G) A) tptp.one_one_assn))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.assn))) (=> (not (@ tptp.finite3207457112153483333omplex A)) (= (@ (@ tptp.groups4150731942483176573x_assn G) A) tptp.one_one_assn))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups129246275422532515t_real G) A) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A)) (= (@ (@ tptp.groups2316167850115554303t_real G) A) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups9004974159866482096r_real G) A) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A)) (= (@ (@ tptp.groups766887009212190081x_real G) A) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups73079841787564623at_rat G) A) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A)) (= (@ (@ tptp.groups1072433553688619179nt_rat G) A) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 7.32/7.62 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 7.32/7.62 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 7.32/7.62 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.gbinomial_real A2) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.32/7.62 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.gbinomial_rat A2) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.32/7.62 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.gbinomial_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.32/7.62 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.gbinomial_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.32/7.62 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 7.32/7.62 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.assn))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.assn))) (let ((_let_1 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= K3 A2)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.assn))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.assn))) (let ((_let_1 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= A2 K3)) (@ B2 K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_1 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) (@ B2 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B2 K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X2) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X2) A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (@ (@ tptp.member_complex X2) A)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A) (=> (not (@ (@ tptp.member_real X2) A)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X2) A)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) Z))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) Z))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2))))
% 7.32/7.62 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X2))))
% 7.32/7.62 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real V)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 7.32/7.62 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.32/7.62 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int))))
% 7.32/7.62 (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)))))))))))
% 7.32/7.62 (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)))))))))))
% 7.32/7.62 (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)))))))))))
% 7.32/7.62 (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)))))))))))
% 7.32/7.62 (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)))))))))))
% 7.32/7.62 (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))))))))))))
% 7.32/7.62 (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))))))))))))
% 7.32/7.62 (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))))))))))))
% 7.32/7.62 (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))))))))))))
% 7.32/7.62 (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))))))))))))
% 7.32/7.62 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 7.32/7.62 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 7.32/7.62 (assert (forall ((B2 tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B2))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B2)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (= (@ G X4) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A) tptp.one_one_int))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (= (@ G X4) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A) tptp.one_one_int))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (= (@ G X4) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A) tptp.one_one_nat))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.assn)) (A tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6906906614972039071t_assn G) A) tptp.one_one_assn)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (= (@ G A3) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.vEBT_VEBT tptp.assn)) (A tptp.set_VEBT_VEBT)) (=> (not (= (@ (@ tptp.groups569574905686396791T_assn G) A) tptp.one_one_assn)) (not (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (= (@ G A3) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.real tptp.assn)) (A tptp.set_real)) (=> (not (= (@ (@ tptp.groups1155561341820557179l_assn G) A) tptp.one_one_assn)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A) (= (@ G A3) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.assn)) (A tptp.set_int)) (=> (not (= (@ (@ tptp.groups7882442080178216443t_assn G) A) tptp.one_one_assn)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A) (= (@ G A3) tptp.one_one_assn)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (A tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A) tptp.one_one_real)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (= (@ G A3) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.vEBT_VEBT tptp.real)) (A tptp.set_VEBT_VEBT)) (=> (not (= (@ (@ tptp.groups2703838992350267259T_real G) A) tptp.one_one_real)) (not (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (= (@ G A3) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.real tptp.real)) (A tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A) tptp.one_one_real)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A) (= (@ G A3) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.real)) (A tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A) tptp.one_one_real)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A) (= (@ G A3) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (A tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G) A) tptp.one_one_rat)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (= (@ G A3) tptp.one_one_rat)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.vEBT_VEBT tptp.rat)) (A tptp.set_VEBT_VEBT)) (=> (not (= (@ (@ tptp.groups5726676334696518183BT_rat G) A) tptp.one_one_rat)) (not (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (= (@ G A3) tptp.one_one_rat)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ G I4)) B))) A) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A))) B))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int tptp.int)) (B tptp.set_int) (A tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I4)) B))) A) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A))) B))))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.nat tptp.int)) (B tptp.set_nat) (A tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups705719431365010083at_int (@ G I4)) B))) A) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ G I4) J3))) A))) B))))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B tptp.set_int) (A tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I4)) B))) A) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ G I4) J3))) A))) B))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ G I4)) B))) A) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A))) B))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_int (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A)) (@ (@ tptp.groups705719431365010083at_int H2) A)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.times_times_int (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A)) (@ (@ tptp.groups1705073143266064639nt_int H2) A)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat (@ G X3)) (@ H2 X3)))) A) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A)) (@ (@ tptp.groups708209901874060359at_nat H2) A)))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X3 tptp.nat)) (@ (@ tptp.power_power_int (@ F X3)) N))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.power_power_int (@ F X3)) N))) A))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X3)) N))) A))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_nat) (G (-> tptp.vEBT_VEBT tptp.nat tptp.int)) (R (-> tptp.vEBT_VEBT tptp.nat Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups6359315924273963643BT_int (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.groups705719431365010083at_int (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y tptp.nat)) (@ (@ tptp.groups6359315924273963643BT_int (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ G X3) Y))) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.int)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X3 tptp.real)) (@ (@ tptp.groups705719431365010083at_int (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y tptp.nat)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X3 tptp.real)) (@ (@ G X3) Y))) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.int)) (R (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((X3 tptp.code_integer)) (@ (@ tptp.groups705719431365010083at_int (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y tptp.nat)) (@ (@ tptp.groups3188404863801439024er_int (lambda ((X3 tptp.code_integer)) (@ (@ G X3) Y))) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.int)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ tptp.groups705719431365010083at_int (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y tptp.nat)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ G X3) Y))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_int) (G (-> tptp.vEBT_VEBT tptp.int tptp.int)) (R (-> tptp.vEBT_VEBT tptp.int Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups6359315924273963643BT_int (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X3)) (@ tptp.collect_int (lambda ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y tptp.int)) (@ (@ tptp.groups6359315924273963643BT_int (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ G X3) Y))) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X3 tptp.real)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X3)) (@ tptp.collect_int (lambda ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y tptp.int)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X3 tptp.real)) (@ (@ G X3) Y))) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (B tptp.set_int) (G (-> tptp.code_integer tptp.int tptp.int)) (R (-> tptp.code_integer tptp.int Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((X3 tptp.code_integer)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X3)) (@ tptp.collect_int (lambda ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y tptp.int)) (@ (@ tptp.groups3188404863801439024er_int (lambda ((X3 tptp.code_integer)) (@ (@ G X3) Y))) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (B tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X3)) (@ tptp.collect_int (lambda ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y tptp.int)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ G X3) Y))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (B tptp.set_nat) (G (-> tptp.vEBT_VEBT tptp.nat tptp.nat)) (R (-> tptp.vEBT_VEBT tptp.nat Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups6361806394783013919BT_nat (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ tptp.groups708209901874060359at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups6361806394783013919BT_nat (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ G X3) Y))) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X3 tptp.real)) (@ (@ tptp.groups708209901874060359at_nat (@ G X3)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B) (@ (@ R X3) Y))))))) A) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X3 tptp.real)) (@ (@ G X3) Y))) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ (@ R X3) Y))))))) B))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.int) (A tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A2))) A)) A2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A)) A2))))
% 7.32/7.62 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.int) (A tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A2))) A)) A2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A)) A2))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (A tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A2))) A)) A2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A)) A2))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A)) (@ (@ tptp.groups129246275422532515t_real G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((I2 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_VEBT_VEBT I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2703838992350267259T_real F) A)) (@ (@ tptp.groups2703838992350267259T_real G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A)) (@ (@ tptp.groups1681761925125756287l_real G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A)) (@ (@ tptp.groups2316167850115554303t_real G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A)) (@ (@ tptp.groups73079841787564623at_rat G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((I2 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_VEBT_VEBT I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5726676334696518183BT_rat F) A)) (@ (@ tptp.groups5726676334696518183BT_rat G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A)) (@ (@ tptp.groups4061424788464935467al_rat G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A)) (@ (@ tptp.groups1072433553688619179nt_rat G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((I2 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_VEBT_VEBT I2) A) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups6361806394783013919BT_nat F) A)) (@ (@ tptp.groups6361806394783013919BT_nat G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A)) (@ (@ tptp.groups4696554848551431203al_nat G) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2703838992350267259T_real F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups5726676334696518183BT_rat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups6361806394783013919BT_nat F) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2))) X2)))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2))) X2)))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y3)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y3)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y3)) (@ (@ tptp.ord_less_rat X2) Y3))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.assn)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo1959793692361082170t_assn (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.assn)) (@ (@ tptp.times_times_assn (@ F A5)) __flatten_var_0))) A2) B2) tptp.one_one_assn))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A5)) __flatten_var_0))) A2) B2) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A5)) __flatten_var_0))) A2) B2) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A5)) __flatten_var_0))) A2) B2) tptp.one_one_int))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A5)) __flatten_var_0))) A2) B2) tptp.one_one_nat))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim7802044766580827645g_real X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim2889992004027027881ng_rat X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim8280529875227126926d_real X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim7778729529865785530nd_rat X2))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ (@ tptp.groups569574905686396791T_assn G) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ P X3))))) (@ (@ tptp.groups569574905686396791T_assn (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (@ P X3)) (@ G X3)) tptp.one_one_assn))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (G (-> tptp.real tptp.assn)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A) (= (@ (@ tptp.groups1155561341820557179l_assn G) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ P X3))))) (@ (@ tptp.groups1155561341820557179l_assn (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_assn (@ P X3)) (@ G X3)) tptp.one_one_assn))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.assn)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P X3))))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_assn (@ P X3)) (@ G X3)) tptp.one_one_assn))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.assn)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ P X3))))) (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_assn (@ P X3)) (@ G X3)) tptp.one_one_assn))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ P X3))))) (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ P X3)) (@ G X3)) tptp.one_one_assn))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.assn)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ (@ tptp.groups4150731942483176573x_assn G) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ P X3))))) (@ (@ tptp.groups4150731942483176573x_assn (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_assn (@ P X3)) (@ G X3)) tptp.one_one_assn))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ (@ tptp.groups2703838992350267259T_real G) (@ tptp.collect_VEBT_VEBT (lambda ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) A) (@ P X3))))) (@ (@ tptp.groups2703838992350267259T_real (lambda ((X3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.one_one_real))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A) (= (@ (@ tptp.groups1681761925125756287l_real G) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A) (@ P X3))))) (@ (@ tptp.groups1681761925125756287l_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.one_one_real))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.real)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P X3))))) (@ (@ tptp.groups129246275422532515t_real (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.one_one_real))) A)))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.groups2316167850115554303t_real G) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ P X3))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.one_one_real))) A)))))
% 7.32/7.62 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.32/7.62 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.32/7.62 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.32/7.62 (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 ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.32/7.62 (assert (forall ((C2 tptp.real) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.power_power_real C2) (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_real C2) (@ F A5)))) A))))
% 7.32/7.62 (assert (forall ((C2 tptp.complex) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.power_power_complex C2) (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_complex C2) (@ F A5)))) A))))
% 7.32/7.62 (assert (forall ((C2 tptp.code_integer) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.power_8256067586552552935nteger C2) (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((A5 tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger C2) (@ F A5)))) A))))
% 7.32/7.62 (assert (forall ((C2 tptp.int) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.power_power_int C2) (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_int C2) (@ F A5)))) A))))
% 7.32/7.62 (assert (forall ((C2 tptp.int) (F (-> tptp.int tptp.nat)) (A tptp.set_int)) (= (@ (@ tptp.power_power_int C2) (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A5 tptp.int)) (@ (@ tptp.power_power_int C2) (@ F A5)))) A))))
% 7.32/7.62 (assert (forall ((C2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.power_power_nat C2) (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_nat C2) (@ F A5)))) A))))
% 7.32/7.62 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.32/7.62 (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 ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A) (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) A)) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (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) A)) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A) (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) A)) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A) (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) A)) tptp.one_one_real))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A) (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) A)) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (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) A)) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A) (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) A)) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A) (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) A)) tptp.one_one_rat))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_VEBT_VEBT X4) A) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups6361806394783013919BT_nat F) A)) tptp.one_one_nat))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A)) tptp.one_one_nat))))
% 7.32/7.62 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X15 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X15) Y1)) (@ (@ tptp.times_times_assn X23) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups6906906614972039071t_assn H2) S)) (@ (@ tptp.groups6906906614972039071t_assn G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X15 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X15) Y1)) (@ (@ tptp.times_times_assn X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups7882442080178216443t_assn H2) S)) (@ (@ tptp.groups7882442080178216443t_assn G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S 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 ((X15 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X15) Y1)) (@ (@ tptp.times_times_assn X23) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups1304777262505850412r_assn H2) S)) (@ (@ tptp.groups1304777262505850412r_assn G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.assn)) (G (-> tptp.complex tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X15 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X15) Y1)) (@ (@ tptp.times_times_assn X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups4150731942483176573x_assn H2) S)) (@ (@ tptp.groups4150731942483176573x_assn G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X15) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H2) S)) (@ (@ tptp.groups129246275422532515t_real G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X15) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H2) S)) (@ (@ tptp.groups2316167850115554303t_real G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X15) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups9004974159866482096r_real H2) S)) (@ (@ tptp.groups9004974159866482096r_real G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X15) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups766887009212190081x_real H2) S)) (@ (@ tptp.groups766887009212190081x_real G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_rat X15) Y1)) (@ (@ tptp.times_times_rat X23) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups73079841787564623at_rat H2) S)) (@ (@ tptp.groups73079841787564623at_rat G) S))))))))
% 7.32/7.62 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_rat X15) Y1)) (@ (@ tptp.times_times_rat X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups1072433553688619179nt_rat H2) S)) (@ (@ tptp.groups1072433553688619179nt_rat G) S))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (= A2 C2) (=> (= B2 D2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X4) (=> (@ (@ tptp.ord_less_nat X4) D2) (= (@ G X4) (@ H2 X4))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat A2) B2)) (@ (@ tptp.groups705719431365010083at_int H2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (C2 tptp.nat) (B2 tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (= A2 C2) (=> (= B2 D2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X4) (=> (@ (@ tptp.ord_less_nat X4) D2) (= (@ G X4) (@ H2 X4))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat A2) B2)) (@ (@ tptp.groups708209901874060359at_nat H2) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (C2 tptp.int) (B2 tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int))) (=> (= A2 C2) (=> (= B2 D2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) X4) (=> (@ (@ tptp.ord_less_int X4) D2) (= (@ G X4) (@ H2 X4))))) (= (@ (@ tptp.groups1705073143266064639nt_int G) (@ (@ tptp.set_or4662586982721622107an_int A2) B2)) (@ (@ tptp.groups1705073143266064639nt_int H2) (@ (@ tptp.set_or4662586982721622107an_int C2) D2))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A)))) (let ((_let_4 (@ (@ tptp.member_real X2) A))) (=> (@ tptp.finite_finite_real A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A)))) (let ((_let_4 (@ (@ tptp.member_int X2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X2) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A))) (=> (@ tptp.finite3207457112153483333omplex A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A)))) (let ((_let_4 (@ (@ tptp.member_real X2) A))) (=> (@ tptp.finite_finite_real A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A)))) (let ((_let_4 (@ (@ tptp.member_int X2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_VEBT_VEBT) (S 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 S7) (=> (@ tptp.finite5795047828879050333T_VEBT T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_VEBT_VEBT (@ J A3)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S) (@ (@ tptp.groups569574905686396791T_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_real) (S 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 S7) (=> (@ tptp.finite_finite_real T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T6)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S) (@ (@ tptp.groups1155561341820557179l_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_VEBT_VEBT) (S 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 S7) (=> (@ tptp.finite5795047828879050333T_VEBT T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_VEBT_VEBT (@ J A3)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S) (@ (@ tptp.groups569574905686396791T_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_real) (S 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 S7) (=> (@ tptp.finite_finite_real T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T5) T6)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S) (@ (@ tptp.groups1155561341820557179l_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_int) (S 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 S7) (=> (@ tptp.finite_finite_int T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T6)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_int) (S 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 S7) (=> (@ tptp.finite_finite_int T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T5) T6)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_Code_integer) (S 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 S7) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_Code_integer (@ J A3)) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_Code_integer) (S 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 S7) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_Code_integer (@ J A3)) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_VEBT_VEBT) (T6 tptp.set_complex) (S 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 S7) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T6)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T6)) (@ (@ tptp.member_VEBT_VEBT (@ I B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT S) S7)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S) (@ (@ tptp.groups4150731942483176573x_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((S7 tptp.set_real) (T6 tptp.set_complex) (S 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 S7) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (= (@ I (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S7)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T5) T6)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T6)) (= (@ J (@ I B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T5) T6)) (@ (@ tptp.member_real (@ I B3)) (@ (@ tptp.minus_minus_set_real S) S7)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S7) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T6) (= (@ H2 B3) tptp.one_one_assn))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S) (@ (@ tptp.groups4150731942483176573x_assn H2) T5)))))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups6361806394783013919BT_nat F) A)) (@ (@ tptp.groups6361806394783013919BT_nat G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A)) (@ (@ tptp.groups4696554848551431203al_nat G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups3190895334310489300er_nat F) A)) (@ (@ tptp.groups3190895334310489300er_nat G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A)) (@ (@ tptp.groups861055069439313189ex_nat G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int)) (G (-> tptp.vEBT_VEBT tptp.int))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups6359315924273963643BT_int F) A)) (@ (@ tptp.groups6359315924273963643BT_int G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A)) (@ (@ tptp.groups4694064378042380927al_int G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups3188404863801439024er_int F) A)) (@ (@ tptp.groups3188404863801439024er_int G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A)) (@ (@ tptp.groups858564598930262913ex_int G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A)) (@ (@ tptp.groups1707563613775114915nt_nat G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups705719431365010083at_int F) A)) (@ (@ tptp.groups705719431365010083at_int G) B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X2)))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X2)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y3))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y3)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y3))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y3)))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (=> (= X2 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (=> (= X2 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 7.32/7.62 (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))))
% 7.32/7.62 (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))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 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) P6) (= (@ (@ tptp.times_times_real (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P6) (= (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 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) P6) (= (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (P6 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) P6) (= (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P6))) (@ _let_2 (@ _let_1 P6)))))))))
% 7.32/7.62 (assert (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A5) (@ tptp.semiri8010041392384452111omplex I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat K3) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3)))))
% 7.32/7.62 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat K3) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3)))))
% 7.32/7.62 (assert (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A5) (@ tptp.semiri5074537144036343181t_real I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat K3) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3)))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A2))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A2) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A2))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.one_one_assn))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.one_one_assn))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G X3) tptp.one_one_assn))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.one_one_real))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.one_one_real))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G X3) tptp.one_one_real))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.one_one_rat))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ tptp.collect_Code_integer (lambda ((X3 tptp.code_integer)) (= (@ G X3) tptp.one_one_rat))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G X3) tptp.one_one_rat))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.one_one_nat))))) (@ _let_1 A))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.32/7.62 (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 ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2703838992350267259T_real F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups9004974159866482096r_real F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5726676334696518183BT_rat F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I6)))))))))
% 7.32/7.62 (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 ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I6)))))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (not (= I6 tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2703838992350267259T_real F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (not (= I6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups9004974159866482096r_real F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (not (= I6 tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups5726676334696518183BT_rat F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (not (= I6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I2) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2555765274223993564er_rat F) I6)))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I6)))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ G X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups569574905686396791T_assn G) T5) (@ (@ tptp.groups569574905686396791T_assn H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ G X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) T5) (@ (@ tptp.groups1155561341820557179l_assn H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) T5) (@ (@ tptp.groups1304777262505850412r_assn H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.assn)) (H2 (-> tptp.complex tptp.assn))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4150731942483176573x_assn G) T5) (@ (@ tptp.groups4150731942483176573x_assn H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2703838992350267259T_real G) T5) (@ (@ tptp.groups2703838992350267259T_real H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T5) (@ (@ tptp.groups1681761925125756287l_real H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups9004974159866482096r_real G) T5) (@ (@ tptp.groups9004974159866482096r_real H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups766887009212190081x_real G) T5) (@ (@ tptp.groups766887009212190081x_real H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (H2 (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups5726676334696518183BT_rat G) T5) (@ (@ tptp.groups5726676334696518183BT_rat H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) T5) (@ (@ tptp.groups4061424788464935467al_rat H2) S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.assn)) (G (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ H2 X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S) (@ (@ tptp.groups569574905686396791T_assn H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.assn)) (G (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ H2 X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S) (@ (@ tptp.groups1155561341820557179l_assn H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ H2 X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.assn)) (G (-> tptp.complex tptp.assn))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ H2 X4) tptp.one_one_assn))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4150731942483176573x_assn G) S) (@ (@ tptp.groups4150731942483176573x_assn H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2703838992350267259T_real G) S) (@ (@ tptp.groups2703838992350267259T_real H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S) (@ (@ tptp.groups1681761925125756287l_real H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups9004974159866482096r_real G) S) (@ (@ tptp.groups9004974159866482096r_real H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups766887009212190081x_real G) S) (@ (@ tptp.groups766887009212190081x_real H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S) T5) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups5726676334696518183BT_rat G) S) (@ (@ tptp.groups5726676334696518183BT_rat H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S) T5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T5) S)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) S) (@ (@ tptp.groups4061424788464935467al_rat H2) T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_assn))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_assn))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_int))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_int))) (= (@ _let_1 T5) (@ _let_1 S))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T5) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) (@ (@ tptp.minus_2355218937544613996nteger T5) S)) (= (@ G X4) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((T5 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T5) S)) (= (@ G X4) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T5))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B 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 C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.one_one_assn))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B 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 C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.one_one_assn))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B 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 C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.one_one_assn))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_complex) (A tptp.set_complex) (B 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 C) (=> (@ (@ tptp.ord_le211207098394363844omplex A) C) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C) B)) (= (@ H2 B3) tptp.one_one_assn))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B 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 C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.one_one_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B 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 C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.one_one_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B 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 C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.one_one_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_complex) (A tptp.set_complex) (B 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 C) (=> (@ (@ tptp.ord_le211207098394363844omplex A) C) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C) B)) (= (@ H2 B3) tptp.one_one_real))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (H2 (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat H2))) (let ((_let_2 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.one_one_rat))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat H2))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.one_one_rat))) (=> (= (@ _let_2 C) (@ _let_1 C)) (= (@ _let_2 A) (@ _let_1 B))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B 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 C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B 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 C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B 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 C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_complex) (A tptp.set_complex) (B 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 C) (=> (@ (@ tptp.ord_le211207098394363844omplex A) C) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C) A)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C) B)) (= (@ H2 B3) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B 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 C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.one_one_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B 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 C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.one_one_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_Code_integer) (A tptp.set_Code_integer) (B 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 C) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) C) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C) B)) (= (@ H2 B3) tptp.one_one_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_complex) (A tptp.set_complex) (B 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 C) (=> (@ (@ tptp.ord_le211207098394363844omplex A) C) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C) A)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C) B)) (= (@ H2 B3) tptp.one_one_real))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (B tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (H2 (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat H2))) (let ((_let_2 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) C) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B) C) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) A)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT C) B)) (= (@ H2 B3) tptp.one_one_rat))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((C tptp.set_real) (A tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat H2))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real C) (=> (@ (@ tptp.ord_less_eq_set_real A) C) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C) A)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C) B)) (= (@ H2 B3) tptp.one_one_rat))) (= (= (@ _let_2 A) (@ _let_1 B)) (= (@ _let_2 C) (@ _let_1 C))))))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_1 A) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) B))) (@ _let_1 B))))))))
% 7.32/7.62 (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))))
% 7.32/7.62 (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))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A2))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B2)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A2) B2))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A2))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B2)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A2) B2))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N))) (@ G N)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.times_times_real (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_2 (@ _let_1 (@ tptp.suc B2))) (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 B2))) (@ G B2))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (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))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.32/7.62 (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))))))))))
% 7.32/7.62 (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))))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_nat))))
% 7.32/7.62 (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 N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ G N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (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 N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (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 N)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 7.32/7.62 (assert (= tptp.archim7802044766580827645g_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X3))) (@ (@ (@ tptp.if_int (= X3 (@ tptp.ring_1_of_int_real _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 7.32/7.62 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X3 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X3))) (@ (@ (@ tptp.if_int (= X3 (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 7.32/7.62 (assert (forall ((X2 tptp.nat) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) A2) (@ (@ tptp.ord_less_eq_nat X2) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A2))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A2) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A2) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A2) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim6058952711729229775r_real X2))) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim3151403230148437115or_rat X2))) tptp.one_one_int)))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A2))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A2) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A2))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real A2) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A2))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A2))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real _let_3) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A2) K)) (@ (@ tptp.times_times_rat A2) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A2) K)) (@ (@ tptp.times_times_real A2) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A2) _let_1)) K)) (@ (@ tptp.gbinomial_real A2) K))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A2) _let_1)) K)) (@ (@ tptp.gbinomial_rat A2) K))))))
% 7.32/7.62 (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))))
% 7.32/7.62 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 7.32/7.62 (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))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (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)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) (@ tptp.suc I4))))) _let_1)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) (@ tptp.suc I4))))) _let_1)))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A2 I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A2 I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((M6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M6) K))) (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N) K))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((M6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M6) K))) (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N) K))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (forall ((I2 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_VEBT_VEBT I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bo8194388402131092736T_VEBT)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2703838992350267259T_real F) A)) (@ (@ tptp.groups2703838992350267259T_real G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A)) (@ (@ tptp.groups1681761925125756287l_real G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((I2 tptp.code_integer)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_Code_integer I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups9004974159866482096r_real F) A)) (@ (@ tptp.groups9004974159866482096r_real G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A)) (@ (@ tptp.groups766887009212190081x_real G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A)) (@ (@ tptp.groups129246275422532515t_real G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A)) (@ (@ tptp.groups2316167850115554303t_real G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (forall ((I2 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_VEBT_VEBT I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bo8194388402131092736T_VEBT)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5726676334696518183BT_rat F) A)) (@ (@ tptp.groups5726676334696518183BT_rat G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F) A)) (@ (@ tptp.groups4061424788464935467al_rat G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((I2 tptp.code_integer)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_Code_integer I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2555765274223993564er_rat F) A)) (@ (@ tptp.groups2555765274223993564er_rat G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I2)))))) (=> (not (= A tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F) A)) (@ (@ tptp.groups225925009352817453ex_rat G) A)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1707563613775114915nt_nat F) A)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3190895334310489300er_nat F) A)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A)) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3188404863801439024er_int F) A)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A)) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups705719431365010083at_int F) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1705073143266064639nt_int F) A)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X3))))))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) Z))))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X2) Z))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (A2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A2))) (= (= (@ tptp.archim6058952711729229775r_real X2) A2) (and (@ (@ tptp.ord_less_eq_real _let_1) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (A2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A2))) (= (= (@ tptp.archim3151403230148437115or_rat X2) A2) (and (@ (@ tptp.ord_less_eq_rat _let_1) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 7.32/7.62 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I4)))))))
% 7.32/7.62 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X2))) (let ((_let_2 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.real)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.real)) (X2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X2))) (let ((_let_2 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.rat)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.rat)) (X2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ (@ tptp.member_VEBT_VEBT X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X2) tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.member_complex X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (@ (@ tptp.member_VEBT_VEBT X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A) (=> (@ (@ tptp.member_real X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (X2 tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X2) tptp.bot_bo3990330152332043303nteger))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (@ (@ tptp.member_complex X2) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 7.32/7.62 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A2)) (@ tptp.archim6058952711729229775r_real B2))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A2) B2))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A2)) (@ tptp.archim3151403230148437115or_rat B2))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A2) B2))))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.one_one_assn)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N))) (@ G N))))))))))
% 7.32/7.62 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 7.32/7.62 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X2))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb) Xc) Y3) (and (=> _let_2 (= Y3 Xc)) (=> (not _let_2) (= Y3 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X2 Xa) Xc))))))))))
% 7.32/7.62 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F7 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B6 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B6) A5)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F7) (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) B6) (@ (@ F7 A5) Acc2))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A2) K)))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A2) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A2) K)))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A2) _let_1)) (@ (@ tptp.times_times_rat A2) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)) K))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A2) _let_1)) (@ (@ tptp.times_times_real A2) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A2) tptp.one_one_real)) K))))))
% 7.32/7.62 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.real)) (C2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2703838992350267259T_real C2) (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_2 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.real)) (C2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C2) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.real)) (C2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ (@ tptp.groups9004974159866482096r_real C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups9004974159866482096r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups9004974159866482096r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.real)) (C2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C2) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B2 (-> tptp.int tptp.real)) (C2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups2316167850115554303t_real C2) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B2 (-> tptp.nat tptp.real)) (C2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.groups129246275422532515t_real C2) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_real (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_VEBT_VEBT) (A2 tptp.vEBT_VEBT) (B2 (-> tptp.vEBT_VEBT tptp.rat)) (C2 (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5726676334696518183BT_rat C2) (@ (@ tptp.minus_5127226145743854075T_VEBT S) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A2) S))) (=> (@ tptp.finite5795047828879050333T_VEBT S) (and (=> _let_2 (= (@ (@ tptp.groups5726676334696518183BT_rat (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5726676334696518183BT_rat (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B2 (-> tptp.real tptp.rat)) (C2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups4061424788464935467al_rat C2) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer) (B2 (-> tptp.code_integer tptp.rat)) (C2 (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ (@ tptp.groups2555765274223993564er_rat C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A2) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups2555765274223993564er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2555765274223993564er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B2 (-> tptp.complex tptp.rat)) (C2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups225925009352817453ex_rat C2) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B2 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B2 K3)) (@ C2 K3)))) S) _let_1))))))))
% 7.32/7.62 (assert (forall ((B2 tptp.int) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A2) (@ tptp.ring_1_of_int_real B2))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A2)) B2)))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (M tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (M tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (Z (-> tptp.vEBT_VEBT tptp.real)) (W (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups2703838992350267259T_real Z) I6)) (@ (@ tptp.groups2703838992350267259T_real W) I6)))) (@ (@ tptp.groups2240296850493347238T_real (lambda ((I4 tptp.vEBT_VEBT)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_real) (Z (-> tptp.real tptp.real)) (W (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups1681761925125756287l_real Z) I6)) (@ (@ tptp.groups1681761925125756287l_real W) I6)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_int) (Z (-> tptp.int tptp.real)) (W (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups2316167850115554303t_real Z) I6)) (@ (@ tptp.groups2316167850115554303t_real W) I6)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_VEBT_VEBT) (Z (-> tptp.vEBT_VEBT tptp.complex)) (W (-> tptp.vEBT_VEBT tptp.complex))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups127312072573709053omplex Z) I6)) (@ (@ tptp.groups127312072573709053omplex W) I6)))) (@ (@ tptp.groups2240296850493347238T_real (lambda ((I4 tptp.vEBT_VEBT)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_real) (Z (-> tptp.real tptp.complex)) (W (-> tptp.real tptp.complex))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups713298508707869441omplex Z) I6)) (@ (@ tptp.groups713298508707869441omplex W) I6)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_int) (Z (-> tptp.int tptp.complex)) (W (-> tptp.int tptp.complex))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7440179247065528705omplex Z) I6)) (@ (@ tptp.groups7440179247065528705omplex W) I6)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_nat) (Z (-> tptp.nat tptp.real)) (W (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups129246275422532515t_real Z) I6)) (@ (@ tptp.groups129246275422532515t_real W) I6)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((I6 tptp.set_nat) (Z (-> tptp.nat tptp.complex)) (W (-> tptp.nat tptp.complex))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups6464643781859351333omplex Z) I6)) (@ (@ tptp.groups6464643781859351333omplex W) I6)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I4)) (@ W I4))))) I6))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat N) M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat N) M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))
% 7.32/7.62 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N4 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4)))))
% 7.32/7.62 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N4 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4)))))
% 7.32/7.62 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4)))))
% 7.32/7.62 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4)))))
% 7.32/7.62 (assert (forall ((Q3 tptp.real) (P6 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 P6) Q3)))) Q3)) P6))))
% 7.32/7.62 (assert (forall ((Q3 tptp.rat) (P6 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 P6) Q3)))) Q3)) P6))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B) A)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B) A)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B) A)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_VEBT_VEBT) (A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat F))) (=> (@ tptp.finite5795047828879050333T_VEBT B) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A) B) (=> (forall ((B3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B3) (@ (@ tptp.minus_5127226145743854075T_VEBT B) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A3) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_real) (A tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_complex) (A tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A) B) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.complex)) (A2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.groups127312072573709053omplex F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.complex)) (A2 tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite_finite_real A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.complex)) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups862514429393162674omplex F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.complex)) (A2 tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite_finite_int A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.complex)) (A2 tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite_finite_nat A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (A2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.groups2703838992350267259T_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A) (@ (@ tptp.insert_VEBT_VEBT A2) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real)) (A2 tptp.real)) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite_finite_real A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups9004974159866482096r_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.real)) (A2 tptp.complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A2) A))) (let ((_let_5 (@ F A2))) (=> (@ tptp.finite3207457112153483333omplex A) (=> (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))))))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A2) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A2) K)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A2) K)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A2) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A2) K)))))))
% 7.32/7.62 (assert (forall ((A2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A2) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A2) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A2) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A2) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A2) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A2) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A2) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A2) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A2) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A2) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A2) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A2) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N4 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 7.32/7.62 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N4 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 7.32/7.62 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 7.32/7.62 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 7.32/7.62 (assert (forall ((Q3 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P6) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P6) Q3)))) tptp.one_one_real)) Q3)))))
% 7.32/7.62 (assert (forall ((Q3 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat P6) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P6) Q3)))) tptp.one_one_rat)) Q3)))))
% 7.32/7.62 (assert (= tptp.archim8280529875227126926d_real (lambda ((X3 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.32/7.62 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X3 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A2) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A2) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A2) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A5)) __flatten_var_0))) A2) B2) tptp.zero_zero_complex))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.rat)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A5)) __flatten_var_0))) A2) B2) tptp.zero_zero_rat))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A5)) __flatten_var_0))) A2) B2) tptp.zero_zero_int))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A5)) __flatten_var_0))) A2) B2) tptp.zero_zero_nat))))
% 7.32/7.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A5)) __flatten_var_0))) A2) B2) tptp.zero_zero_real))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A2) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A2) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A2) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A2) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A2) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A2) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A2) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A2) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A2) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 7.32/7.62 (assert (forall ((K tptp.nat) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A2) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A2) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 7.32/7.62 (assert (forall ((X2 tptp.real) (B2 tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B2) X2)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X2) (@ (@ tptp.ord_less_real X2) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 7.32/7.62 (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))))))))
% 7.32/7.62 (assert (forall ((B2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 7.32/7.62 (assert (forall ((A2 tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A2) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 7.32/7.62 (assert (forall ((A2 tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A2) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A2) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 7.32/7.63 (assert (= tptp.archim8280529875227126926d_real (lambda ((X3 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 X3))) (@ tptp.archim7802044766580827645g_real X3)) (@ tptp.archim6058952711729229775r_real X3)))))
% 7.32/7.63 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X3 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 X3))) (@ tptp.archim2889992004027027881ng_rat X3)) (@ tptp.archim3151403230148437115or_rat X3)))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 7.32/7.63 (assert (forall ((X1 tptp.code_integer) (X22 tptp.code_integer) (Y15 tptp.code_integer) (Y2 tptp.code_integer)) (= (= (@ (@ tptp.produc1086072967326762835nteger X1) X22) (@ (@ tptp.produc1086072967326762835nteger Y15) Y2)) (and (= X1 Y15) (= X22 Y2)))))
% 7.32/7.63 (assert (forall ((X1 tptp.heap_e7401611519738050253t_unit) (X22 tptp.set_nat) (Y15 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (= (= (@ (@ tptp.produc7507926704131184380et_nat X1) X22) (@ (@ tptp.produc7507926704131184380et_nat Y15) Y2)) (and (= X1 Y15) (= X22 Y2)))))
% 7.32/7.63 (assert (forall ((X1 tptp.num) (X22 tptp.num) (Y15 tptp.num) (Y2 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y15) Y2)) (and (= X1 Y15) (= X22 Y2)))))
% 7.32/7.63 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y15 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y15) Y2)) (and (= X1 Y15) (= X22 Y2)))))
% 7.32/7.63 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y15 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y15) Y2)) (and (= X1 Y15) (= X22 Y2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (A4 tptp.code_integer) (B4 tptp.code_integer)) (= (= (@ (@ tptp.produc1086072967326762835nteger A2) B2) (@ (@ tptp.produc1086072967326762835nteger A4) B4)) (and (= A2 A4) (= B2 B4)))))
% 7.32/7.63 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat) (A4 tptp.heap_e7401611519738050253t_unit) (B4 tptp.set_nat)) (= (= (@ (@ tptp.produc7507926704131184380et_nat A2) B2) (@ (@ tptp.produc7507926704131184380et_nat A4) B4)) (and (= A2 A4) (= B2 B4)))))
% 7.32/7.63 (assert (forall ((A2 tptp.num) (B2 tptp.num) (A4 tptp.num) (B4 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A2) B2) (@ (@ tptp.product_Pair_num_num A4) B4)) (and (= A2 A4) (= B2 B4)))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (A4 tptp.nat) (B4 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A2) B2) (@ (@ tptp.product_Pair_nat_nat A4) B4)) (and (= A2 A4) (= B2 B4)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int) (A4 tptp.int) (B4 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A2) B2) (@ (@ tptp.product_Pair_int_int A4) B4)) (and (= A2 A4) (= B2 B4)))))
% 7.32/7.63 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I) K))))
% 7.32/7.63 (assert (forall ((I tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I) K))))
% 7.32/7.63 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I) K))))
% 7.32/7.63 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I) K))))
% 7.32/7.63 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I) K))))
% 7.32/7.63 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I) K))))
% 7.32/7.63 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X2)) (@ tptp.set_or58775011639299419et_int Y3)) (@ (@ tptp.ord_less_eq_set_int X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X2)) (@ tptp.set_ord_atMost_rat Y3)) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X2)) (@ tptp.set_ord_atMost_num Y3)) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X2)) (@ tptp.set_ord_atMost_nat Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X2)) (@ tptp.set_ord_atMost_int Y3)) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.32/7.63 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A) tptp.one_one_nat) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (= (@ F X3) tptp.one_one_nat)))))))
% 7.32/7.63 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (= (= (@ (@ tptp.groups3190895334310489300er_nat F) A) tptp.one_one_nat) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (= (@ F X3) tptp.one_one_nat)))))))
% 7.32/7.63 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A) tptp.one_one_nat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A) (= (@ F X3) tptp.one_one_nat)))))))
% 7.32/7.63 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A) tptp.one_one_nat) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (= (@ F X3) tptp.one_one_nat)))))))
% 7.32/7.63 (assert (forall ((L tptp.set_int) (H2 tptp.set_int) (H4 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H2)) (@ tptp.set_or58775011639299419et_int H4)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H4)))))
% 7.32/7.63 (assert (forall ((L tptp.rat) (H2 tptp.rat) (H4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H2)) (@ tptp.set_ord_atMost_rat H4)) (or (not (@ (@ tptp.ord_less_eq_rat L) H2)) (@ (@ tptp.ord_less_eq_rat H2) H4)))))
% 7.32/7.63 (assert (forall ((L tptp.num) (H2 tptp.num) (H4 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H2)) (@ tptp.set_ord_atMost_num H4)) (or (not (@ (@ tptp.ord_less_eq_num L) H2)) (@ (@ tptp.ord_less_eq_num H2) H4)))))
% 7.32/7.63 (assert (forall ((L tptp.nat) (H2 tptp.nat) (H4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H2)) (@ tptp.set_ord_atMost_nat H4)) (or (not (@ (@ tptp.ord_less_eq_nat L) H2)) (@ (@ tptp.ord_less_eq_nat H2) H4)))))
% 7.32/7.63 (assert (forall ((L tptp.int) (H2 tptp.int) (H4 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H2)) (@ tptp.set_ord_atMost_int H4)) (or (not (@ (@ tptp.ord_less_eq_int L) H2)) (@ (@ tptp.ord_less_eq_int H2) H4)))))
% 7.32/7.63 (assert (forall ((L tptp.code_integer) (H2 tptp.code_integer) (H4 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger L) H2)) (@ tptp.set_or9101266186257409494nteger H4)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger L) H2)) (@ (@ tptp.ord_le3102999989581377725nteger H2) H4)))))
% 7.32/7.63 (assert (forall ((L tptp.real) (H2 tptp.real) (H4 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H2)) (@ tptp.set_ord_atMost_real H4)) (or (not (@ (@ tptp.ord_less_eq_real L) H2)) (@ (@ tptp.ord_less_eq_real H2) H4)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.32/7.63 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 7.32/7.63 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups3190895334310489300er_nat F) A)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 7.32/7.63 (assert (forall ((A tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A)) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 7.32/7.63 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X3)))) A))))
% 7.32/7.63 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X3) U2))))))
% 7.32/7.63 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X3) U2))))))
% 7.32/7.63 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X3 tptp.num)) (@ (@ tptp.ord_less_eq_num X3) U2))))))
% 7.32/7.63 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) U2))))))
% 7.32/7.63 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) U2))))))
% 7.32/7.63 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 7.32/7.63 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 7.32/7.63 (assert (forall ((H2 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real tptp.top_top_set_real) (@ tptp.set_ord_atMost_real H2)))))
% 7.32/7.63 (assert (forall ((H2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_set_nat tptp.top_top_set_nat) (@ tptp.set_ord_atMost_nat H2)))))
% 7.32/7.63 (assert (forall ((H2 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int tptp.top_top_set_int) (@ tptp.set_ord_atMost_int H2)))))
% 7.32/7.63 (assert (forall ((H2 tptp.int) (L4 tptp.int) (H4 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L4) H4)))))
% 7.32/7.63 (assert (forall ((H2 tptp.real) (L4 tptp.real) (H4 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L4) H4)))))
% 7.32/7.63 (assert (= tptp.finite_finite_nat (lambda ((S8 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S8) (@ tptp.set_ord_atMost_nat K3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X2)) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X2)) tptp.one_one_rat)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X2))))
% 7.32/7.63 (assert (forall ((Y3 tptp.produc8923325533196201883nteger)) (not (forall ((A3 tptp.code_integer) (B3 tptp.code_integer)) (not (= Y3 (@ (@ tptp.produc1086072967326762835nteger A3) B3)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.produc3658429121746597890et_nat)) (not (forall ((A3 tptp.heap_e7401611519738050253t_unit) (B3 tptp.set_nat)) (not (= Y3 (@ (@ tptp.produc7507926704131184380et_nat A3) B3)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.product_prod_num_num)) (not (forall ((A3 tptp.num) (B3 tptp.num)) (not (= Y3 (@ (@ tptp.product_Pair_num_num A3) B3)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y3 (@ (@ tptp.product_Pair_nat_nat A3) B3)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (not (= Y3 (@ (@ tptp.product_Pair_int_int A3) B3)))))))
% 7.32/7.63 (assert (forall ((P6 tptp.produc8923325533196201883nteger)) (exists ((X4 tptp.code_integer) (Y4 tptp.code_integer)) (= P6 (@ (@ tptp.produc1086072967326762835nteger X4) Y4)))))
% 7.32/7.63 (assert (forall ((P6 tptp.produc3658429121746597890et_nat)) (exists ((X4 tptp.heap_e7401611519738050253t_unit) (Y4 tptp.set_nat)) (= P6 (@ (@ tptp.produc7507926704131184380et_nat X4) Y4)))))
% 7.32/7.63 (assert (forall ((P6 tptp.product_prod_num_num)) (exists ((X4 tptp.num) (Y4 tptp.num)) (= P6 (@ (@ tptp.product_Pair_num_num X4) Y4)))))
% 7.32/7.63 (assert (forall ((P6 tptp.product_prod_nat_nat)) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (= P6 (@ (@ tptp.product_Pair_nat_nat X4) Y4)))))
% 7.32/7.63 (assert (forall ((P6 tptp.product_prod_int_int)) (exists ((X4 tptp.int) (Y4 tptp.int)) (= P6 (@ (@ tptp.product_Pair_int_int X4) Y4)))))
% 7.32/7.63 (assert (forall ((P (-> tptp.produc8923325533196201883nteger Bool)) (P6 tptp.produc8923325533196201883nteger)) (=> (forall ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ P (@ (@ tptp.produc1086072967326762835nteger A3) B3))) (@ P P6))))
% 7.32/7.63 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (P6 tptp.produc3658429121746597890et_nat)) (=> (forall ((A3 tptp.heap_e7401611519738050253t_unit) (B3 tptp.set_nat)) (@ P (@ (@ tptp.produc7507926704131184380et_nat A3) B3))) (@ P P6))))
% 7.32/7.63 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P6 tptp.product_prod_num_num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A3) B3))) (@ P P6))))
% 7.32/7.63 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P6 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P P6))))
% 7.32/7.63 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P6 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B3))) (@ P P6))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (A4 tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.produc1086072967326762835nteger A2) B2) (@ (@ tptp.produc1086072967326762835nteger A4) B4)) (not (=> (= A2 A4) (not (= B2 B4)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat) (A4 tptp.heap_e7401611519738050253t_unit) (B4 tptp.set_nat)) (=> (= (@ (@ tptp.produc7507926704131184380et_nat A2) B2) (@ (@ tptp.produc7507926704131184380et_nat A4) B4)) (not (=> (= A2 A4) (not (= B2 B4)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.num) (B2 tptp.num) (A4 tptp.num) (B4 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A2) B2) (@ (@ tptp.product_Pair_num_num A4) B4)) (not (=> (= A2 A4) (not (= B2 B4)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (A4 tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A2) B2) (@ (@ tptp.product_Pair_nat_nat A4) B4)) (not (=> (= A2 A4) (not (= B2 B4)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int) (A4 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A2) B2) (@ (@ tptp.product_Pair_int_int A4) B4)) (not (=> (= A2 A4) (not (= B2 B4)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A2)) (@ tptp.set_ord_lessThan_rat B2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A2)) (@ tptp.set_ord_lessThan_num B2)) (@ (@ tptp.ord_less_num A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A2)) (@ tptp.set_ord_lessThan_nat B2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A2)) (@ tptp.set_ord_lessThan_int B2)) (@ (@ tptp.ord_less_int A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A2)) (@ tptp.set_or5984915006950818249n_real B2)) (@ (@ tptp.ord_less_real A2) B2))))
% 7.32/7.63 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 7.32/7.63 (assert (= tptp.archim2898591450579166408c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real X3) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X3))))))
% 7.32/7.63 (assert (= tptp.archimedean_frac_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat X3) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X3))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (I tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (D2 (-> tptp.nat tptp.complex))) (= (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex X3) I4)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ D2 I4)) (@ (@ tptp.power_power_complex X3) I4)))) _let_1)))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C2 I4) (@ D2 I4)))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (D2 (-> tptp.nat tptp.real))) (= (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real X3) I4)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ D2 I4)) (@ (@ tptp.power_power_real X3) I4)))) _let_1)))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C2 I4) (@ D2 I4)))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.32/7.63 (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 ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A2 I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A2 I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A2 I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A2 I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A2 I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) X2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) X2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X2)) (@ tptp.archim2898591450579166408c_real Y3)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X2) Y3)))) (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)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X2)) (@ tptp.archimedean_frac_rat Y3)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X2) Y3)))) (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)))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex W3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C2 K) tptp.zero_zero_complex)))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real W3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C2 K) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex X3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C2 I4) tptp.zero_zero_complex))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real X3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ C2 I4) tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A2) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A2) (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) N))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A2) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A2) (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) N))))
% 7.32/7.63 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X2)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (K tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex Z4) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (K tptp.nat) (N tptp.nat)) (=> (not (= (@ C2 K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real Z4) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex X3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (not (= (@ C2 I4) tptp.zero_zero_complex)))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real X3) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (not (= (@ C2 I4) tptp.zero_zero_real)))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (A2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex A2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B3 (-> tptp.nat tptp.complex))) (not (forall ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.code_integer)) (A2 tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ C2 I4)) (@ (@ tptp.power_8256067586552552935nteger A2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger) (not (forall ((B3 (-> tptp.nat tptp.code_integer))) (not (forall ((Z5 tptp.code_integer)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ C2 I4)) (@ (@ tptp.power_8256067586552552935nteger Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger Z5) A2)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ B3 I4)) (@ (@ tptp.power_8256067586552552935nteger Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.rat)) (A2 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat A2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B3 (-> tptp.nat tptp.rat))) (not (forall ((Z5 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.int)) (A2 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I4)) (@ (@ tptp.power_power_int A2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B3 (-> tptp.nat tptp.int))) (not (forall ((Z5 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (A2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real A2) I4)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B3 (-> tptp.nat tptp.real))) (not (forall ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (A2 tptp.complex)) (exists ((B3 (-> tptp.nat tptp.complex))) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex A2) I4)))) _let_1))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.code_integer)) (N tptp.nat) (A2 tptp.code_integer)) (exists ((B3 (-> tptp.nat tptp.code_integer))) (forall ((Z5 tptp.code_integer)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ C2 I4)) (@ (@ tptp.power_8256067586552552935nteger Z5) I4)))) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger Z5) A2)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ B3 I4)) (@ (@ tptp.power_8256067586552552935nteger Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ C2 I4)) (@ (@ tptp.power_8256067586552552935nteger A2) I4)))) _let_1))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.rat)) (N tptp.nat) (A2 tptp.rat)) (exists ((B3 (-> tptp.nat tptp.rat))) (forall ((Z5 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I4)) (@ (@ tptp.power_power_rat Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I4)) (@ (@ tptp.power_power_rat A2) I4)))) _let_1))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.int)) (N tptp.nat) (A2 tptp.int)) (exists ((B3 (-> tptp.nat tptp.int))) (forall ((Z5 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I4)) (@ (@ tptp.power_power_int Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I4)) (@ (@ tptp.power_power_int Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ C2 I4)) (@ (@ tptp.power_power_int A2) I4)))) _let_1))))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (A2 tptp.real)) (exists ((B3 (-> tptp.nat tptp.real))) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real A2) I4)))) _let_1))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (let ((_let_2 (@ tptp.groups7501900531339628137nteger _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.complex)) (N tptp.nat) (B2 (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A2 I2) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B2 J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 I4)) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 J3)) (@ (@ tptp.power_power_complex X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 K3)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_complex X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.code_integer)) (N tptp.nat) (B2 (-> tptp.nat tptp.code_integer)) (X2 tptp.code_integer)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A2 I2) tptp.zero_z3403309356797280102nteger))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B2 J2) tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ (@ tptp.power_8256067586552552935nteger X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups7501900531339628137nteger (lambda ((J3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ B2 J3)) (@ (@ tptp.power_8256067586552552935nteger X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups7501900531339628137nteger (lambda ((R5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 K3)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_8256067586552552935nteger X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.rat)) (N tptp.nat) (B2 (-> tptp.nat tptp.rat)) (X2 tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A2 I2) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B2 J2) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ (@ tptp.power_power_rat X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 J3)) (@ (@ tptp.power_power_rat X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 K3)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_rat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.int)) (N tptp.nat) (B2 (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A2 I2) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B2 J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 I4)) (@ (@ tptp.power_power_int X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 J3)) (@ (@ tptp.power_power_int X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 K3)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_int X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.real)) (N tptp.nat) (B2 (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A2 I2) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B2 J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 J3)) (@ (@ tptp.power_power_real X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 K3)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_real X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.complex)) (= (forall ((X3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex X3) I4)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C2 tptp.zero_zero_nat) K) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C2 X3) tptp.zero_zero_complex)))))))
% 7.32/7.63 (assert (forall ((C2 (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.real)) (= (forall ((X3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real X3) I4)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C2 tptp.zero_zero_nat) K) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C2 X3) tptp.zero_zero_real)))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.nat)) (N tptp.nat) (B2 (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A2 I2) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B2 J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A2 I4)) (@ (@ tptp.power_power_nat X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B2 J3)) (@ (@ tptp.power_power_nat X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A2 K3)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y3)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y3)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X2)) (@ tptp.archim2898591450579166408c_real Y3))) 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)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y3)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y3)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X2)) (@ tptp.archimedean_frac_rat Y3))) 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)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.zero_zero_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.zero_zero_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.zero_zero_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.zero_zero_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.zero_zero_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.assn)) (H2 (-> tptp.nat tptp.assn))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_assn (= J3 K)) tptp.one_one_assn) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.one_one_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P6) (=> (@ (@ tptp.ord_less_eq_nat K) P6) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P6)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P6) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X2)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X2)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X2)))))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) M))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) M))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) M))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A2)) K3)) (@ (@ tptp.power_power_complex X2) K3))) (@ (@ tptp.power_power_complex Y3) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K3)) A2)) tptp.one_one_complex)) K3)) (@ (@ tptp.power_power_complex X2) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y3)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A2)) K3)) (@ (@ tptp.power_power_rat X2) K3))) (@ (@ tptp.power_power_rat Y3) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A2)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X2) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y3)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A2)) K3)) (@ (@ tptp.power_power_real X2) K3))) (@ (@ tptp.power_power_real Y3) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K3)) A2)) tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X2) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y3)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 I4)) (@ (@ tptp.power_power_complex X2) I4)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 I4)) (@ (@ tptp.power_power_complex Y3) I4)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y3)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y3) K3))) (@ (@ tptp.power_power_complex X2) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.code_integer)) (X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ (@ tptp.power_8256067586552552935nteger X2) I4)))) _let_1)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ (@ tptp.power_8256067586552552935nteger Y3) I4)))) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X2) Y3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((J3 tptp.nat)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_8256067586552552935nteger Y3) K3))) (@ (@ tptp.power_8256067586552552935nteger X2) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.rat)) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ (@ tptp.power_power_rat X2) I4)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ (@ tptp.power_power_rat Y3) I4)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y3) K3))) (@ (@ tptp.power_power_rat X2) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.int)) (X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 I4)) (@ (@ tptp.power_power_int X2) I4)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 I4)) (@ (@ tptp.power_power_int Y3) I4)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y3) K3))) (@ (@ tptp.power_power_int X2) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.real)) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ (@ tptp.power_power_real X2) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ (@ tptp.power_power_real Y3) I4)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y3) K3))) (@ (@ tptp.power_power_real X2) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((E tptp.real) (C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.real)) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z5))) (=> (@ (@ tptp.ord_less_eq_real M9) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C2 I4)) (@ (@ tptp.power_power_complex Z5) I4)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 7.32/7.63 (assert (forall ((E tptp.real) (C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.real)) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z5))) (=> (@ (@ tptp.ord_less_eq_real M9) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C2 I4)) (@ (@ tptp.power_power_real Z5) I4)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 I4)) (@ (@ tptp.power_power_complex X2) I4)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 I4)) (@ (@ tptp.power_power_complex Y3) I4)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y3)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 I4)) (@ (@ tptp.power_power_complex Y3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_complex X2) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.code_integer)) (X2 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ (@ tptp.power_8256067586552552935nteger X2) I4)))) _let_1)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ (@ tptp.power_8256067586552552935nteger Y3) I4)))) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X2) Y3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((J3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ (@ tptp.power_8256067586552552935nteger Y3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_8256067586552552935nteger X2) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.rat)) (X2 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ (@ tptp.power_power_rat X2) I4)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ (@ tptp.power_power_rat Y3) I4)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ (@ tptp.power_power_rat Y3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_rat X2) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.int)) (X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 I4)) (@ (@ tptp.power_power_int X2) I4)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 I4)) (@ (@ tptp.power_power_int Y3) I4)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A2 I4)) (@ (@ tptp.power_power_int Y3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_int X2) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.real)) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ (@ tptp.power_power_real X2) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ (@ tptp.power_power_real Y3) I4)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ (@ tptp.power_power_real Y3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I4) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_real X2) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I4))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I4))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I4))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I4))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 7.32/7.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 7.32/7.63 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 7.32/7.63 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A2) B2))))) (let ((_let_2 (@ tptp.suc A2))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B2)) (@ _let_1 A2)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A2) B2)) 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 A2) K3))) (@ (@ tptp.power_power_nat B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A2) B2)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_complex A2) K3))) (@ (@ tptp.power_power_complex B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) N) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_8256067586552552935nteger A2) K3))) (@ (@ tptp.power_8256067586552552935nteger B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A2) B2)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_rat A2) K3))) (@ (@ tptp.power_power_rat B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A2) B2)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_int A2) K3))) (@ (@ tptp.power_power_int B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A2) B2)) 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 A2) K3))) (@ (@ tptp.power_power_nat B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A2) B2)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_real A2) K3))) (@ (@ tptp.power_power_real B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N) I4))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat K) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))))))
% 7.32/7.63 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat K) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))))))
% 7.32/7.63 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat K) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A2) B2)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A2) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A2) B2)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A2) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A2) B2)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A2) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 7.32/7.63 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (A2 tptp.array_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (@ (@ (@ tptp.hoare_6478655245392655262rray_o (@ (@ tptp.snga_assn_o A2) Xs)) (@ (@ (@ tptp.array_upd_o I) X2) A2)) (lambda ((R5 tptp.array_o)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_o A2) (@ (@ (@ tptp.list_update_o Xs) I) X2))) (@ tptp.pure_assn (= R5 A2))))))))
% 7.32/7.63 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (A2 tptp.array_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (@ (@ (@ tptp.hoare_6807272225193264096ay_nat (@ (@ tptp.snga_assn_nat A2) Xs)) (@ (@ (@ tptp.array_upd_nat I) X2) A2)) (lambda ((R5 tptp.array_nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_nat A2) (@ (@ (@ tptp.list_update_nat Xs) I) X2))) (@ tptp.pure_assn (= R5 A2))))))))
% 7.32/7.63 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBTi) (A2 tptp.array_VEBT_VEBTi) (X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (@ (@ (@ tptp.hoare_3353465787467722821_VEBTi (@ (@ tptp.snga_assn_VEBT_VEBTi A2) Xs)) (@ (@ (@ tptp.array_upd_VEBT_VEBTi I) X2) A2)) (lambda ((R5 tptp.array_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi A2) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs) I) X2))) (@ tptp.pure_assn (= R5 A2))))))))
% 7.32/7.63 (assert (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A5) (@ tptp.semiri8010041392384452111omplex L3))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 7.32/7.63 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat L3))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 7.32/7.63 (assert (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A5) (@ tptp.semiri5074537144036343181t_real L3))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 7.32/7.63 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) N4)))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.ord_less_eq_real A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_eq_rat A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_int A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.ord_less_real A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))
% 7.32/7.63 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 7.32/7.63 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A2) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) (@ tptp.uminus_uminus_real B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A2) B2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ tptp.uminus1482373934393186551omplex B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.uminus_uminus_rat B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.plus_plus_int A2) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.plus_plus_real A2) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ (@ tptp.plus_plus_complex A2) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.plus_plus_rat A2) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) B2)) B2)))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A2)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A2)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A2)) B2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A2)) B2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A2)) B2) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.times_times_int A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A2)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.times_times_complex A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.times_3573771949741848930nteger A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.times_times_rat A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A2))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat (@ _let_1 B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.minus_minus_int B2) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A2) B2)) (@ (@ tptp.minus_minus_real B2) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A2) B2)) (@ (@ tptp.minus_minus_complex B2) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.minus_8373710615458151222nteger B2) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.minus_minus_rat B2) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.divide_divide_int A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.divide6298287555418463151nteger A2) B2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A2)) (@ _let_1 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A2)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A2)) (@ _let_1 tptp.zero_zero_rat)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ tptp.uminus_uminus_int A2)) (@ _let_1 tptp.zero_zero_int)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 7.32/7.63 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (= (= (@ (@ tptp.divide_divide_int A2) B2) (@ tptp.uminus_uminus_int A2)) (= B2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 7.32/7.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B2)))) (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) B2))))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) B2))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A2)) B2))) (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 B2) _let_1)))))))))
% 7.32/7.63 (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)))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 7.32/7.63 (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 ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 7.32/7.63 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B) N)) (@ (@ tptp.divide_divide_int A) N))))))
% 7.32/7.63 (assert (forall ((B2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.divide_divide_int _let_1) B2) _let_1)))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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 ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 7.32/7.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 7.32/7.63 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B2) (@ (@ tptp.minus_minus_int B2) tptp.one_one_int)))))
% 7.32/7.63 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A2) B2)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A2)) B2))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A2) B2) tptp.zero_zero_int))) (=> (not (= B2 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))))))))))
% 7.32/7.63 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B2)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B2)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A2) B2) tptp.zero_zero_int))) (=> (not (= B2 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)))))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 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 A2) B2) (@ (@ tptp.product_Pair_int_int Q3) R2)) (=> (not (= B2 tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A2)) B2) (@ (@ 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 B2) R2))))))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B9) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 7.32/7.63 (assert (forall ((K tptp.nat) (A2 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) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) _let_2)) (@ (@ tptp.times_times_int _let_1) _let_2))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) A2)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((A2 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 A2) _let_3))) (=> (@ (@ tptp.ord_less_int A2) (@ 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)))))))))
% 7.32/7.63 (assert (forall ((K tptp.nat) (A2 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)) A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) _let_2)) (@ (@ tptp.times_times_int _let_1) _let_2))) _let_3)))))))
% 7.32/7.63 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K3))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real A2)) tptp.zero_zero_real) (= X2 A2))))
% 7.32/7.63 (assert (forall ((B2 tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B2)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B2)))))
% 7.32/7.63 (assert (forall ((U tptp.real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X2) X2))))
% 7.32/7.63 (assert (= tptp.minus_minus_real (lambda ((X3 tptp.real) (Y tptp.real)) (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real Y)))))
% 7.32/7.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y3) (@ tptp.uminus_uminus_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X2)) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X2) Y3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.uminus_uminus_real X2)))))
% 7.32/7.63 (assert (forall ((U tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real (@ _let_1 X2)) Y3) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B2) (@ tptp.uminus_uminus_real Y3))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N)))))))
% 7.32/7.63 (assert (= tptp.cos_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ tptp.semiri2265585572941072030t_real N4))) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (= tptp.sin_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N4)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.sin_real X2))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.cos_real X2))))
% 7.32/7.63 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L3 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) (= L3 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L3) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 7.32/7.63 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 7.32/7.63 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X2) Y3)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) tptp.one_one_real)))
% 7.32/7.63 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) (@ tptp.sin_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X2))))
% 7.32/7.63 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 7.32/7.63 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 7.32/7.63 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 7.32/7.63 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.32/7.63 (assert (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y5) tptp.zero_zero_real)) (= Y5 X4))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.32/7.63 (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)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y3) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X2) Y3)) _let_1)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X2))) tptp.one_one_real))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_real T7) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X2)) (@ tptp.sin_real X2))))
% 7.32/7.63 (assert (forall ((Y3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 7.32/7.63 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))))
% 7.32/7.63 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.32/7.63 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 7.32/7.63 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 7.32/7.63 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.cos_real X2))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 7.32/7.63 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y3))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_2 Y3) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y3)) (@ _let_1 X2))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (=> (= (@ tptp.cos_real X2) (@ tptp.cos_real Y3)) (= X2 Y3)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real Y3) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y3)) (@ tptp.cos_real X2)))))))
% 7.32/7.63 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 7.32/7.63 (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)))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (=> (@ (@ tptp.ord_less_real Y3) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y3)) (@ tptp.cos_real X2)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.cos_real X4) Y3) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.cos_real Y5) Y3)) (= Y5 X4)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (exists ((Y4 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.sin_real Y4) (@ tptp.sin_real X2)) (= (@ tptp.cos_real Y4) (@ tptp.cos_real X2))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (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))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y3)) (@ tptp.sin_real X2))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y3)) (@ _let_1 Y3)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) _let_1) (=> (= (@ tptp.sin_real X2) (@ tptp.sin_real Y3)) (= X2 Y3))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (exists ((X3 tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y3) (=> (@ (@ tptp.ord_less_real Y3) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y3)) (@ tptp.sin_real X2))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.sin_real X4) Y3) (forall ((Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y5) (@ (@ tptp.ord_less_eq_real Y5) _let_1) (= (@ tptp.sin_real Y5) Y3)) (= Y5 X4)))))))))))
% 7.32/7.63 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (or (exists ((X3 tptp.nat)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X3 tptp.nat)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) tptp.pi) (= X2 (@ tptp.cos_real T7)) (= Y3 (@ tptp.sin_real T7)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X2 (@ tptp.cos_real T7)) (= Y3 (@ tptp.sin_real T7)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X2 (@ tptp.cos_real T7)) (= Y3 (@ tptp.sin_real T7))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (not (forall ((T7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (=> (@ (@ tptp.ord_less_real T7) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X2 (@ tptp.cos_real T7)) (not (= Y3 (@ tptp.sin_real T7))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T7 tptp.real)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_real T7) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T7) (@ (@ tptp.ord_less_real T7) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T7) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.32/7.63 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.tan_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) (@ tptp.abs_abs_real X2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B2) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y5))) D4) (and (@ (@ tptp.ord_less_real A2) Y5) (@ (@ tptp.ord_less_real Y5) B2))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X2))) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X2 Y3) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) U)) Y3))) V)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X2))) tptp.one_one_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (exists ((Z2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X2)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B2) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y5))) D4) (and (@ (@ tptp.ord_less_eq_real A2) Y5) (@ (@ tptp.ord_less_eq_real Y5) B2))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 7.32/7.63 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y3))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y3))))) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y3) (@ tptp.tan_real X4)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y3) (forall ((Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y5) (@ (@ tptp.ord_less_real Y5) _let_1) (= (@ tptp.tan_real Y5) Y3)) (= Y5 X4)))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y3) (=> (@ (@ tptp.ord_less_real Y3) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y3)) (@ tptp.tan_real X2))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y3))) (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 Y3) (=> (@ _let_1 _let_2) (=> (@ _let_3 X2) (=> (@ (@ tptp.ord_less_real X2) _let_2) (= (@ _let_1 X2) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y3)) (@ tptp.tan_real X2))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y3) (=> (@ (@ tptp.ord_less_real Y3) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y3)) (@ _let_1 Y3)))))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y3))))))
% 7.32/7.63 (assert (= (@ tptp.tan_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y3)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y3)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X4) Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (=> (@ (@ tptp.ord_less_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y3))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_less_real Y3) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arctan X2) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X2) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ tptp.suc N4))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 7.32/7.63 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (= (@ tptp.ln_ln_real X2) tptp.zero_zero_real) (= X2 tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (= (@ _let_1 (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4)))) (@ tptp.summable_real F))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) (@ tptp.arctan Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) (@ tptp.arctan Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M6 tptp.int)) (exists ((N4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N4)) (@ (@ tptp.member_int N4) S)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X2)) (=> (@ _let_1 X2) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N10 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N10) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X2) Y3)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y3))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (= (@ tptp.ln_ln_real X2) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (= X2 tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X2) Y3)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y3))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y3))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) Y3)) Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B2)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A2) B2))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B2) A2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A2) B2))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2))) (@ tptp.uminus_uminus_real X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A2)) A2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X2)) A2)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A2) A2)) X2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (not (= A2 tptp.one_one_real)) (=> (@ _let_1 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A2) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B2)) (@ tptp.ln_ln_real A2))) (@ (@ tptp.log B2) X2)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X2))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I2)) tptp.one_one_real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z) I4))))))))))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_nat I2) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K)))))))))
% 7.32/7.63 (assert (forall ((D2 tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 7.32/7.63 (assert (forall ((D2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D2))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K))))))))
% 7.32/7.63 (assert (forall ((Y3 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 Y3))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y3))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arctan Y3))) (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) Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X2)) X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (= (@ tptp.tan_real X2) Y3) (= (@ tptp.arctan Y3) X2)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X2)) (@ tptp.arctan Y3)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y3)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D4))) (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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X2) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 7.32/7.63 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real X2) _let_1) _let_1)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X2) Y3))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y3))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y3) Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y3) (@ (@ tptp.ord_less_real X2) (@ tptp.sqrt Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y3) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y3) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (= (@ tptp.sqrt X2) Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y3)))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) Y3) (= X2 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) X2) (= Y3 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (C2 tptp.real) (B2 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 A2) C2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B2) D2)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A2) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C2) _let_1)) (@ (@ tptp.power_power_real D2) _let_1))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y3))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ tptp.sqrt _let_1))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))) (@ (@ tptp.plus_plus_real X2) Y3))))))))
% 7.32/7.63 (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)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y3))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.sqrt X2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) N) (@ (@ tptp.power_power_real X2) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y3))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X2)))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))) tptp.one_one_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (U tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y3)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2)))) U))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.arcosh_real X2) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (U tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X2) _let_4) (=> (@ (@ tptp.ord_less_real Y3) _let_4) (=> (@ _let_3 X2) (=> (@ _let_3 Y3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2)))) U)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 7.32/7.63 (assert (= tptp.arctan (lambda ((X3 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 X3) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 7.32/7.63 (assert (= tptp.arsinh_real (lambda ((X3 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 7.32/7.63 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (=> (@ (@ tptp.ord_less_real T7) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T7)) (@ tptp.sin_real T7)))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ F N4)))) (@ tptp.summable_real F))))
% 7.32/7.63 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A2) B2)) (@ (@ tptp.complex2 C2) D2)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A2) C2)) (@ (@ tptp.minus_minus_real B2) D2)))))
% 7.32/7.63 (assert (forall ((R2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X2) Y3)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X2)) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X2) Y3)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X2) R2)) Y3))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A2) B2)) (@ (@ tptp.complex2 C2) D2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A2) C2)) (@ (@ tptp.plus_plus_real B2) D2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A2) B2)) (@ (@ tptp.complex2 C2) D2)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C2)) (@ _let_1 D2))) (@ (@ tptp.plus_plus_real (@ _let_2 D2)) (@ _let_1 C2))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.complex2 A2) B2) tptp.one_one_complex) (and (= A2 tptp.one_one_real) (= B2 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.complex2 A2) B2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A2 (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B2 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X2) Y3)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T7 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T7))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y3)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real X2) tptp.one_one_real) (= X2 tptp.zero_zero_real))))
% 7.32/7.63 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y3)) Y3)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y3)) Y3)))))
% 7.32/7.63 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (= (@ tptp.arcsin (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2))))
% 7.32/7.63 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y3)) (@ tptp.arccos X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real)) (= (= (@ tptp.arccos X2) (@ tptp.arccos Y3)) (= X2 Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X2)) (@ tptp.arccos Y3)) (@ (@ tptp.ord_less_eq_real Y3) X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (= (@ tptp.arcsin X2) (@ tptp.arcsin Y3)) (= X2 Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y3) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real Y3) tptp.one_one_real)) (= (@ tptp.exp_real X4) Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y3)) X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y3)) Y3)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y3)) (@ tptp.arccos X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X2)) (@ tptp.arccos Y3)) (@ (@ tptp.ord_less_real Y3) X2))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y3)) tptp.pi)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X2)) X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y3)) (@ (@ tptp.ord_less_real X2) Y3))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y3)) Y3))))
% 7.32/7.63 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arccos Y3))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_real Y3) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arccos Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X2)) tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (= (@ tptp.arccos (@ tptp.cos_real X2)) (@ tptp.uminus_uminus_real X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X2)) tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arccos Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X2))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y3))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_real Y3) 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))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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 Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X2)) X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 X2) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X2)))))))
% 7.32/7.63 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.log _let_1) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y3))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y3) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y3)) X2))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) Y3) (@ _let_1 (@ tptp.sin_real Y3)))))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3)))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y3))) (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)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3))))))))
% 7.32/7.63 (assert (forall ((Theta tptp.real)) (not (forall ((K2 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X2)) N)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X2)) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X2))))
% 7.32/7.63 (assert (forall ((Y3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y3)) A2) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y3) A2))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D4 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D4) E2) (=> (@ P D4) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real _let_1) X2) (@ tptp.inverse_inverse_real _let_1))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A2) (=> (not (= A2 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.cot_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y3))) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y3)) (@ _let_1 X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y3)) (@ (@ tptp.ord_less_real Y3) X2))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y3)) (@ (@ tptp.ord_less_real X2) Y3)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.arcosh_real (@ tptp.cosh_real X2)) X2))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A2) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A2) B2)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A2) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B2)) _let_2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 7.32/7.63 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 7.32/7.63 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.32/7.63 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.32/7.63 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.32/7.63 (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))
% 7.32/7.63 (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))
% 7.32/7.63 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.32/7.63 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 7.32/7.63 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (= (@ (@ tptp.complex2 X2) Y3) tptp.imaginary_unit) (and (= X2 tptp.zero_zero_real) (= Y3 tptp.one_one_real)))))
% 7.32/7.63 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 7.32/7.63 (assert (= tptp.complex2 (lambda ((A5 tptp.real) (B6 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A5)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B6))))))
% 7.32/7.63 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A3))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A3)))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A2))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A2))))) tptp.one_one_real)))
% 7.32/7.63 (assert (forall ((R2 tptp.real) (A2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A2))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A2)))))) (@ tptp.abs_abs_real R2))))
% 7.32/7.63 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 7.32/7.63 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 7.32/7.63 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X2)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X2))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A2)) tptp.one_one_real)))
% 7.32/7.63 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 7.32/7.63 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 7.32/7.63 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 7.32/7.63 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 7.32/7.63 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A2)) (@ tptp.cis B2)) (@ tptp.cis (@ (@ tptp.plus_plus_real A2) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A2)) (@ tptp.cis B2)) (@ tptp.cis (@ (@ tptp.minus_minus_real A2) B2)))))
% 7.32/7.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Xa tptp.num) (Y3 tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y3 tptp.one))))) (let ((_let_3 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa) Y3) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y3 (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _let_1) (not (= Y3 _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y3 (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit1 M5)) (not (= Y3 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit1 M5)) (not (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))))))))))))))))))
% 7.32/7.63 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X2)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X2)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (= tptp.nat_set_decode (lambda ((X3 tptp.nat)) (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat _let_1) N4))))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 7.32/7.63 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L3 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 L3))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))
% 7.32/7.63 (assert (forall ((C2 tptp.complex) (N tptp.nat)) (=> (not (= C2 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 C2)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C2)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Xa tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X2)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa) Y3) (and (=> _let_5 (= Y3 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y3 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 7.32/7.63 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 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 L3)))))) (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 L3) _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 L3) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X2) (@ _let_1 Y3)) (= X2 Y3))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_real X2) Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_real X2) Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.one_one_real) (= X2 tptp.one_one_real)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X2) (@ (@ tptp.root M) (@ (@ tptp.root N) X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y3)) Z)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y3) Ya)) Z)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y3)) Y3))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y3)) X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X2) Y3))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y3)) (@ (@ tptp.bit_se1409905431419307370or_int X2) Y3)) (@ (@ tptp.plus_plus_int X2) Y3))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y3)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y3)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ _let_1 X2)) K))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ _let_1 X2)))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((Y3 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y3) Ya)) Z)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y3)) Z)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (N7 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N7) X2)) (@ (@ tptp.root N) X2)))))))
% 7.32/7.63 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y3) N))) (@ tptp.abs_abs_real Y3)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X2))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (N7 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N7) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N7) X2))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (N7 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N7) X2)) (@ (@ tptp.root N) X2)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y3) N) X2) (= (@ (@ tptp.root N) X2) Y3)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (= (@ (@ tptp.power_power_real Y3) N) X2) (= (@ (@ tptp.root N) X2) Y3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (N7 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N7) X2))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (A2 tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ _let_1 (@ (@ tptp.root N) A2)) (@ (@ tptp.divide_divide_real (@ _let_1 A2)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (B2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ (@ tptp.log (@ (@ tptp.root N) B2)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B2) X2)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B2)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 7.32/7.63 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 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 L3))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) X2) (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.32/7.63 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 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) (= L3 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L3) (@ (@ (@ tptp.if_int (= L3 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Xa tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa) Y3) (=> _let_1 (not (=> (and (=> _let_6 (= Y3 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y3 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc (@ tptp.suc X2))) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc X2)) (@ P (@ tptp.suc I4))))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) tptp.zero_zero_nat)))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 7.32/7.63 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) tptp.one_one_nat)))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool)) (I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) tptp.zero_zero_nat) (@ P I5))))
% 7.32/7.63 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 7.32/7.63 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 7.32/7.63 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K2 tptp.int) (L2 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) L2)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L2) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))) (@ (@ P K2) L2)))))) (@ (@ P A0) A12)))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc X2)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) X2) (@ P (@ tptp.suc I4))))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc tptp.zero_zero_nat)) (@ P I4))) (@ P tptp.zero_zero_nat))))
% 7.32/7.63 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I2 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)) (@ (@ P I2) J2)))) (@ (@ P A0) A12)))))
% 7.32/7.63 (assert (= tptp.size_size_uint32 (lambda ((P4 tptp.uint32)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))
% 7.32/7.63 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 7.32/7.63 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X4 tptp.num)) (=> (@ P X4) (@ P (@ tptp.inc X4)))) (@ P X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X2))) (= (@ _let_1 (@ tptp.inc Y3)) (@ tptp.inc (@ _let_1 Y3))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X2)) (@ tptp.bit0 (@ tptp.inc X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X2)) (@ tptp.bit1 X2))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.plus_plus_num X2) tptp.one) (@ tptp.inc X2))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X2))) (= (@ _let_1 (@ tptp.inc Y3)) (@ (@ tptp.plus_plus_num (@ _let_1 Y3)) X2)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L3))) (@ (@ (@ 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))))
% 7.32/7.63 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N4)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 7.32/7.63 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L3))) (@ (@ (@ 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))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (= tptp.unique4921790084139445826nteger (lambda ((L3 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L3))) (@ (@ (@ 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))))
% 7.32/7.63 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N4 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N4))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q5)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N4)) N4))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 7.32/7.63 (assert (= tptp.one_one_int tptp.one_one_int))
% 7.32/7.63 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.32/7.63 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_int))))
% 7.32/7.63 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))
% 7.32/7.63 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N4)) (@ (@ tptp.modulo_modulo_nat M6) N4)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 7.32/7.63 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)))
% 7.32/7.63 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 7.32/7.63 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L) (@ tptp.uminus1351360451143612070nteger L))))
% 7.32/7.63 (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))))))))))
% 7.32/7.63 (assert (= tptp.int_ge_less_than (lambda ((D3 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D3) Z8) (@ (@ tptp.ord_less_int Z8) Z4))))))))
% 7.32/7.63 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 7.32/7.63 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_eq_int Xa) X2))))
% 7.32/7.63 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa) X2)))))
% 7.32/7.63 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa) X2)))))
% 7.32/7.63 (assert (= tptp.int_ge_less_than2 (lambda ((D3 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D3) Z4) (@ (@ tptp.ord_less_int Z8) Z4))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 (@ 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))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ 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))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V3352910403632780892pi_rel))) (let ((_let_3 (= Y3 tptp.one_one_int))) (=> (= (@ tptp.vEBT_V9176841429113362141ildupi X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat N3) _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_int _let_2))) (let ((_let_6 (@ (@ tptp.power_power_int _let_5) _let_4))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.vEBT_V9176841429113362141ildupi _let_7))) (let ((_let_9 (@ (@ tptp.times_times_int _let_8) _let_6))) (let ((_let_10 (@ tptp.bit0 _let_2))) (let ((_let_11 (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_10)))) (let ((_let_12 (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))) (let ((_let_13 (@ (@ tptp.dvd_dvd_nat _let_3) N3))) (=> (= X2 _let_1) (=> (and (=> _let_13 (= Y3 (@ _let_12 (@ (@ tptp.plus_plus_int _let_8) (@ (@ tptp.plus_plus_int (@ _let_11 _let_6)) (@ (@ tptp.times_times_int _let_5) _let_9)))))) (=> (not _let_13) (= Y3 (@ _let_12 (@ (@ tptp.plus_plus_int (@ tptp.vEBT_V9176841429113362141ildupi (@ tptp.suc _let_7))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 _let_10))) _let_6)) (@ _let_11 _let_9))))))) (not (@ (@ tptp.accp_nat tptp.vEBT_V3352910403632780892pi_rel) _let_1))))))))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 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 (= Y3 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X2 _let_1) (=> (and (=> _let_8 (= Y3 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y3 (@ (@ _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)))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 (@ 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))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ 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))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 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 (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (=> (= (@ tptp.vEBT_V8646137997579335489_i_l_d X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.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))) (=> (= X2 _let_1) (=> (and (=> _let_8 (= Y3 (@ (@ 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) (= Y3 (@ (@ 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)))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 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 (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (=> (= (@ tptp.vEBT_V8346862874174094_d_u_p X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.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))) (=> (= X2 _let_1) (=> (and (=> _let_9 (= Y3 (@ (@ 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) (= Y3 (@ (@ 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))))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_VEBT_Tb_rel2))) (let ((_let_3 (= Y3 (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))) (=> (= (@ tptp.vEBT_VEBT_Tb X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ tptp.suc (@ (@ tptp.divide_divide_nat N3) _let_3)))) (let ((_let_5 (@ tptp.suc _let_4))) (let ((_let_6 (@ tptp.power_power_int (@ tptp.numeral_numeral_int _let_2)))) (let ((_let_7 (@ tptp.vEBT_VEBT_Tb _let_4))) (let ((_let_8 (@ tptp.times_times_int _let_7))) (let ((_let_9 (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 _let_2))))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_3) N3))) (=> (= X2 _let_1) (=> (and (=> _let_10 (= Y3 (@ (@ tptp.plus_plus_int (@ _let_9 _let_7)) (@ _let_8 (@ _let_6 _let_4))))) (=> (not _let_10) (= Y3 (@ (@ tptp.plus_plus_int (@ _let_9 (@ tptp.vEBT_VEBT_Tb _let_5))) (@ _let_8 (@ _let_6 _let_5)))))) (not (@ (@ tptp.accp_nat tptp.vEBT_VEBT_Tb_rel2) _let_1)))))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_VEBT_Tb_rel))) (let ((_let_3 (= Y3 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (=> (= (@ tptp.vEBT_VEBT_Tb2 X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ tptp.suc (@ (@ tptp.divide_divide_nat N3) _let_3)))) (let ((_let_5 (@ tptp.suc _let_4))) (let ((_let_6 (@ tptp.power_power_nat _let_3))) (let ((_let_7 (@ tptp.vEBT_VEBT_Tb2 _let_4))) (let ((_let_8 (@ tptp.times_times_nat _let_7))) (let ((_let_9 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_2))))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_3) N3))) (=> (= X2 _let_1) (=> (and (=> _let_10 (= Y3 (@ (@ tptp.plus_plus_nat (@ _let_9 _let_7)) (@ _let_8 (@ _let_6 _let_4))))) (=> (not _let_10) (= Y3 (@ (@ tptp.plus_plus_nat (@ _let_9 (@ tptp.vEBT_VEBT_Tb2 _let_5))) (@ _let_8 (@ _let_6 _let_5)))))) (not (@ (@ tptp.accp_nat tptp.vEBT_VEBT_Tb_rel) _let_1)))))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel2) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 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))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ 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))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V2957053500504383685pi_rel))) (let ((_let_3 (= Y3 _let_1))) (=> (= (@ tptp.vEBT_V441764108873111860ildupi X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat N3) _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) N3))) (=> (= X2 _let_1) (=> (and (=> _let_11 (= Y3 (@ 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) (= Y3 (@ 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))))))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_cnt2 X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 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))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ 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))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBTi) (Y3 tptp.heap_T2636463487746394924on_nat)) (=> (= (@ tptp.vEBT_vebt_minti X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_minti_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi A3) B3))) (=> (= X2 _let_1) (=> (and (=> A3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.zero_zero_nat)))) (=> (not A3) (and (=> B3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.one_one_nat)))) (=> (not B3) (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)))))) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_minti_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.array_VEBT_VEBTi) (Uw2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_minti_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.array_VEBT_VEBTi) (Uz2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat Mi2))) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_minti_rel) _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBTi) (Y3 tptp.heap_T2636463487746394924on_nat)) (=> (= (@ tptp.vEBT_vebt_maxti X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_maxti_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi A3) B3))) (=> (= X2 _let_1) (=> (and (=> B3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.one_one_nat)))) (=> (not B3) (and (=> A3 (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat tptp.zero_zero_nat)))) (=> (not A3) (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)))))) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_maxti_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.array_VEBT_VEBTi) (Uw2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_T3487192422709364219on_nat tptp.none_nat)) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_maxti_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.array_VEBT_VEBTi) (Uz2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_T3487192422709364219on_nat (@ tptp.some_nat Ma2))) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_vebt_maxti_rel) _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y3 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (and (=> A3 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y3 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_T_m_i_n_t X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y3 (@ _let_2 (@ (@ (@ tptp.if_nat A3) tptp.zero_zero_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_T_m_a_x_t X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y3 (@ _let_2 (@ (@ (@ tptp.if_nat B3) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBTi) (Y3 tptp.heap_Time_Heap_o)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBTi tptp.vEBT_V5740978063120863272li_rel))) (=> (= (@ tptp.vEBT_VEBT_minNulli X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_Time_return_o true)) (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi true) Uv2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_Time_return_o false)) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_V5740978063120863272li_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi Uu2) true))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_Time_return_o false)) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_V5740978063120863272li_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.array_VEBT_VEBTi) (Uy2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_Time_return_o true)) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_V5740978063120863272li_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.array_VEBT_VEBTi) (Vc2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.heap_Time_return_o false)) (not (@ (@ tptp.accp_VEBT_VEBTi tptp.vEBT_V5740978063120863272li_rel) _let_1)))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y3 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Xa tptp.num) (Y3 tptp.num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa) Y3) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y3 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bit1 M5)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X2 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X2 _let_1) (=> (= Xa tptp.one) (=> (= Y3 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y3) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> Y3 (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> Y3 (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 7.32/7.63 (assert (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((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))))))))
% 7.32/7.63 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L3))) (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 L3))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L3 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 L3) K3))))) _let_2)))))))))))
% 7.32/7.63 (assert (= tptp.ln_ln_real (lambda ((X3 tptp.real)) (@ tptp.the_real (lambda ((U2 tptp.real)) (= (@ tptp.exp_real U2) X3))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X2) (@ tptp.the_real (lambda ((X3 tptp.real)) false))))))
% 7.32/7.63 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.32/7.63 (assert (= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))))
% 7.32/7.63 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A32) (=> (=> (= A23 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q4 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q4) A23)))))) (not (forall ((R3 tptp.int) (Q4 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q4) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) A23)) R3)))))))))))))
% 7.32/7.63 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L3 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A1 K3) (= A22 L3) (= A33 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (not (= L3 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q5) L3)))) (exists ((R5 tptp.int) (L3 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A1 K3) (= A22 L3) (= A33 (@ (@ tptp.product_Pair_int_int Q5) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L3)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L3)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L3)) R5))))))))
% 7.32/7.63 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((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))))))
% 7.32/7.63 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((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)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X2) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 7.32/7.63 (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)))))))))))))))))))
% 7.32/7.63 (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)))))))))))))))))
% 7.32/7.63 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L3))))) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L3))) (@ 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 L3) K3))))))))))))
% 7.32/7.63 (assert (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((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))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X2)) (@ _let_1 X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X2)) (@ tptp.sgn_sgn_real X2)))))
% 7.32/7.63 (assert (= tptp.sgn_sgn_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (= A5 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A5)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (N tptp.nat) (X2 tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A2)) N)) X2) (=> (= X2 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B2)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B2))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X2)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N))) Y3))))
% 7.32/7.63 (assert (forall ((Z tptp.complex) (X2 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X2)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arg Z) X2))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X2 tptp.real)) (= (@ P (@ (@ tptp.root N) X2)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)) X2) (@ P Y))))))))
% 7.32/7.63 (assert (= tptp.archim6058952711729229775r_real (lambda ((X3 tptp.real)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X2))))))
% 7.32/7.63 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((K tptp.int)) (not (forall ((N3 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 N3) M3) (= (@ _let_1 M3) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 7.32/7.63 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 7.32/7.63 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N4)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 7.32/7.63 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X3 tptp.rat)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 7.32/7.63 (assert (= tptp.root (lambda ((N4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N4)))) X3)))))
% 7.32/7.63 (assert (= tptp.arg (lambda ((Z4 tptp.complex)) (@ (@ (@ tptp.if_real (= Z4 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A5 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z4) (@ tptp.cis A5)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A5) (@ (@ tptp.ord_less_eq_real A5) tptp.pi))))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (assert (= tptp.sgn_sgn_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (= A5 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A5)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 7.32/7.63 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y) (= X3 Y)))))
% 7.32/7.63 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T7) (not (= R2 (@ (@ tptp.plus_plus_rat S3) T7)))))))))))
% 7.32/7.63 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 7.32/7.63 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 7.32/7.63 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.32/7.63 (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)))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 7.32/7.63 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((I4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger I4)) tptp.one_one_Code_integer))))
% 7.32/7.63 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L3 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 L3)) (@ (@ (@ tptp.if_int (= L3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L3) (@ (@ (@ tptp.if_int (= L3 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 L3) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X2) Y3)))))))
% 7.32/7.63 (assert (= tptp.minus_minus_rat (lambda ((Q5 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q5) (@ tptp.uminus_uminus_rat R5)))))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y3) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y3)) _let_1)))))))
% 7.32/7.63 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L3 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 L3)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))
% 7.32/7.63 (assert (forall ((Xa tptp.int) (X2 Bool)) (= (@ (@ tptp.bits_Bit_integer (@ tptp.code_integer_of_int Xa)) X2) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int X2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Xa))))))
% 7.32/7.63 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))))
% 7.32/7.63 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3)))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 7.32/7.63 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 7.32/7.63 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N4)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.32/7.63 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= (@ tptp.code_dup tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 7.32/7.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.pow X2) tptp.one) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.int)) (= (@ tptp.code_dup (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int X2) X2)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (B6 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A5 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A5)) B6)) (@ tptp.abs_abs_int A5))))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (forall ((S2 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 S2) M) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Listy)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= M (@ tptp.suc N)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Listy)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height X4)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))) (=> (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height S2)) _let_1) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT S2) (@ tptp.set_VEBT_VEBT2 Listy))))) _let_1)))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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)))))))))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (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))))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D3) N)))) N))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 7.32/7.63 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y3) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= Y3 tptp.zero_zero_nat))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2)) (not (= Y3 (@ (@ 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))))))))))))))
% 7.32/7.63 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M6))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A5)) __flatten_var_0))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A5)) __flatten_var_0))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (= tptp.ord_less_rat (lambda ((P4 tptp.rat) (Q5 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B6 tptp.int) (D3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A5) D3)) (@ (@ tptp.times_times_int C4) B6)))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P4)))))
% 7.32/7.63 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P4 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P4)))))
% 7.32/7.63 (assert (= tptp.ord_less_eq_rat (lambda ((P4 tptp.rat) (Q5 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B6 tptp.int) (D3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A5) D3)) (@ (@ tptp.times_times_int C4) B6)))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P4)))))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) X2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X2 _let_1) (=> (= Y3 tptp.zero_zero_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1)))))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ 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))))))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A2)) (@ (@ tptp.product_Pair_int_int A2) tptp.one_one_int))))
% 7.32/7.63 (assert (forall ((M8 tptp.set_nat) (N7 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M8) N7) (= (@ (@ tptp.image_nat_nat tptp.suc) M8) N7))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D3 tptp.int)) (@ (@ tptp.dvd_dvd_int D3) N)))) (@ tptp.abs_abs_int N)))))
% 7.32/7.63 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A)))))
% 7.32/7.63 (assert (= tptp.finite_finite_int (lambda ((S8 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S8)) (@ tptp.set_ord_lessThan_int K3))))))
% 7.32/7.63 (assert (= tptp.finite_finite_int (lambda ((S8 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S8)) (@ tptp.set_ord_atMost_int K3))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.32/7.63 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 7.32/7.63 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((X3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger X3) L))) (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger U) L))) (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((C2 tptp.nat) (Y3 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X2) Y3))) (let ((_let_2 (@ (@ tptp.ord_less_nat X2) Y3))) (let ((_let_3 (@ (@ tptp.ord_less_nat C2) Y3))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C2))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C2)) (@ (@ tptp.minus_minus_nat Y3) C2)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C2))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C2))) _let_1) tptp.bot_bot_set_nat))))))))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P6) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A5) D3)) (@ (@ tptp.times_times_int B6) C4))) (@ (@ tptp.times_times_int C4) D3))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P6) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A5) D3)) (@ (@ tptp.times_times_int B6) C4))) (@ (@ tptp.times_times_int C4) D3))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (forall ((P6 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P6) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) B6)) (@ (@ tptp.times_times_int C4) D3))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (forall ((P6 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P6) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) D3)) (@ (@ tptp.times_times_int C4) B6))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P6)))))
% 7.32/7.63 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X2 tptp.int)) (= (@ tptp.bits_b2549910563261871055nteger (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int X2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 7.32/7.63 (assert (= tptp.bits_b2549910563261871055nteger (lambda ((I4 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger I4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (assert (= tptp.bit_se3222712562003087583nteger (lambda ((X3 tptp.code_integer) (Y tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X3 tptp.zero_z3403309356797280102nteger)) Y) (@ (@ (@ tptp.if_Code_integer (= X3 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (@ tptp.bit_ri7632146776885996613nteger Y)) (@ (@ tptp.bits_Bit_integer (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bits_b2549910563261871055nteger X3)) (@ tptp.bits_b2549910563261871055nteger Y))) (= (not (@ tptp.bits_b8758750999018896077nteger X3)) (@ tptp.bits_b8758750999018896077nteger Y))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.32/7.63 (assert (forall ((I tptp.code_integer)) (= (@ tptp.zero_n356916108424825756nteger (@ tptp.bits_b8758750999018896077nteger I)) (@ (@ tptp.bit_se3949692690581998587nteger I) tptp.one_one_Code_integer))))
% 7.32/7.63 (assert (= tptp.bit_se3928097537394005634nteger (lambda ((N4 tptp.nat) (X3 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger X3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (assert (= tptp.bits_b8758750999018896077nteger (lambda ((I4 tptp.code_integer)) (not (= (@ (@ tptp.bit_se3949692690581998587nteger I4) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (assert (= tptp.bits_b8758750999018896077nteger (lambda ((I4 tptp.code_integer)) (not (= (@ (@ tptp.modulo364778990260209775nteger I4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))))
% 7.32/7.63 (assert (forall ((X2 tptp.int)) (= (@ tptp.bits_b8758750999018896077nteger (@ tptp.code_integer_of_int X2)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) X2)))))
% 7.32/7.63 (assert (= tptp.bit_se1080825931792720795nteger (lambda ((X3 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (@ (@ (@ tptp.if_Code_integer (= X3 tptp.zero_z3403309356797280102nteger)) Y) (@ (@ (@ tptp.if_Code_integer (= X3 _let_1)) _let_1) (@ (@ tptp.bits_Bit_integer (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.bits_b2549910563261871055nteger X3)) (@ tptp.bits_b2549910563261871055nteger Y))) (or (@ tptp.bits_b8758750999018896077nteger X3) (@ tptp.bits_b8758750999018896077nteger Y)))))))))
% 7.32/7.63 (assert (= tptp.bit_se3949692690581998587nteger (lambda ((X3 tptp.code_integer) (Y tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= X3 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) Y) (@ (@ tptp.bits_Bit_integer (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.bits_b2549910563261871055nteger X3)) (@ tptp.bits_b2549910563261871055nteger Y))) (and (@ tptp.bits_b8758750999018896077nteger X3) (@ tptp.bits_b8758750999018896077nteger Y))))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 7.32/7.63 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 7.32/7.63 (assert (forall ((I tptp.code_integer)) (= (@ (@ tptp.bits_Bit_integer I) false) (@ (@ tptp.bit_se7788150548672797655nteger tptp.one_one_nat) I))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 7.32/7.63 (assert (= tptp.bit_se7788150548672797655nteger (lambda ((N4 tptp.nat) (X3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger X3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 7.32/7.63 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.generi2397576812484419408nteger (lambda ((X3 tptp.code_integer) (I4 tptp.nat) (B6 Bool)) (let ((_let_1 (@ (@ tptp.bit_se7788150548672797655nteger I4) tptp.one_one_Code_integer))) (@ (@ (@ tptp.if_Code_integer B6) (@ (@ tptp.bit_se1080825931792720795nteger X3) _let_1)) (@ (@ tptp.bit_se3949692690581998587nteger X3) (@ tptp.bit_ri7632146776885996613nteger _let_1)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (= tptp.generi8991105624351003935it_int (lambda ((I4 tptp.int) (N4 tptp.nat) (B6 Bool)) (let ((_let_1 (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))) (@ (@ (@ tptp.if_int B6) (@ (@ tptp.bit_se1409905431419307370or_int I4) _let_1)) (@ (@ tptp.bit_se725231765392027082nd_int I4) (@ tptp.bit_ri7919022796975470100ot_int _let_1)))))))
% 7.32/7.63 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (= tptp.bit_concat_bit (lambda ((N4 tptp.nat) (K3 tptp.int) (L3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N4) K3)) (@ (@ tptp.bit_se545348938243370406it_int N4) L3)))))
% 7.32/7.63 (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)))))))
% 7.32/7.63 (assert (@ tptp.least_4859182151741483524sb_int tptp.one_one_int))
% 7.32/7.63 (assert (forall ((W tptp.num)) (not (@ tptp.least_4859182151741483524sb_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))))))
% 7.32/7.63 (assert (@ tptp.least_4859182151741483524sb_int (@ tptp.numeral_numeral_int tptp.one)))
% 7.32/7.63 (assert (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 7.32/7.63 (assert (forall ((W tptp.num)) (not (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))))))
% 7.32/7.63 (assert (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))))
% 7.32/7.63 (assert (= (lambda ((A5 tptp.int)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5))) tptp.least_4859182151741483524sb_int))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M10 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M6) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M6)) (@ X7 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (= (@ (@ tptp.signed6714573509424544716de_int A2) B2) (@ tptp.uminus_uminus_int A2)) (= B2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int A2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A2))))
% 7.32/7.63 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int A2) tptp.one_one_int) A2)))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (= (@ (@ tptp.signed6714573509424544716de_int A2) B2) A2) (= B2 tptp.one_one_int)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((P tptp.assn) (Q tptp.assn) (F3 tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) F3) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) F3)))))
% 7.32/7.63 (assert (= tptp.fI_QUERY (lambda ((P3 tptp.assn) (Q7 tptp.assn) (F8 tptp.assn)) (@ (@ tptp.entails P3) (@ (@ tptp.times_times_assn Q7) F8)))))
% 7.32/7.63 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.one_one_assn) (@ (@ tptp.entails P) Q))))
% 7.32/7.63 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B2))) (=> (not (= B2 tptp.zero_zero_int)) (@ (@ tptp.member_int (@ (@ tptp.signed6292675348222524329lo_int A2) B2)) (@ (@ 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)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.signed6292675348222524329lo_int A2) B2)) B2)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 (@ (@ tptp.signed6292675348222524329lo_int A2) B2)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.signed6292675348222524329lo_int A2) B2)) tptp.zero_zero_int)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.signed6292675348222524329lo_int A2) B2)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.signed6292675348222524329lo_int A2) B2)) tptp.zero_zero_int)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.signed6292675348222524329lo_int A2) B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (= (@ (@ tptp.signed6292675348222524329lo_int A2) B2) (@ (@ tptp.modulo_modulo_int A2) B2)))))))
% 7.32/7.63 (assert (= tptp.signed6292675348222524329lo_int (lambda ((K3 tptp.int) (L3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ (@ tptp.signed6714573509424544716de_int K3) L3)) L3)))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.signed6292675348222524329lo_int A2) B2)) (@ tptp.uminus_uminus_int B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.signed6292675348222524329lo_int A2) B2))))))
% 7.32/7.63 (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)))
% 7.32/7.63 (assert (= tptp.type_l4264026598287037465l_num1 (lambda ((Uu4 tptp.itself_Numeral_num1)) tptp.one_one_nat)))
% 7.32/7.63 (assert (= tptp.type_l31302759751748491nite_1 (lambda ((X3 tptp.itself_finite_1)) tptp.one_one_nat)))
% 7.32/7.63 (assert (= tptp.type_l31302759751748492nite_2 (lambda ((X3 tptp.itself_finite_2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.32/7.63 (assert (= tptp.type_l31302759751748493nite_3 (lambda ((X3 tptp.itself_finite_3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat _let_1) B2) _let_1)))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat B2) _let_1) _let_1)))))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A2) B2)) (@ (@ tptp.ord_min_nat B2) A2)) A2)))
% 7.32/7.63 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_min_nat B2) A2)) (@ (@ tptp.minus_minus_nat A2) B2)) A2)))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A2) B2)) (@ (@ tptp.ord_min_nat A2) B2)) A2)))
% 7.32/7.63 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_min_nat A2) B2)) (@ (@ tptp.minus_minus_nat A2) B2)) A2)))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))))
% 7.32/7.63 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q3) tptp.zero_z5237406670263579293d_enat)))
% 7.32/7.63 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q3) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((N7 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N7) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) K))) N7))))
% 7.32/7.63 (assert (forall ((N7 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N7)))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)))) tptp.top_top_set_real))))
% 7.32/7.63 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D2) (@ (@ tptp.vEBT_invar_vebt T) D2))))
% 7.32/7.63 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D2) (@ (@ tptp.vEBT_VEBT_valid T) D2))))
% 7.32/7.63 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 7.32/7.63 (assert (forall ((Uu Bool) (Uv Bool) (D2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D2) (= D2 tptp.one_one_nat))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D2) (= (@ F X2) (@ F Y4)))) (= L tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A2) Z2) (@ (@ tptp.ord_less_real Z2) B2) (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A2)) (@ F5 Z2)))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (Y3 tptp.real) (X2 tptp.real)) (= (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real (@ tptp.uminus_uminus_real X2)) tptp.top_top_set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ F (@ tptp.uminus_uminus_real X3)))) (@ tptp.uminus_uminus_real Y3)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (@ (@ tptp.ord_less_eq_real (@ G A2)) (@ G B2)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B2)) (@ F A2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_eq_real (@ F A2)) (@ F B2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B2)) (@ F A2))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_real (@ F A2)) (@ F B2))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.minus_minus_real X2) H6))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X2) H6))) (@ F X2)))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X2) H6))) (@ F X2)))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D4) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.plus_plus_real X2) H6))))))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A2 B2)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A2)) K))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A2 B2)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2))) (@ (@ tptp.minus_minus_real B2) A2)) K)))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A2 B2)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) B2)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A2)) (@ V B2))) _let_1)))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D2) (@ (@ tptp.ord_less_eq_real (@ F X2)) (@ F Y4)))) (= L tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D2) (@ (@ tptp.ord_less_eq_real (@ F Y4)) (@ F X2)))) (= L tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real X3) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X2) S2))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ G X3)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X2)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 7.32/7.63 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z4 tptp.real)) (@ (@ tptp.powr_real Z4) 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)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G X3)) 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)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B2)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G X3)) (@ F X3)))) (@ (@ 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)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A)))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 7.32/7.63 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.32/7.63 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M5 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 7.32/7.63 (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 ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_real T7) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 7.32/7.63 (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 ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 7.32/7.63 (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 ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real H2) T7) (@ (@ tptp.ord_less_eq_real T7) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T7) (@ (@ tptp.ord_less_real T7) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 7.32/7.63 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (forall ((M5 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T7 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T7))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))))
% 7.32/7.63 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T7)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A2) T7) (@ (@ tptp.ord_less_eq_real T7) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A2) C2) (=> (@ (@ tptp.ord_less_eq_real C2) B2) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real A2) T7) (@ (@ tptp.ord_less_real T7) C2) (= (@ F A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C2)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A2) C2)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A2) C2)) N)))))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A2 tptp.real) (B2 tptp.real) (C2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A2) T7) (@ (@ tptp.ord_less_eq_real T7) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A2) C2) (=> (@ (@ tptp.ord_less_real C2) B2) (exists ((T7 tptp.real)) (and (@ (@ tptp.ord_less_real C2) T7) (@ (@ tptp.ord_less_real T7) B2) (= (@ F B2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C2)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C2)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C2)) N)))))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A2 tptp.real) (B2 tptp.real) (C2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A2) T7) (@ (@ tptp.ord_less_eq_real T7) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (=> (@ _let_1 C2) (=> (@ (@ tptp.ord_less_eq_real C2) B2) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B2) (=> (not (= X2 C2)) (exists ((T7 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T7))) (let ((_let_2 (@ tptp.ord_less_real X2))) (let ((_let_3 (@ _let_2 C2))) (and (=> _let_3 (and (@ _let_2 T7) (@ _let_1 C2))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C2) T7) (@ _let_1 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C2)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C2)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T7)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C2)) N))))))))))))))))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B tptp.real)) (=> (forall ((M5 tptp.nat) (T7 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T7)) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M3 tptp.nat) (T8 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) T8) (@ (@ tptp.ord_less_eq_real T8) 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 ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M3) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real U2) P4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T8)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M3)) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real T8) P4)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T8) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T8) tptp.top_top_set_real))))))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X10 tptp.real)) (@ tptp.suminf_real (lambda ((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 X2) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.32/7.63 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X4) N4)))))) (=> (@ (@ 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 ((X3 tptp.real)) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real X3) (@ tptp.suc N4))))))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X0) N4))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X2)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F5 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A2 tptp.real) (B2 tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F5 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ F X3) N3))) (@ (@ F5 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A2) B2)) (@ tptp.summable_real (@ F X4)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A2) B2)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X4 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A2) B2))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X4) N3)) (@ (@ F Y4) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y4)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ tptp.suminf_real (@ F X3)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 7.32/7.63 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 7.32/7.63 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X4) (@ (@ tptp.ord_less_eq_real X4) B2)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X8 tptp.real)) (let ((_let_1 (@ F X8))) (=> (and (@ (@ tptp.ord_less_eq_real A2) X8) (@ (@ tptp.ord_less_eq_real X8) B2)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y5) (@ (@ tptp.ord_less_eq_real Y5) M9)) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A2) X4) (@ (@ tptp.ord_less_eq_real X4) B2) (= (@ F X4) Y5)))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C2) 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 ((X8 tptp.real)) (=> (and (not (= X8 C2)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C2) X8))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X8))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C2) 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 ((X8 tptp.real)) (=> (and (not (= X8 C2)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C2) X8))) R3)) (not (= (@ F X8) tptp.zero_zero_real))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C2) 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 ((X8 tptp.real)) (=> (and (not (= X8 C2)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C2) X8))) R3)) (@ (@ tptp.ord_less_real (@ F X8)) tptp.zero_zero_real)))))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B2) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G)))))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcosh_real))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X3)) (@ tptp.sin_real X3)))) (@ 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)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arccos)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcsin)))))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B2) X2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real B2) X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X2)))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.artanh_real)))))
% 7.32/7.63 (assert (forall ((D2 tptp.real) (X2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X2))) D2) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X2))) D2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Z2) (=> (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Z2) (=> (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A2) C3) (@ (@ tptp.ord_less_real C3) B2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B2)) (@ G A2))) (@ F5 C3))))))))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A2 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A2) (=> (@ (@ tptp.ord_less_real (@ A2 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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 7.32/7.63 (assert (forall ((C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C2))) tptp.at_top_nat) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C2)) tptp.at_top_nat) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((X (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X I2))) B)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.root N4) (@ tptp.semiri5074537144036343181t_real N4)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L2))) (and (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N9)) L2)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ G N9))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 7.32/7.63 (assert (forall ((X (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N10 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N10) N3) (@ (@ tptp.ord_less_real R3) (@ X N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ X N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 7.32/7.63 (assert (forall ((C2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.root N4) C2))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) 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))))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real A2) (@ (@ tptp.power_power_real X2) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((C2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((C2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C2))) (=> (@ (@ 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)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N4)))) N4))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_nat)))
% 7.32/7.63 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 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 N4)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A2) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A2 N4))))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A2 (@ tptp.suc N3))) (@ A2 N3))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A2 N4)))))))))
% 7.32/7.63 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K2 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 7.32/7.63 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K2 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))))) tptp.at_top_nat)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A2 (@ tptp.suc N3))) (@ A2 N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))))) tptp.at_top_nat))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A2 (@ tptp.suc N3))) (@ A2 N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4))))))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A2 (@ tptp.suc N3))) (@ A2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A2 N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L2))) (and (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)))) L2)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ 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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))))) tptp.at_top_nat)))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A2 (@ tptp.suc N3))) (@ A2 N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))))) tptp.at_top_nat))))))
% 7.32/7.63 (assert (forall ((A2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A2) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A2 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A2 (@ tptp.suc N3))) (@ A2 N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 7.32/7.63 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X3 tptp.complex) (Y tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y)))))
% 7.32/7.63 (assert (= tptp.real_V975177566351809787t_real (lambda ((X3 tptp.real) (Y tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y)))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.32/7.63 (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))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (@ (@ tptp.inj_on_real_real (@ tptp.log B2)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B2))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_bot_real) F3))))))
% 7.32/7.63 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_top_real) F3))))))
% 7.32/7.63 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 7.32/7.63 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_top_real) tptp.at_top_real))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) tptp.at_top_real) tptp.at_top_real))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_top_real) tptp.at_top_nat))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_bot_real) tptp.at_top_real))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_top_real) tptp.at_bot_real))
% 7.32/7.63 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) X3))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 7.32/7.63 (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))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) K)) (@ tptp.exp_real X3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) Y))) Y))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_real)))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) X4) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B2))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y3))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N4) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((F3 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F3) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F3)))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N4) (@ P N4)))))))
% 7.32/7.63 (assert (forall ((C2 tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X4) (@ P X4))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 7.32/7.63 (assert (not (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) false)) tptp.at_top_nat)))
% 7.32/7.63 (assert (forall ((P (-> tptp.real Bool)) (A2 tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5849166863359141190n_real A2))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X3) A2)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.real Bool)) (A2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A2))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5984915006950818249n_real A2))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.uminus_uminus_real X3)))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A2) B2)))) (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5849166863359141190n_real A2))))))
% 7.32/7.63 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A2) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B2) A2)))) (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5984915006950818249n_real A2))))))
% 7.32/7.63 (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 ((X3 tptp.real)) (@ P (@ tptp.inverse_inverse_real X3)))) tptp.at_top_real))))
% 7.32/7.63 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) tptp.at_top_real) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.inverse_inverse_real X3)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (A2 tptp.real) (G (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A2) 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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_top_real) _let_1)))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) 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 ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F3) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (A2 tptp.real) (G (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5849166863359141190n_real A2)))) (=> (@ (@ (@ 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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_top_real) _let_1)))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (A2 tptp.real) (G (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A2) 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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_bot_real) _let_1)))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (A2 tptp.real) (G (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5984915006950818249n_real A2)))) (=> (@ (@ (@ 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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_top_real) _let_1)))))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y3))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_1) tptp.at_top_real)))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (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 ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F3) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 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 ((X3 tptp.real)) (not (= (@ G0 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X3)) (@ G0 X3)))) F3) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (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 ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F3) _let_1))))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (A2 tptp.real) (G (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5849166863359141190n_real A2)))) (=> (@ (@ (@ 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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_bot_real) _let_1)))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.real tptp.real)) (A2 tptp.real) (G (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5984915006950818249n_real A2)))) (=> (@ (@ (@ 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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_bot_real) _let_1)))))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y3))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 7.32/7.63 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (X2 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 X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 7.32/7.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 7.32/7.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X2)) tptp.at_top_nat)))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool)) (B2 tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (@ P (@ tptp.order_Greatest_nat P))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 7.32/7.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (@ P (@ tptp.order_Greatest_nat P))))))
% 7.32/7.63 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 7.32/7.63 (assert (forall ((X (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I2))) (= (@ tptp.suminf_real X) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X) (@ tptp.set_ord_lessThan_nat I4)))) tptp.top_top_set_nat)))))))
% 7.32/7.63 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B) (@ X I2))) (@ (@ tptp.bfun_nat_real X) tptp.at_top_nat)))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((X (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B) (@ X I2))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I5 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X I5)))))))))))
% 7.32/7.63 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 7.32/7.63 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 7.32/7.63 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 7.32/7.63 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 7.32/7.63 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X4) (@ (@ tptp.ord_less_eq_real X4) B2)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A2) X4) (@ (@ tptp.ord_less_real X4) B2)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X4) (@ (@ tptp.ord_less_eq_real X4) B2)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) G))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A2) X4) (@ (@ tptp.ord_less_real X4) B2)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 A2) C3) (@ (@ tptp.ord_less_real C3) B2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B2)) (@ G A2))) F_c))))))))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((L2 tptp.real) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A2) Z2) (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A2)) L2)))))))))
% 7.32/7.63 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 7.32/7.63 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 7.32/7.63 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 7.32/7.63 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 7.32/7.63 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.32/7.63 (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))))
% 7.32/7.63 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 7.32/7.63 (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)))))
% 7.32/7.63 (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))))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) F) (exists ((C3 tptp.real) (D4 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) (@ (@ tptp.set_or1222579329274155063t_real C3) D4)) (@ (@ tptp.ord_less_eq_real C3) D4)))))))
% 7.32/7.63 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A))) (=> (@ _let_1 F) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.arsinh_real (@ F X3))))))))
% 7.32/7.63 (assert (forall ((M8 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M8)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M8) (@ (@ tptp.ord_less_nat K3) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M8) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 7.32/7.63 (assert (forall ((M8 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M8) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M8) (@ (@ tptp.ord_less_nat K3) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M8) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 7.32/7.63 (assert (forall ((M8 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M8) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M8) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 7.32/7.63 (assert (forall ((A tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A))))) (=> (@ (@ tptp.ord_less_eq_set_nat A) _let_1) (= A _let_1)))))
% 7.32/7.63 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A))) (=> (@ _let_1 F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.arcosh_real (@ F X3)))))))))
% 7.32/7.63 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A) tptp.arcosh_real))))
% 7.32/7.63 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 7.32/7.63 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 7.32/7.63 (assert (forall ((N7 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N7) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N7)) N))))
% 7.32/7.63 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S))))))
% 7.32/7.63 (assert (forall ((S tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) S))))
% 7.32/7.63 (assert (forall ((A tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A))) (=> (@ _let_1 F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A) (@ (@ tptp.member_real (@ F X4)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.artanh_real (@ F X3)))))))))
% 7.32/7.63 (assert (forall ((C2 tptp.complex) (N tptp.nat)) (=> (not (= C2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C2)))) N)))))
% 7.32/7.63 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) N))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F5 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (not (forall ((Xi3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Xi3) (=> (@ (@ tptp.ord_less_real Xi3) B2) (not (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A2)) (@ (@ F5 Xi3) (@ (@ tptp.minus_minus_real B2) A2)))))))))))))
% 7.32/7.63 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A) tptp.artanh_real))))
% 7.32/7.63 (assert (forall ((A2 tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B2)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) B2) (= (@ F X2) (@ F A2)))))))))
% 7.32/7.63 (assert (= (@ tptp.finite6454714172617411597l_num1 tptp.top_to3689904429138878997l_num1) tptp.one_one_nat))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X7 tptp.real)) (@ P X7)))))
% 7.32/7.63 (assert (forall ((X2 tptp.assn) (Y3 tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.assn) (Y3 tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.list_int) (Y3 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.list_int) (Y3 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.option_nat) (Y3 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.option_nat) (Y3 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_Time_Heap_o) (Y3 tptp.heap_Time_Heap_o)) (= (@ (@ (@ tptp.if_Heap_Time_Heap_o false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_Time_Heap_o) (Y3 tptp.heap_Time_Heap_o)) (= (@ (@ (@ tptp.if_Heap_Time_Heap_o true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_Time_Heap_nat) (Y3 tptp.heap_Time_Heap_nat)) (= (@ (@ (@ tptp.if_Hea2662716070787841314ap_nat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_Time_Heap_nat) (Y3 tptp.heap_Time_Heap_nat)) (= (@ (@ (@ tptp.if_Hea2662716070787841314ap_nat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_T8145700208782473153_VEBTi) (Y3 tptp.heap_T8145700208782473153_VEBTi)) (= (@ (@ (@ tptp.if_Hea8453224502484754311_VEBTi false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_T8145700208782473153_VEBTi) (Y3 tptp.heap_T8145700208782473153_VEBTi)) (= (@ (@ (@ tptp.if_Hea8453224502484754311_VEBTi true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_T2636463487746394924on_nat) (Y3 tptp.heap_T2636463487746394924on_nat)) (= (@ (@ (@ tptp.if_Hea5867803462524415986on_nat false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.heap_T2636463487746394924on_nat) (Y3 tptp.heap_T2636463487746394924on_nat)) (= (@ (@ (@ tptp.if_Hea5867803462524415986on_nat true) X2) Y3) X2)))
% 7.32/7.63 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 7.32/7.63 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y3 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X2) Y3) Y3)))
% 7.32/7.63 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y3 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X2) Y3) X2)))
% 7.32/7.63 (assert (= tptp.tia (@ (@ (@ (@ tptp.vEBT_Nodei (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) (@ tptp.suc (@ tptp.suc tptp.va))) tptp.x13) tptp.x14)))
% 7.32/7.63 (assert (= (@ tptp.size_s7982070591426661849_VEBTi tptp.tree_is) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 7.32/7.63 (assert (not (= tptp.xa tptp.mi)))
% 7.32/7.63 (assert (not (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)))
% 7.32/7.63 (assert (not (@ (@ tptp.ord_less_nat tptp.ma) tptp.xa)))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.suc (@ (@ tptp.divide_divide_nat tptp.va) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (= tptp.xaa (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1)))))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.suc (@ (@ tptp.divide_divide_nat tptp.va) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (= (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1))) tptp.none_nat)))
% 7.32/7.63 (assert (= tptp.xba tptp.none_nat))
% 7.32/7.63 (assert (not (= tptp.xa tptp.ma)))
% 7.32/7.63 (assert (let ((_let_1 (@ tptp.suc (@ tptp.suc tptp.va)))) (let ((_let_2 (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma)))) (let ((_let_3 (@ (@ tptp.vEBT_Node _let_2) _let_1))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ tptp.vEBT_VEBT_low tptp.xa))) (let ((_let_6 (@ tptp.suc (@ (@ tptp.divide_divide_nat tptp.va) _let_4)))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_6))) (let ((_let_8 (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_7)))) (let ((_let_9 (@ _let_8 (@ _let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))))) (let ((_let_10 (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_7))) (let ((_let_11 (@ _let_3 (@ _let_10 _let_9)))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete tptp.summary) _let_7))) (let ((_let_13 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi tptp.tree_is) _let_7) tptp.xb))) (not (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw _let_12) tptp.xc)) (@ (@ tptp.snga_assn_VEBT_VEBTi tptp.x13) _let_13))) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) (@ _let_10 (@ _let_8 (@ _let_5 _let_6)))) _let_13))) (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ tptp/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 5800 Alarm clock ( read result; case "$result" in
% 299.52/300.16 unsat)
% 299.52/300.16 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.52/300.16 ;;
% 299.52/300.16 sat)
% 299.52/300.16 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.52/300.16 ;;
% 299.52/300.16 esac; exit 1 )
% 299.52/300.17 Alarm clock
% 299.52/300.17 % cvc5---1.0.5 exiting
% 299.52/300.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------